# Submarine Landslide Tsunami Linearity

### From Gerris

## This page documents tests on the scaling of tsunami waves with Earthquake volume

As part of our work developing a Probabilistic Tsunami Hazard Assessment (PTHA) for submarine landslide generated tsunamis we are investigating the scaling of tsunami waves with volume of the landslide.

For the initial test we are using the TOPICS submarine-landslide-generated-tsunami initialisation code. There are some questions as to its applicability in the shallow canyon environment but it will do for the initial investigation.

In TOPICS both the volume is specified and the length/width and maximum thickness. This overspecifies the problem (although as it is maximum thickness there is some room for a range of volumes to be consistent with the given dimensions).

We are using the standard Nicholson Canyon setup used in XXXXXXXX with four different volumes: 100,000,000 m^3, 400,000,000 m^3, 333,333,333 m^3 and 1,000,000,000 m^3. The maximum thickness is held constant at 200 m. The landslide length and width are taken as equal and are 2,400 m, 1,500 m, 1,400 m and 760 m respectively for the four cases.

In order to investigate the influence of different dimensions given the same volume we are doing three simulations with volume set as 400,000,000 m^3 and maximum thickness given as 50 m, 100 m and 200 m.

There does not seem to be a strong relationship between volume and water height (i.e. changing the thickness has a large effect on wave height at the places of interest. Some areas appear to be inundated while others aren't. Is this correct or is this a bug of the inundation programme?

One issue that has just been uncovered is that the centroid of the landscape was in fact incorrect and was the middle of the canyon instead. So the first question is how much difference will this make to the results. Joshu Mountjoy has given me 4 new scenarios which are:

# SCENARIO 1

# The InitSubmarineLandslide event of the topics module is used to generate the initial

# conditions (elevation D, initial velocities D_U and D_V) from the geometrical parameters

# of the landslide.

GModule topics

Init {} { D = 0 }

InitSubmarineLandslide D {

x = 174.75

y = -41.453

alpha = 310

depth = 160.0

theta = 2

length = 2300

width = 2300

thickness = 100

volume = 500000000

gamma = 2.0

}

# We apply the initial conditions at the start of the simulation.

# NB: The initial conditions are representative of the wave generated by the landslide

# at a characteristic time after the start of the landslide

Init { start = 0 } { P = (Zb < 0 ? MAX (0., D - Zb):0) U = (D_U) V = (D_V) }

# SCENARIO 2

# The InitSubmarineLandslide event of the topics module is used to generate the initial

# conditions (elevation D, initial velocities D_U and D_V) from the geometrical parameters

# of the landslide.

GModule topics

Init {} { D = 0 }

InitSubmarineLandslide D {

x = 174.782

y = -41.473

alpha = 295

depth = 230.0

theta = 4

length = 1700

width = 1400

thickness = 100

volume = 250000000

gamma = 2.0

}

# We apply the initial conditions at the start of the simulation.

# NB: The initial conditions are representative of the wave generated by the landslide

# at a characteristic time after the start of the landslide

Init { start = 0 } { P = (Zb < 0 ? MAX (0., D - Zb):0) U = (D_U) V = (D_V) }

# SCENARIO 3

# The InitSubmarineLandslide event of the topics module is used to generate the initial

# conditions (elevation D, initial velocities D_U and D_V) from the geometrical parameters

# of the landslide.

GModule topics

Init {} { D = 0 }

InitSubmarineLandslide D {

x = 174.787

y = -41.449

alpha = 150

depth = 120.0

theta = 15.

length = 1100

width = 1000

thickness = 50

volume = 55000000

gamma = 2.2

}

# We apply the initial conditions at the start of the simulation.

# NB: The initial conditions are representative of the wave generated by the landslide

# at a characteristic time after the start of the landslide

Init { start = 0 } { P = (Zb < 0 ? MAX (0., D - Zb):0) U = (D_U) V = (D_V) }

# SCENARIO 4

# The InitSubmarineLandslide event of the topics module is used to generate the initial

# conditions (elevation D, initial velocities D_U and D_V) from the geometrical parameters

# of the landslide.

GModule topics

Init {} { D = 0 }

InitSubmarineLandslide D {

x = 174.823

y = -41.461

alpha = 150

depth = 120.0

theta = 15.

length = 500

width = 4500

thickness =450

volume = 1000000000

gamma = 2.2

}

# We apply the initial conditions at the start of the simulation.

# NB: The initial conditions are representative of the wave generated by the landslide

# at a characteristic time after the start of the landslide

Init { start = 0 } { P = (Zb < 0 ? MAX (0., D - Zb):0) U = (D_U) V = (D_V) }

### Outputting data at certain points

William Power provided the file Cook_points.csv to output time series or maximum wave heights at. This Includes all of Marlborough sounds which might be more than is needed so we may wish to cut it down.

As a start to cutting it down we will just use a box 174 - 175.5 in longitude, -41.8 - -41.15 in latitude. This will include some of the inner Marlborough sounds but not to much.

First I needed to dos2unix the file to get rid of dos endoflines Then I used the following awk file convert_Cook.awk

BEGIN{

FS=","

}

{

x=$1

y=$2

if ((x > 174) && (x < 175.5) && (y > -41.8) && (y < -41.15)) {

print $1, $2, " 0"

}

}

awk -f convertCook < Cook_points.csv > Cook_points.out

The .awk file timeseries.awk given below post-processes the output data to give time and the sea level heights. X and Y are also given in case these are mixed up in parallel runs.

BEGIN{

FS=" |:"

}

{

if ($1 == "#") {

# get column indices of relevant fields

for (i=1; i <= NF; i++) {

if ($i == "H")

iH = $(i-1);

if ($i == "x")

ix = $(i-1);

if ($i == "y")

iy = $(i-1);

}

}

if (NR > 1) {

print $1, $ix, $iy, $iH

}

}

Which is run using the command

GfsOutputLocation {step = 1} { awk -f timeseries.awk > timeseries_interp1.out } Cook_points.out { interpolate = 1}

Currently I am exploring whether or not it is best to interpolate (1 or 0). I am also trying to set it so that if the land is not inundated then the height is set to zero - I am not sure whether this is best or whether it is better to output wave height and also Z for that point and compare this. I tried only outputting if P>0 but that made minimal difference.

There is an issue with the time series in that in some places (especially where there is a steep transition e.g. coastal cliffs. We are getting outputs of positive wave heights even though we are well higher than the water should be. My guess is that it is a mismatch in the way that H is calculated compared to Zb and P. By ensuring that the coast is refine to the highest level looks like it may have solved this problem. We may want to be a bit more selective about how we do this and rather only refine at the points where we are reading the time series off at.

### Superposition of two landslides

Anther question I am investigating is whether we can linearly add the results of two landslides that occur simultaneously. In order to test this I will use the 0.1 km^3 volume as this seems less affected by the problems with the TOPICS initialisation hitting the coast too soon. I will run two simulations. The first in the standard position and the second the same size but centred on -41.531198,174.841129 with the landslide oriented towards 70 degrees east of North. I will run the two separately as well as simultaneously (This I will achieve by outputting the ascii grid for each initialisation, summing them and then reinitialising a run with the sum of the two). I will compare maximum wave height at the end of the simulation as well as time series at certain points.