30:[{"id":"7c6167b65013c12f3978b4d8e85dd28a27e3b5eb580d1e76696ce5b0d399c196de2b02c45e734462931e1af823698e36bb072722253d5e03e7fb61222755bc0c","href":"https://static.observableusercontent.com/files/7c6167b65013c12f3978b4d8e85dd28a27e3b5eb580d1e76696ce5b0d399c196de2b02c45e734462931e1af823698e36bb072722253d5e03e7fb61222755bc0c","name":"countries-110m.json","type":"application/json","lastModified":1751397229537.44,"size":107761},{"id":"fbf870449f01ef341b542a5cd88a9bda698b2a41d3b57b84e00266b958abd64cbb80a87e6ec490ce7ad14adea3d4cdf6833c4706e8125fa514609bc2322a55b1","href":"https://static.observableusercontent.com/files/fbf870449f01ef341b542a5cd88a9bda698b2a41d3b57b84e00266b958abd64cbb80a87e6ec490ce7ad14adea3d4cdf6833c4706e8125fa514609bc2322a55b1","name":"global_dem_1deg.csv","type":"text/csv","lastModified":1779821649730.952,"size":462936}] 2e:{"title":"Earth Gravitational Model","cells":[{"id":0,"value":"title = md`# Earth Gravitational Model`","pinned":false,"hidden":false,"mode":"ojs"},{"id":280,"value":"intro = md`The geoid (\"JEE-oyd\") is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent.\n\nEven if the shape of the earth was a perfect spheroid, the strength of gravity would not be the same everywhere because density varies throughout the planet.\n\nThe gravitation model [EGM-2008](https://en.wikipedia.org/wiki/Earth_Gravitational_Model) is used in the interactive globe below to illustrate how geoid height varies (smoothly!) along meridian and parallel lines.\n\nThe globe defaults to the approximate location of a Mount Everest.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":660,"value":"\n \n \n \n

\n ${globe}\n

\n ${globe_2}\n

\n \n","pinned":false,"hidden":false,"mode":"html"},{"id":326,"value":"arrowKeys = md`*Use Arrow Keys ← → after clicking a slider to scrub meridians and parallels while you scroll down the page.*`","pinned":false,"hidden":false,"mode":"ojs"},{"id":12,"value":"viewof longitude = Inputs.range([-179.5, 179.5], {\n label: \"longitude\",\n step: 1,\n value: 87\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":138,"value":"viewof latitude = Inputs.range([-89.5, 89.5], {\n label: \"latitude\",\n step: 1,\n value: 28\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":305,"value":"meridian_description = md`The vertical line on the globe above can be sampled along varying latitude to show how the geoid height varies along a particular *slice* or meridian line.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":85,"value":"meridianPlot = Plot.plot({\n title: `Geoid Height along the ${ordinalSuffix(\n Math.abs(longitude)\n )} Meridian ${longitude < 0 ? \"West\" : \"East\"}`,\n color: {\n legend: true,\n type: \"diverging\",\n domain: geoidDomain\n },\n y: { domain: [-100, 100] },\n x: { grid: true, axis: \"both\", domain: [-90, 90] },\n height: plotHeight,\n width: width,\n marks: [\n Plot.ruleY([0], { strokeOpacity: 0.2 }),\n // Plot.line(\n // insertNullsAtGaps(\n // elevation_meridian_map.get(longitude),\n // (d) => d.latitude\n // ).map((d) => (d ? [d.latitude, d.elevation_m / 1e2] : null)),\n // { stroke: \"black\" }\n // ),\n Plot.dot(\n meridianHeights.map((d, i) => [meridian[i][1], d]),\n {\n fill: (d, i) => meridianHeights[i]\n }\n ),\n Plot.axisX({ anchor: \"bottom\", label: \"latitude\" }),\n Plot.axisY({ anchor: \"left\", label: \"Height (meters)\" })\n ]\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":309,"value":"parallel_description = md`The horizontal lines parallel to the equator on the globe above can be sampled along varying longitude to show how the geoid height varies along *parallels*.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":179,"value":"parallelPlot = Plot.plot({\n title: `Geoid Height along the ${ordinalSuffix(\n Math.abs(latitude)\n )} Parallel ${latitude < 0 ? \"South\" : \"North\"} `,\n x: { grid: true, axis: \"both\" },\n y: { domain: [-100, 100] },\n color: {\n legend: true,\n type: \"diverging\",\n domain: geoidDomain\n },\n height: plotHeight,\n width: width,\n marks: [\n Plot.ruleY([0], { strokeOpacity: 0.2 }),\n // Plot.line(\n // insertNullsAtGaps(\n // elevation_parallels_map.get(latitude),\n // (d) => d.longitude\n // ).map((d) => (d ? [d.longitude, d.elevation_m / 1e2] : null)),\n // { stroke: \"black\" }\n // ),\n Plot.dot(\n parallelHeights.map((d, i) => [parallel[i][0], d]),\n { fill: (d, i) => parallelHeights[i] }\n ),\n Plot.axisX({ anchor: \"bottom\", label: \"longitude\" }),\n Plot.axisY({ anchor: \"left\", label: \"Height (meters)\" })\n ]\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":216,"value":"---\n## Appendix","pinned":false,"hidden":false,"mode":"md"},{"id":3,"value":"// Graphic placed side by side above\nglobe = Plot.plot({\n title: md`**${d3.format(\".5\")(\n await geoidHeight(latitude, longitude)\n )} geoid height** @ (${longitude}, ${latitude})`,\n color: {\n legend: true,\n type: \"diverging\",\n domain: geoidDomain\n },\n height: 500,\n projection: { type: projection, rotate: [-longitude, -latitude] },\n style: \"overflow: visible;\", // allow dots to escape\n marks: [\n Plot.geo(land, {\n fill: \"currentColor\",\n stroke: \"currentCOlor\",\n fillOpacity: 0.2\n }),\n Plot.raster(matrix, {\n clip: \"sphere\",\n fill: \"MAG_IGRF90\",\n interpolate: \"barycentric\",\n fill: (d, i) => d[2],\n fillOpacity: 0.7\n }),\n Plot.dot(meridian, {\n r: 2,\n fill: (d, i) => meridianHeights[i],\n fillOpacity: 1\n }),\n Plot.dot(parallel, {\n r: 2,\n fill: (d, i) => parallelHeights[i],\n fillOpacity: 1\n }),\n Plot.sphere()\n ]\n})","pinned":false,"hidden":true,"mode":"ojs"},{"id":641,"value":"// Graphic placed side by side above with HTML\nglobe_2 = Plot.plot({\n title: md`Elevation (meters) *without bathymetry*`,\n color: {\n legend: true,\n type: \"linear\",\n scheme: \"Viridis\"\n },\n height: 500,\n projection: { type: projection, rotate: [-longitude, -latitude] },\n style: \"overflow: visible;\", // allow dots to escape\n marks: [\n Plot.geo(land, {\n fill: \"currentColor\",\n stroke: \"currentCOlor\",\n fillOpacity: 0.2\n }),\n Plot.raster(elevation, {\n clip: \"sphere\",\n fill: \"MAG_IGRF90\",\n interpolate: \"barycentric\",\n x: (d) => d.longitude,\n y: (d) => d.latitude,\n fill: (d, i) => d.elevation_m,\n fillOpacity: 0.7\n }),\n Plot.sphere()\n ]\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":630,"value":"pageview","pinned":false,"hidden":false,"mode":"ojs"},{"id":618,"value":"plotHeight = 300","pinned":false,"hidden":false,"mode":"ojs"},{"id":613,"value":"projection = \"orthographic\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":250,"value":"geoidDomain = [100, -100]","pinned":false,"hidden":false,"mode":"ojs"},{"id":636,"value":"elevation = FileAttachment(\"global_dem_1deg.csv\").csv({ typed: true })","pinned":false,"hidden":false,"mode":"ojs"},{"id":677,"value":"elevation_meridian_map = d3.group(elevation, (d) => d.longitude)","pinned":false,"hidden":false,"mode":"ojs"},{"id":779,"value":"elevation_parallels_map = d3.group(elevation, (d) => d.latitude)","pinned":false,"hidden":false,"mode":"ojs"},{"id":731,"value":"insertNullsAtGaps(elevation_meridian_map.get(longitude), (d) => d.latitude)","pinned":false,"hidden":false,"mode":"ojs"},{"id":727,"value":"insertNullsAtGaps = function (arr, f) {\n const result = [];\n for (let i = 0; i < arr.length; i++) {\n result.push(arr[i]);\n if (i < arr.length - 1) {\n let a = f(arr[i]);\n let b = f(arr[i + 1]);\n let min = Math.min(a, b);\n let max = Math.max(a, b);\n\n if (max - min > 1) {\n result.push(null);\n }\n }\n }\n return result;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":43,"value":"meridian = d3.range(-90, 90, 0.5).map((d) => [longitude, d])","pinned":false,"hidden":false,"mode":"ojs"},{"id":68,"value":"meridianHeights = Promise.all(meridian.map((d) => geoidHeight(d[1], longitude)))","pinned":false,"hidden":false,"mode":"ojs"},{"id":171,"value":"parallel = d3.range(-180, 180, 0.5).map((d) => [d, latitude])","pinned":false,"hidden":false,"mode":"ojs"},{"id":174,"value":"parallelHeights = Promise.all(parallel.map((d) => geoidHeight(latitude, d[0])))","pinned":false,"hidden":false,"mode":"ojs"},{"id":218,"value":"matrix = {\n let all = [];\n for (let lon = -180; lon < 180; lon += 3) {\n for (let lat = -90; lat < 90; lat += 3) {\n all.push([lon, lat, await geoidHeight(lat, lon)]);\n }\n }\n return all;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":8,"value":"world = FileAttachment(\"countries-110m.json\").json()","pinned":false,"hidden":false,"mode":"ojs"},{"id":9,"value":"land = topojson.feature(world, world.objects.land)","pinned":false,"hidden":false,"mode":"ojs"},{"id":29,"value":"import { geoidHeight } from \"@earthscope/geoid-height-function/2\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":272,"value":"import { ordinalSuffix } from \"@earthscope/utilities\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":627,"value":"import { pageview } from \"@earthscope/pageview\"","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W30","stdlib":"2","titling":"auto"}