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{
"cells": [
{
"cell_type": "markdown",
"id": "daaba752",
"metadata": {},
"source": [
"After reading reading in a [tweet](https://twitter.com/LeahNeukirchen/status/1482461732886876163) that you can measure the shockwave of the Hunga Tonga–Hunga Haʻapai erruption using simple air pressure sensors I decided to to check the log of my home automation setup.\n",
"Sure enough there was nice little spike about 15h after the erruption.\n",
"Since many folks in my electronics bubble on mastodon also run sensors with continous data,\n",
"I postet [a screenshot](https://chaos.social/@sebastian/107628740679869429) there.\n",
"\n",
"Sure enough I got quite a few replies of people reporting the time when the wave hit their location.\n",
"So I decided to collect some data points and see if we can estimate the propagation speed of the wave,\n",
"and maybe find a way to estimate the point of origin from the data."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "4dbd5465",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Defaulting to user installation because normal site-packages is not writeable\n",
"Requirement already satisfied: geopy in /home/sebastian/.local/lib/python3.10/site-packages (2.2.0)\n",
"Requirement already satisfied: geographiclib<2,>=1.49 in /home/sebastian/.local/lib/python3.10/site-packages (from geopy) (1.52)\n",
"Defaulting to user installation because normal site-packages is not writeable\n",
"Requirement already satisfied: ipyleaflet in /home/sebastian/.local/lib/python3.10/site-packages (0.15.0)\n",
"Requirement already satisfied: ipywidgets<8,>=7.6.0 in /usr/lib/python3.10/site-packages (from ipyleaflet) (7.6.5)\n",
"Requirement already satisfied: xyzservices>=2021.8.1 in /home/sebastian/.local/lib/python3.10/site-packages (from ipyleaflet) (2021.11.0)\n",
"Requirement already satisfied: traittypes<3,>=0.2.1 in /home/sebastian/.local/lib/python3.10/site-packages (from ipyleaflet) (0.2.1)\n",
"Requirement already satisfied: traitlets>=4.2.2 in /usr/lib/python3.10/site-packages (from traittypes<3,>=0.2.1->ipyleaflet) (5.1.0)\n",
"Defaulting to user installation because normal site-packages is not writeable\n",
"Requirement already satisfied: tabulate in /home/sebastian/.local/lib/python3.10/site-packages (0.8.9)\n"
]
}
],
"source": [
"import sys\n",
"!{sys.executable} -m pip install geopy\n",
"!{sys.executable} -m pip install ipyleaflet\n",
"!{sys.executable} -m pip install tabulate"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "1ced7adc",
"metadata": {},
"outputs": [],
"source": [
"from datetime import datetime\n",
"from pytz import timezone\n",
"\n",
"data_points = [\n",
" (\"Kaiserslautern\", datetime(2022, 1, 16, 20, 30, 0, tzinfo=timezone(\"Europe/Berlin\")), \"https://chaos.social/@sebastian/107628740679869429\"),\n",
" (\"Aachen\", datetime(2022, 1, 16, 20, 25, 0, tzinfo=timezone(\"Europe/Berlin\")), \"https://chaos.social/@trilader/107628784664752716\"),\n",
" (\"Hamburg\", datetime(2022, 1, 16, 20, 10, 0, tzinfo=timezone(\"Europe/Berlin\")),\"https://chaos.social/@tsia_/107628923762308800\"),\n",
" (\"Edinburgh\", datetime(2022, 1, 16, 18, 45, 0, tzinfo=timezone(\"UTC\")), \"https://toot.cat/@river/107629146900457261\"),\n",
" (\"Copenhagen\", datetime(2022, 1, 16, 19, 55, 0, tzinfo=timezone(\"CET\")), \"https://mcd.dk/@rune/107629163090789143\"),\n",
" (\"Augsburg\", datetime(2022, 1, 16, 20, 38, 0, tzinfo=timezone(\"Europe/Berlin\")), \"https://chaos.social/@phjl/107629214329242643\"),\n",
" (\"Frankfurt\", datetime(2022, 1, 16, 20, 25, 0, tzinfo=timezone(\"Europe/Berlin\")), \"https://mastodon.social/@hko/107629722849924036\"),\n",
" (\"Melbourne\", datetime(2022, 1, 16, 8, 0, 0, tzinfo=timezone(\"UTC\")), \"https://aus.social/@futzle/107631253370573653\"),\n",
"]"
]
},
{
"cell_type": "markdown",
"id": "1f554c69",
"metadata": {},
"source": [
"Since we know roughly where and when the explosion happened we can do a quick sanity check of our data points."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "6b525fc1",
"metadata": {},
"outputs": [],
"source": [
"from geopy.distance import distance\n",
"from geopy.geocoders import Nominatim\n",
"\n",
"geolocator = Nominatim(user_agent=\"pressure_wave_triangulation\")\n",
"\n",
"ORIGIN = (-20.5, -175.4)\n",
"T_ZERO = datetime(2022, 1, 16, 4, 27, 0, tzinfo=timezone(\"UTC\"))\n",
"\n",
"SPEED_OF_SOUND = 343.0 # Speed of sound in air at 20°C\n",
"\n",
"enhanced_data_points = []\n",
"\n",
"for location, ts, url in data_points:\n",
" geolocation = geolocator.geocode(location)\n",
" coordinates = (geolocation.latitude, geolocation.longitude)\n",
" dist = distance(ORIGIN, coordinates)\n",
" \n",
" delta_t = ts - T_ZERO\n",
" \n",
" speed = dist.meters / delta_t.total_seconds()\n",
" mach = speed / SPEED_OF_SOUND\n",
"\n",
" enhanced_data_points += [(location, coordinates, ts, dist, delta_t, speed, mach, url)]\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "842f682a",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<table>\n",
"<tbody>\n",
"<tr><td>Location </td><td>Coordinates </td><td>Timestamp </td><td>Distance </td><td>Time difference</td><td>Speed [m/s] </td><td>Mach Number </td><td>Toot </td></tr>\n",
"<tr><td>Kaiserslautern</td><td>49.443217 7.768995 </td><td>2022-01-16 20:30:00+00:53</td><td>16780.572549711476 km</td><td>15:10:00 </td><td>307.3364935844593 </td><td>0.8960247626369076</td><td>https://chaos.social/@sebastian/107628740679869429</td></tr>\n",
"<tr><td>Aachen </td><td>50.776351 6.083862 </td><td>2022-01-16 20:25:00+00:53</td><td>16641.951165318445 km</td><td>15:05:00 </td><td>306.4816052544834 </td><td>0.8935323768352286</td><td>https://chaos.social/@trilader/107628784664752716 </td></tr>\n",
"<tr><td>Hamburg </td><td>53.550341 10.000654 </td><td>2022-01-16 20:10:00+00:53</td><td>16307.144415681687 km</td><td>14:50:00 </td><td>305.3772362487207 </td><td>0.8903126421245501</td><td>https://chaos.social/@tsia_/107628923762308800 </td></tr>\n",
"<tr><td>Edinburgh </td><td>55.953346 -3.188375 </td><td>2022-01-16 18:45:00+00:00</td><td>16015.614674425336 km</td><td>14:18:00 </td><td>311.1036261543383 </td><td>0.9070076564266423</td><td>https://toot.cat/@river/107629146900457261 </td></tr>\n",
"<tr><td>Copenhagen </td><td>55.686724 12.570072 </td><td>2022-01-16 19:55:00+01:00</td><td>16042.101561186751 km</td><td>14:28:00 </td><td>308.02806377086694</td><td>0.8980410022474254</td><td>https://mcd.dk/@rune/107629163090789143 </td></tr>\n",
"<tr><td>Augsburg </td><td>48.366804 10.898697 </td><td>2022-01-16 20:38:00+00:53</td><td>16861.97644995329 km </td><td>15:18:00 </td><td>306.13610112478744</td><td>0.8925250761655611</td><td>https://chaos.social/@phjl/107629214329242643 </td></tr>\n",
"<tr><td>Frankfurt </td><td>50.110644 8.682092 </td><td>2022-01-16 20:25:00+00:53</td><td>16699.02015177992 km </td><td>15:05:00 </td><td>307.53259948029324</td><td>0.8965964999425459</td><td>https://mastodon.social/@hko/107629722849924036 </td></tr>\n",
"<tr><td>Melbourne </td><td>-37.814218 144.963161</td><td>2022-01-16 08:00:00+00:00</td><td>4264.645211600706 km </td><td>3:33:00 </td><td>333.6968084194606 </td><td>0.9728769924765615</td><td>https://aus.social/@futzle/107631253370573653 </td></tr>\n",
"</tbody>\n",
"</table>"
],
"text/plain": [
"'<table>\\n<tbody>\\n<tr><td>Location </td><td>Coordinates </td><td>Timestamp </td><td>Distance </td><td>Time difference</td><td>Speed [m/s] </td><td>Mach Number </td><td>Toot </td></tr>\\n<tr><td>Kaiserslautern</td><td>49.443217 7.768995 </td><td>2022-01-16 20:30:00+00:53</td><td>16780.572549711476 km</td><td>15:10:00 </td><td>307.3364935844593 </td><td>0.8960247626369076</td><td>https://chaos.social/@sebastian/107628740679869429</td></tr>\\n<tr><td>Aachen </td><td>50.776351 6.083862 </td><td>2022-01-16 20:25:00+00:53</td><td>16641.951165318445 km</td><td>15:05:00 </td><td>306.4816052544834 </td><td>0.8935323768352286</td><td>https://chaos.social/@trilader/107628784664752716 </td></tr>\\n<tr><td>Hamburg </td><td>53.550341 10.000654 </td><td>2022-01-16 20:10:00+00:53</td><td>16307.144415681687 km</td><td>14:50:00 </td><td>305.3772362487207 </td><td>0.8903126421245501</td><td>https://chaos.social/@tsia_/107628923762308800 </td></tr>\\n<tr><td>Edinburgh </td><td>55.953346 -3.188375 </td><td>2022-01-16 18:45:00+00:00</td><td>16015.614674425336 km</td><td>14:18:00 </td><td>311.1036261543383 </td><td>0.9070076564266423</td><td>https://toot.cat/@river/107629146900457261 </td></tr>\\n<tr><td>Copenhagen </td><td>55.686724 12.570072 </td><td>2022-01-16 19:55:00+01:00</td><td>16042.101561186751 km</td><td>14:28:00 </td><td>308.02806377086694</td><td>0.8980410022474254</td><td>https://mcd.dk/@rune/107629163090789143 </td></tr>\\n<tr><td>Augsburg </td><td>48.366804 10.898697 </td><td>2022-01-16 20:38:00+00:53</td><td>16861.97644995329 km </td><td>15:18:00 </td><td>306.13610112478744</td><td>0.8925250761655611</td><td>https://chaos.social/@phjl/107629214329242643 </td></tr>\\n<tr><td>Frankfurt </td><td>50.110644 8.682092 </td><td>2022-01-16 20:25:00+00:53</td><td>16699.02015177992 km </td><td>15:05:00 </td><td>307.53259948029324</td><td>0.8965964999425459</td><td>https://mastodon.social/@hko/107629722849924036 </td></tr>\\n<tr><td>Melbourne </td><td>-37.814218 144.963161</td><td>2022-01-16 08:00:00+00:00</td><td>4264.645211600706 km </td><td>3:33:00 </td><td>333.6968084194606 </td><td>0.9728769924765615</td><td>https://aus.social/@futzle/107631253370573653 </td></tr>\\n</tbody>\\n</table>'"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import tabulate\n",
"\n",
"table_data = [(\"Location\", \"Coordinates\", \"Timestamp\", \"Distance\", \"Time difference\", \"Speed [m/s]\", \"Mach Number\", \"Toot\")]\n",
"for location, coordinates, ts, dist, delta_t, speed, mach, url in enhanced_data_points:\n",
" table_data += [(location, \"%f %f\" % coordinates, ts, dist, delta_t, speed, mach, url)]\n",
"\n",
"table = tabulate.tabulate(table_data, tablefmt='html')\n",
"table\n"
]
},
{
"cell_type": "markdown",
"id": "5341fa32",
"metadata": {},
"source": [
"That looks quite consistent, considering the we pretty much guestimated the timestamps from screenshots.\n",
"On the other hand it's easy mode because we know the time and point of origin for the wave.\n",
"\n",
"Let's see if we can estimate the propagation speed using the relative delay between the diffrent locations:"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "5ff0ee40",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Kaiserslautern 322.0800766318187\n",
"Aachen 306.3924371618201\n",
"Hamburg 219.6723878081226\n",
"Edinburgh 315.16138946596874\n",
"Copenhagen 283.03327184485505\n",
"Augsburg 298.8056038343784\n",
"Frankfurt 319.0927106279109\n"
]
}
],
"source": [
"relative_speed_data = []\n",
"\n",
"for location, coordinates, ts, _, _, _, _, url in enhanced_data_points:\n",
" count = 0\n",
" speed = 0.0\n",
" for _, other_coordinates, other_ts, _, _, _, _, _ in enhanced_data_points:\n",
" relative_delay = other_ts - ts\n",
" if abs(relative_delay.total_seconds()) < 1:\n",
" continue\n",
" \n",
" relative_dist = distance(coordinates, other_coordinates)\n",
" relative_speed = relative_dist.meters / abs(relative_delay.total_seconds())\n",
" \n",
" if relative_speed > 343:\n",
" continue\n",
" \n",
" speed += relative_speed\n",
" count += 1.0\n",
" \n",
" \n",
" if count < 1.0:\n",
" continue \n",
" \n",
" speed = speed / count\n",
" print(location, speed)\n",
" \n",
" relative_speed_data += [(location, coordinates, ts, speed)]\n",
" \n",
" "
]
},
{
"cell_type": "markdown",
"id": "5d40d782",
"metadata": {},
"source": [
"Some cleanup was required, so I ended up dropping everthing that is faster then the speed of sound in air.\n",
"I don't think a pressure wave can be supersonic. At least not for long.\n",
"\n",
"Unfortunately the leaftlet map does something weird here. \n",
"It seems to disagree with the distances calculated by geopy.\n",
"If we cicle each of our locations with the distance we got from geopy, the circles never really intersect."
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "1a43cbc5",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "737333cec57943d1890f608c57b7f927",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Map(center=[-37.8142176, 144.9631608], controls=(ZoomControl(options=['position', 'zoom_in_text', 'zoom_in_tit…"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from ipyleaflet import Map, Marker, Circle\n",
"\n",
"\n",
"MELBOURNE = geolocator.geocode(\"Melbourne\")\n",
"\n",
"\n",
"leaflet_map = Map(center=(MELBOURNE.latitude, MELBOURNE.longitude), zoom=2)\n",
"marker = Marker(location=ORIGIN, draggable=False)\n",
"leaflet_map.add_layer(marker);\n",
"\n",
"for _, coordinates, _, dist, _, _, _, _ in enhanced_data_points:\n",
" marker = Marker(location=coordinates, draggable=False)\n",
" leaflet_map.add_layer(marker);\n",
" \n",
" circle = Circle(location=coordinates, radius=int(dist.meters), fill=False, weight=1)\n",
" leaflet_map.add_layer(circle)\n",
"\n",
"\n",
"display(leaflet_map)\n"
]
},
{
"cell_type": "markdown",
"id": "f1a23642",
"metadata": {},
"source": [
"However we can fiddle with that so that things end up in roughly the right spot. (Highly scientific. I know...)"
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "ebcded76",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "004ba4ec8aea474ab35d649141012307",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Map(center=[-37.8142176, 144.9631608], controls=(ZoomControl(options=['position', 'zoom_in_text', 'zoom_in_tit…"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from ipyleaflet import Map, Marker, Circle\n",
"\n",
"\n",
"FUDGE_FACTOR = 0.821\n",
"\n",
"\n",
"leaflet_map = Map(center=(MELBOURNE.latitude, MELBOURNE.longitude), zoom=2)\n",
"marker = Marker(location=ORIGIN, draggable=False)\n",
"leaflet_map.add_layer(marker);\n",
"\n",
"for _, coordinates, _, dist, _, _, _, _ in enhanced_data_points:\n",
" marker = Marker(location=coordinates, draggable=False)\n",
" leaflet_map.add_layer(marker);\n",
" \n",
" circle = Circle(location=coordinates, radius=int(dist.meters * FUDGE_FACTOR), fill=False, weight=1)\n",
" leaflet_map.add_layer(circle)\n",
"\n",
"\n",
"display(leaflet_map)"
]
},
{
"cell_type": "markdown",
"id": "b708c606",
"metadata": {},
"source": [
"Also I don't want to mess with the math required to actually propagate back the circles projected on a sphere until they actually intersec.\n",
"\n",
"So let's just assume we have a rough idea when the event occured and we can use that timestamp +-5min to draw some circles and use our eyes to check for intersections."
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "f74da8ff",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "224a2bdf18334290a7d19b138314fa6c",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Map(center=[-20.5, -175.4], controls=(ZoomControl(options=['position', 'zoom_in_text', 'zoom_in_title', 'zoom_…"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from ipyleaflet import Map, Marker, Circle\n",
"\n",
"\n",
"leaflet_map = Map(center=ORIGIN, zoom=2)\n",
"marker = Marker(location=ORIGIN, draggable=False)\n",
"leaflet_map.add_layer(marker);\n",
"\n",
"\n",
"T_MINUS = datetime(2022, 1, 16, 4, 22, 0, tzinfo=timezone(\"UTC\"))\n",
"T_PLUS = datetime(2022, 1, 16, 4, 32, 0, tzinfo=timezone(\"UTC\"))\n",
"\n",
"\n",
"for location, coordinates, ts, speed in relative_speed_data:\n",
" marker = Marker(location=coordinates, draggable=False)\n",
" leaflet_map.add_layer(marker);\n",
" \n",
" for start, color in [(T_MINUS, \"green\"), (T_ZERO, \"red\"), (T_PLUS, \"blue\")]:\n",
" dist = speed * (ts - start).total_seconds()\n",
"\n",
" circle = Circle(location=coordinates, radius=int(dist * FUDGE_FACTOR), fill=False, weight=1, color=color)\n",
" leaflet_map.add_layer(circle)\n",
"\n",
"\n",
"display(leaflet_map)"
]
},
{
"cell_type": "markdown",
"id": "b7106b43",
"metadata": {},
"source": [
"While that looks close, just zoom out until you can see the entire map.\n",
"\n",
"It's a mess.\n",
"Not enough data points, the locations are not spread out wide enough, the timestamps are off, and there is some weird map projection stuff going on...."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "e4f1d967",
"metadata": {},
"outputs": [],
"source": []
}
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