2a:T17b5,// \file Geoid.cpp // \brief Implementation for GeographicLib::Geoid class // // Copyright (c) Charles Karney (2009) // and licensed under the LGPL. For more information, see // http://geographiclib.sourceforge.net/ // model is a string specifying a particular geoid model dataset to be loaded // Resolves a function when the dataset has been loaded that can be called with // lat, long, and cubic interpolation flag to calculate the geoid height above a geoid of a point. async function geoid(model) { let buffer = await files[model]; return new Promise(function (resolve, reject) { resolve(new Uint8Array(buffer)); }) .then(function (rawfile) { if ( !( rawfile[0] === 80 && rawfile[1] === 53 && ((rawfile[2] === 13 && rawfile[3] === 10) || rawfile[2] === 10) ) ) { throw new Error("Geoid model file: no PGM header"); } var i = rawfile[2] === 13 ? 4 : 3; var offset = null; var scale = null; function getline() { var start = i; for (var j = i; ; j++) { if (j >= rawfile.length) { throw new Error("Geoid model file: missing newline in header"); } if (rawfile[j] === 10) { i = j + 1; break; } } if (j > start && rawfile[j - 1] === 13) j--; return String.fromCharCode.apply(null, rawfile.slice(start, j)); } var m, s; for (;;) { s = getline(); if (s[0] !== "#") break; m = s.match(/^# Offset (.*)$/); if (m) { offset = parseInt(m[1], 10); if (!isFinite(offset)) { throw new Error("Geoid model file: bad offset " + m[1]); } } else { m = s.match(/^# Scale (.*)$/); if (m) { scale = parseFloat(m[1]); if (!isFinite(scale)) { throw new Error("Geoid model file: bad scale " + m[1]); } } } } m = s.match(/^\s*(\d+)\s+(\d+)\s*$/); var width = null; var height = null; if (m) { width = parseInt(m[1], 10); height = parseInt(m[2], 10); } if (!(m && width >= 0 && height >= 0)) { throw new Error("Geoid model file: bad PGM width&height line"); } var levels = parseInt(getline()); if (levels != 65535) { throw new Error( "Geoid model file: PGM file must have 65535 gray levels" ); } if (offset === null) { throw new Error("Geoid model file: PGM file does not contain offset"); } if (scale === null) { throw new Error("Geoid model file: PGM file does not contain scale"); } if (width < 2 || height < 2) { throw new Error("Geoid model file: Raster size too small"); } var payload_len = rawfile.length - i; if (payload_len !== width * height * 2) { throw new Error("Geoid model file: File has the wrong length"); } return { scale: scale, offset: offset, width: width, height: height, rlonres: width / 360, rlatres: (height - 1) / 180, rawval: function (ix, iy) { if (iy < 0) { iy = -iy; ix += width / 2; } else if (iy >= height) { iy = 2 * (height - 1) - iy; ix += width / 2; } if (ix < 0) { ix += width; } else if (ix >= width) { ix -= width; } var k = (iy * width + ix) * 2 + i; return (rawfile[k] << 8) | rawfile[k + 1]; } }; }) .then(function (model) { var cached_ix = null; var cached_iy = null; var v00 = null; var v01 = null; var v10 = null; var v11 = null; var t = null; return function (lat, lon, cubic) { if (lon < 0) lon += 360; var fy = (90 - lat) * model.rlatres; var fx = lon * model.rlonres; var iy = Math.floor(fy); var ix = Math.floor(fx); fx -= ix; fy -= iy; if (iy === model.height - 1) { iy--; } if (cached_ix !== ix || cached_iy !== iy) { cached_ix = ix; cached_iy = iy; if (cubic) { var c3x = c3; var c0x = c0; if (iy === 0) { c3x = c3n; c0x = c0n; } else if (iy === model.height - 2) { c3x = c3s; c0x = c0s; } var v = [ model.rawval(ix, iy - 1), model.rawval(ix + 1, iy - 1), model.rawval(ix - 1, iy), model.rawval(ix, iy), model.rawval(ix + 1, iy), model.rawval(ix + 2, iy), model.rawval(ix - 1, iy + 1), model.rawval(ix, iy + 1), model.rawval(ix + 1, iy + 1), model.rawval(ix + 2, iy + 1), model.rawval(ix, iy + 2), model.rawval(ix + 1, iy + 2) ]; t = Array.apply(null, Array(10)).map(function (_, i, arr) { return ( v.reduce(function (acc, vj, j, arr) { return acc + vj * c3x[j][i]; }, 0) / c0x ); }); } else { v00 = model.rawval(ix, iy); v01 = model.rawval(ix + 1, iy); v10 = model.rawval(ix, iy + 1); v11 = model.rawval(ix + 1, iy + 1); } } var h = null; if (cubic) { h = t[0] + fx * (t[1] + fx * (t[3] + fx * t[6])) + fy * (t[2] + fx * (t[4] + fx * t[7]) + fy * (t[5] + fx * t[8] + fy * t[9])); } else { var a = (1 - fx) * v00 + fx * v01; var b = (1 - fx) * v10 + fx * v11; h = (1 - fy) * a + fy * b; } return model.offset + model.scale * h; }; }); 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29:{"title":"Geoid Height Function","cells":[{"id":0,"value":"md`# Geoid Height Function\n\n© [Earthscope](https://www.unavco.org/) (Brooks Mershon, Cassie Hanagan)\n\n[GeographicLib/src/Geoid.cpp](https://geographiclib.sourceforge.io/html/geoid.html) from C++ to JavaScript\n\nby **Kim Vandry** .`","pinned":false,"hidden":false,"mode":"ojs"},{"id":412,"value":"toc()","pinned":false,"hidden":false,"mode":"ojs"},{"id":318,"value":"md`## 📚 Background`","pinned":false,"hidden":false,"mode":"ojs"},{"id":250,"value":"md`The geoid is the gravitational equipotential surface approximately coinciding with mean sea level.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":571,"value":"FileAttachment(\"Deflection-vertical-geoid-spheroid.jpeg\").image()","pinned":false,"hidden":false,"mode":"ojs"},{"id":303,"value":"example1 = md`## ☝️ Example: Evaluate geoid height at a single location`","pinned":false,"hidden":false,"mode":"ojs"},{"id":353,"value":"md`To use in another notebook:\n\n~~~js\nimport {models, geoid} from @unavco/geoid-height\n~~~`","pinned":false,"hidden":false,"mode":"ojs"},{"id":298,"value":"md`*Pick a location on the world map below:*`","pinned":false,"hidden":false,"mode":"ojs"},{"id":288,"value":"// Default Boulder, Colorado :)\nviewof coordinates = worldMapCoordinates([-105.2705, 40.015]) // lon, lat","pinned":false,"hidden":false,"mode":"ojs"},{"id":321,"value":"md`The Geoid Height of **${coordinates[1]} °${coordinates[1] > 0 ? \"N\" : \"S\"}, \n ${coordinates[0]} °${coordinates[0] < 0 ? \"W\" : \"E\"}** is **${d3.format(\n \",.4r\"\n)(height)} meters.**`","pinned":false,"hidden":false,"mode":"ojs"},{"id":244,"value":"md`*Select a [Geoid Dataset](https://geographiclib.sourceforge.io/html/geoid.html) (year/resolution) that will be used to calculate a **height***.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":177,"value":"viewof modelSelection = Inputs.select(models, {\n value: models[0],\n label: \"Geoid Dataset\"\n})","pinned":true,"hidden":false,"mode":"ojs"},{"id":279,"value":"viewof cubic = Inputs.toggle({ label: \"Cubic interpolation\", value: false })","pinned":true,"hidden":false,"mode":"ojs"},{"id":401,"value":"function geoidHeight(lat, lon, cubic = false) {\n return geoid(modelSelection).then(\n // This function is called when the dataset is loaded (a promise resolves).\n function (calculate) {\n // The parameter to this function is a function that takes a lat/long and provides a\n // height using the loaded dataset.\n return calculate(\n lat, // latitude\n lon, // longitude (be careful about the order of the arguments!)\n cubic // true or false\n );\n }\n );\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":87,"value":"height = geoidHeight(coordinates[1], coordinates[0], cubic) // Ensure lat and long order is handled correctly!","pinned":true,"hidden":false,"mode":"ojs"},{"id":420,"value":"example2 = md`## ☝️ Example: Working with Data`","pinned":false,"hidden":false,"mode":"ojs"},{"id":428,"value":"md`We can import a CSV file having at least a *latitude* and *longitude* column headers in order to evaluate the Geoid Height function across an entire dataset.\n\nTry it out!`","pinned":false,"hidden":false,"mode":"ojs"},{"id":386,"value":"viewof data = csvInput({\n initialUrl: await FileAttachment(\"countries.csv\").url()\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":432,"value":"solutions = Promise.all(data.map((d) => geoidHeight(+d.latitude, +d.longitude)))","pinned":true,"hidden":false,"mode":"ojs"},{"id":1024,"value":"data","pinned":true,"hidden":false,"mode":"ojs"},{"id":495,"value":"md`Here is your input data with an extra column added containing the computed geoid heights at leat **latitude** and **longitude**.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":650,"value":"tableData = data.map((d, i) => {\n d.geoid_height = solutions[i];\n return d;\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":384,"value":"viewof solutionTable = Table(tableData)","pinned":false,"hidden":false,"mode":"ojs"},{"id":492,"value":"md`Click the button below to save your computed geoid heights in a CSV file that you can download and open in your favorite spreadsheet program.\n\n*For fun, try changing the geoid dataset used using the dropdown above to get a different set of solutions.*`","pinned":false,"hidden":false,"mode":"ojs"},{"id":483,"value":"download(async () => {\n await Promises.delay(1000);\n return new Blob([d3.csvFormat(solutionTable)], { type: \"text/csv\" });\n}, \"Geoid Height\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":666,"value":"tests = md`## ☝️ Example: Tests, validation, error analysis`","pinned":false,"hidden":false,"mode":"ojs"},{"id":976,"value":"n = 75000 // number of samples","pinned":false,"hidden":false,"mode":"ojs"},{"id":617,"value":"md`[Test data for geoids](https://geographiclib.sourceforge.io/html/geoid.html#testgeoid) from GeographicLib.\n\nWe have **500,000** test points with geoid heights computed from the NGA fortran routine using the **EGM84**, **EGM96**, and **EGM2008** harmonic coefficients to compare against the outputs produced by this notebook's calculations. We take a *random* sample of approximately 5,000 (1%) of these test points to compute the error percentage between the values derived using this notebook and test data values for each model.\n\nThe computed value uses the model and cubic interpolation as selected above. Change the model and interpolation setting to compare the calculators solutions with the test data for the corresponding model year. `","pinned":false,"hidden":false,"mode":"ojs"},{"id":581,"value":"testData = FileAttachment(\"GeoidHeights.dat\")\n .text()\n .then(\n (d) =>\n d3\n .dsvFormat(\" \")\n .parse(d)\n .filter((d) => Math.random() <= n / 500000) // Take a random sample of roughly 1% of the data to test.\n )","pinned":false,"hidden":false,"mode":"ojs"},{"id":645,"value":"testTableData = testData.map((d, i) => {\n let solution = testSolution[i].toFixed(6);\n d[modelSelection] = solution;\n d.error = (solution - d[modelMap[modelSelection]]) / d[modelSelection];\n return d;\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":601,"value":"testSolution = Promise.all(\n testData.map((d) => geoidHeight(+d.latitude, +d.longitude, cubic))\n)","pinned":false,"hidden":false,"mode":"ojs"},{"id":768,"value":"errorPoints = testTableData.map((d) => [d.longitude, d.latitude])","pinned":false,"hidden":false,"mode":"ojs"},{"id":747,"value":"errorExtent = [\n 0,\n d3.quantile(testTableData, upperQuantile, (d) => Math.abs(d.error))\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":615,"value":"viewof testTable = Table(testTableData, {\n columns: [\n \"latitude\",\n \"longitude\",\n modelMap[modelSelection], // Show a column containing known values for the current model year.\n modelSelection, // Show the column title corresponding to the computed values using the SELECTED model.\n \"error\" // Compute error percentages of difference between computed and kown divided by the known value.\n ],\n format: {\n error: (x) =>\n html`${d3.format(\".6%\")(x)}`\n }\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":881,"value":"md`Below you can see **${d3.format(\",.6\")(\n testTableData.length\n)}** random points from the known 500,000 test points plotted on a map with a color scale to encode larger error magnitudes in a darker shade of red.\n\nBy moving the slider below you can interactively experiment with ignoring outliers in the error for any given location in order to gain a sense of the relative magnitude of error as it is distributed throughout the world.\n\nIf you srub the slider all the way to 1, you will easily be able to spot the locaiton of the absolute *worst* error in the test.\n\nExperiment with it!\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":855,"value":"viewof upperQuantile = Inputs.range([0, 1], {\n value: 0.95,\n step: 0.01,\n label: \"P-Quantile\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":916,"value":"viewof symbolLegend = plot({\n autosize: \"pad\",\n data: [\n {\n name: \"values\",\n values: [\n \"Zero Error\",\n d3.format(\".5%\")(errorExtent[1]) + ` (${upperQuantile} quantile error)`\n ]\n }\n ],\n scales: [\n {\n name: \"symbolColor\",\n type: \"ordinal\",\n domain: { data: \"values\", field: \"data\" },\n range: [d3.interpolateReds(0), d3.interpolateReds(1)]\n },\n {\n name: \"symbolSize\",\n type: \"ordinal\",\n domain: { data: \"values\", field: \"data\" },\n range: [200, 200]\n }\n ],\n legends: [Object.assign({ offset: 0 }, symbolLegendDef)]\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":750,"value":"earth = {\n const context = DOM.context2d(width, width / 1.8);\n const path = d3.geoPath(project, context).pointRadius(3);\n (context.fillStyle = \"#fff\"), context.fillRect(0, 0, width, width / 1.8);\n // Plot the gratucule, land, country borders\n context.beginPath(),\n path(graticule),\n (context.lineWidth = 0.75),\n (context.strokeStyle = \"#dddddd\"),\n context.stroke();\n context.beginPath(),\n path(land),\n (context.fillStyle = \"#f4f4f4\"),\n context.fill();\n context.beginPath(),\n path(countries),\n (context.strokeStyle = \"#aaaaaa\"),\n context.stroke();\n // Plots the points in long/lat pairs, divided based on geoid height for color\n context.globalAlpha = 0.2;\n errorPoints.forEach((d, i) => {\n const pointPatha = { type: \"Point\", coordinates: d };\n context.beginPath(),\n path(pointPatha),\n (context.fillStyle = d3.interpolateReds(color(testTableData[i].error))),\n context.fill();\n });\n\n return context.canvas;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":4,"value":"md`## ✨ Appendix`","pinned":false,"hidden":false,"mode":"ojs"},{"id":149,"value":"md`### 🔢 Constants (used in the calculations)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":42,"value":"c0 = 240","pinned":false,"hidden":false,"mode":"ojs"},{"id":64,"value":"c3 = [\n [9, -18, -88, 0, 96, 90, 0, 0, -60, -20],\n [-9, 18, 8, 0, -96, 30, 0, 0, 60, -20],\n [9, -88, -18, 90, 96, 0, -20, -60, 0, 0],\n [186, -42, -42, -150, -96, -150, 60, 60, 60, 60],\n [54, 162, -78, 30, -24, -90, -60, 60, -60, 60],\n [-9, -32, 18, 30, 24, 0, 20, -60, 0, 0],\n [-9, 8, 18, 30, -96, 0, -20, 60, 0, 0],\n [54, -78, 162, -90, -24, 30, 60, -60, 60, -60],\n [-54, 78, 78, 90, 144, 90, -60, -60, -60, -60],\n [9, -8, -18, -30, -24, 0, 20, 60, 0, 0],\n [-9, 18, -32, 0, 24, 30, 0, 0, -60, 20],\n [9, -18, -8, 0, -24, -30, 0, 0, 60, 20]\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":67,"value":"c0n = 372","pinned":false,"hidden":false,"mode":"ojs"},{"id":68,"value":"c3n = [\n [0, 0, -131, 0, 138, 144, 0, 0, -102, -31],\n [0, 0, 7, 0, -138, 42, 0, 0, 102, -31],\n [62, 0, -31, 0, 0, -62, 0, 0, 0, 31],\n [124, 0, -62, 0, 0, -124, 0, 0, 0, 62],\n [124, 0, -62, 0, 0, -124, 0, 0, 0, 62],\n [62, 0, -31, 0, 0, -62, 0, 0, 0, 31],\n [0, 0, 45, 0, -183, -9, 0, 93, 18, 0],\n [0, 0, 216, 0, 33, 87, 0, -93, 12, -93],\n [0, 0, 156, 0, 153, 99, 0, -93, -12, -93],\n [0, 0, -45, 0, -3, 9, 0, 93, -18, 0],\n [0, 0, -55, 0, 48, 42, 0, 0, -84, 31],\n [0, 0, -7, 0, -48, -42, 0, 0, 84, 31]\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":73,"value":"c0s = 372","pinned":false,"hidden":false,"mode":"ojs"},{"id":74,"value":"c3s = [\n [18, -36, -122, 0, 120, 135, 0, 0, -84, -31],\n [-18, 36, -2, 0, -120, 51, 0, 0, 84, -31],\n [36, -165, -27, 93, 147, -9, 0, -93, 18, 0],\n [210, 45, -111, -93, -57, -192, 0, 93, 12, 93],\n [162, 141, -75, -93, -129, -180, 0, 93, -12, 93],\n [-36, -21, 27, 93, 39, 9, 0, -93, -18, 0],\n [0, 0, 62, 0, 0, 31, 0, 0, 0, -31],\n [0, 0, 124, 0, 0, 62, 0, 0, 0, -62],\n [0, 0, 124, 0, 0, 62, 0, 0, 0, -62],\n [0, 0, 62, 0, 0, 31, 0, 0, 0, -31],\n [-18, 36, -64, 0, 66, 51, 0, 0, -102, 31],\n [18, -36, 2, 0, -66, -51, 0, 0, 102, 31]\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":367,"value":"md`### 🌐 Geoid Datasets`","pinned":false,"hidden":false,"mode":"ojs"},{"id":268,"value":"md`Geoid datasets are read from local files and turned into arraybuffer objects that are passed in as an agument to the Geoid Height function.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":196,"value":"// A mapping from model name to an ArrayBuffer containing the model data for use in\n// geoid height calculations.\nfiles = ({\n \"egm84-15\": FileAttachment(\"egm84-15.pgm\").arrayBuffer(),\n \"egm84-30\": FileAttachment(\"egm84-30.pgm\").arrayBuffer(),\n \"egm96-5\": FileAttachment(\"egm96-5.pgm\").arrayBuffer(),\n \"egm96-15\": FileAttachment(\"egm96-15.pgm\").arrayBuffer(),\n \"egm2008-5\": FileAttachment(\"egm2008-5.pgm\").arrayBuffer()\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":271,"value":"md`The user can conveniently select from a few pre-loaded datasets.\n\n*Note: Each cell resolves as a promise Object, and therefore we easily deal with asynronicity by referencing asyncronous values across cell boundaries.*`","pinned":false,"hidden":false,"mode":"ojs"},{"id":153,"value":"md`\n### 🧮 Calculations\n*[Geoid Height Calculator port](https://github.com/vandry/geoidheight/blob/master/geoid.js\n) by [Kim Vandry](https://github.com/vandry).*\n\n*Modified for use in this notebook by [Brooks Mershon](https://www.brooksmershon.com).*`","pinned":false,"hidden":false,"mode":"ojs"},{"id":79,"value":"$2a","pinned":false,"hidden":false,"mode":"ojs"},{"id":540,"value":"models = [\"egm84-30\", \"egm84-15\", \"egm96-5\",\"egm96-15\", \"egm2008-5\"].reverse()","pinned":false,"hidden":false,"mode":"ojs"},{"id":700,"value":"modelMap = {\n let map = {};\n models.forEach((d) => {\n map[d] = d.split(\"-\")[0].toUpperCase();\n });\n return map;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":939,"value":"md`------`","pinned":false,"hidden":false,"mode":"ojs"},{"id":782,"value":"color = d3\n .scaleLinear()\n .domain(errorExtent)\n .range([0, 1])","pinned":false,"hidden":false,"mode":"ojs"},{"id":753,"value":"project = {\n return d3[\"geoNaturalEarth1\"]()\n .rotate([0, 0])\n .precision(0.1)\n .fitSize([width, width / 1.8], { type: \"Sphere\" });\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":756,"value":"graticule = d3.geoGraticule10()","pinned":false,"hidden":false,"mode":"ojs"},{"id":761,"value":"world = FileAttachment(\"world-atlas-110m.json\").json()","pinned":false,"hidden":false,"mode":"ojs"},{"id":763,"value":"countries = topojson.feature(world, world.objects.countries)","pinned":false,"hidden":false,"mode":"ojs"},{"id":758,"value":"land = topojson.feature(world, world.objects.land)","pinned":false,"hidden":false,"mode":"ojs"},{"id":759,"value":"topojson = require(\"topojson@3\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":291,"value":"import { worldMapCoordinates } from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":388,"value":"import {Table} from \"@observablehq/inputs\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":394,"value":"import { csvInput } from \"@bmershon/file-input-with-csv-support\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":415,"value":"import { toc } from \"@mbostock/toc\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":479,"value":"import { download } from \"@mbostock/lazy-download\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":918,"value":"import {\n symbolLegend,\n plot,\n symbolLegendDef\n} from \"@vega/a-guide-to-guides-axes-legends-in-vega\"","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W2b","stdlib":"1","titling":"auto"}