3e:null 3f:["$","title",null,{"children":"Geoid Height Calculator | Fred Lu | Observable"}] 45:Tf6b7,heightstxt = md`## Understanding the geoid and "height" The [*geoid*](https://oceanservice.noaa.gov/facts/geoid.html) is one approximation of Earth's shape due to gravity, roughly coinciding with mean sea level. Because the inside of our planet is non-uniform, gravity is not constant at the surface. If Earth were completely covered in an ocean, the water would swell over gravity highs (where there is more mass below the surface) and depress in areas of gravity lows (where there is less mass below the surface). The geoid approximates this hypothetical ocean surface, representing a geopotential surface. To think of it another way, if we were able to walk on the geoid, we would experience a constant value of gravity.

drawing

*Representation of the geoid, image from [NASA](https://earthobservatory.nasa.gov/ContentFeature/GRACE/Images/geoids_sm.jpg).*

The height of the geoid is often reported relative to the internationally recognized [WGS84 *reference ellipsoid*](https://geodesy.noaa.gov/datums/index.shtml). The GPS in our phones, for example, records elevations relative to this ellispoid. Sometimes, it is useful to know elevations relative to mean sea level—this is where the geoid height calculation comes in: to convert ellipsoidal heights to heights above the geoid (aka *orthometric heights*). The NGA ([National Geospatial-Intelligence Agency](https://earth-info.nga.mil/index.php?action=home)) publishes models that describe the earth's gravitational field (see the Earth Gravitational Models [here](https://earth-info.nga.mil/index.php?dir=wgs84&action=wgs84)), and updates them as we learn more through satellite geodesy. It is becoming standard to use EGM2008 over its predecessors, but a 2020 model is soon to become standard. Here is a helpful sketch of what these surfaces might look like relative to Earth's topography:

drawing

*Image from the [National Center for Polar and Ice Research](https://ncpor.res.in/pages/researchview/11)*

**Terminology definitions:** - **Reference Ellipsoid:** Here, the reference ellipsoid refers to the datum surface derived from the WGS84 reference system. - **Geoid:** The gravitational equipotential surface that approximates global mean sea level, given as the height above the reference ellipsoid. - **Geoid Undulation:** Height of the geoid above the reference ellipsoid. - **Geoid Height**: Same as geoid undulation. - **Orthometric Height:** Height above the geoid. `46:T75e,calculationtxt = md`## Understanding the geoid calculation Computing the height of a geoid from a set of potential coefficients provided in an Earth Gravitational Model (EGM), as done here, is a non-unique problem, dependent on several assumptions. If you'd like to know more about the calculation, a core paper that outlines the methodology can be found here: [*Use of Potential Coefficient Models for Geoid Undulation Determination Using a Spherical Harmonic Representation of the Height Anomaly/Geoid Undulation Difference*](https://link.springer.com/article/10.1007%252Fs001900050096,) by R.H. Rapp, Journal of Geodesy, 1996. Further discussion of the assumptions in computing a geoid from an EGM is presented in [*There is no such thing as "The" EGM96 geoid: Subtle points on the use of a global geopotential model*](https://www.ngs.noaa.gov/PUBS_LIB/EGM96_GEOID_PAPER/egm96_geoid_paper.html), by Dru A. Smith, 1998. A good description of errors in the geoid height calculations, including those introduced by the cubic interpolation method, can be found on the [GeographicLib](https://geographiclib.sourceforge.io/html/geoid.html#geoidinterp) page. In sum, the errors from the calculations presented here (when compared against the NGA geoid [test datasets](https://observablehq.com/@bmershon/geoid-height#tests)) stem from (1) the method of interpolation, (2) the height ambiguity resulting from the fact that the geoid and ellipsoid are not parallel surfaces, and (3) the grid format of the geoid harmonic coefficients, which require quantization of height to 3 mm. A comparison of errors from this calculator with the NGA test datasets is performed in a companion [Notebook](https://observablehq.com/@bmershon/geoid-height) created by Brooks Mershon and Cassie Hanagan at UNAVCO. An associated map highlights areas where the geoid height calculations differ the most. `47:T557,origintxt = md`## Code origin The original UNAVCO tool ran on a NGA ([National Geospatial-Intelligence Agency](https://earth-info.nga.mil/index.php?action=home)) fortran code for the geoid height calculation. The original tool can be found [here](https://www.unavco.org/software/geodetic-utilities/geoid-height-calculator/geoid-height-calculator.html). The geoid height calculation was recoded in C++ as part of a larger library of geodetic functions in [GeographicLib](https://geographiclib.sourceforge.io/). The [GeographicLib::Geoid](https://geographiclib.sourceforge.io/html/classGeographicLib_1_1Geoid.html) class and associated [Geoid.cpp](https://geographiclib.sourceforge.io/html/Geoid_8cpp.html) were translated to JavaScript by [Kim Vandry](vandry@TZoNE.ORG), available [here](https://github.com/vandry/geoidheight). All products are under the [MIT License](https://opensource.org/licenses/MIT). This notebook is run with core functions from another [Notebook](https://observablehq.com/@bmershon/geoid-height) created by Brooks Mershon and Cassie Hanagan at UNAVCO, which makes Kim Vandry's JavaScript port of GeographicLib::Geoid available in Observable Notebooks like this one. That notebook includes a [suite of test cases](https://observablehq.com/@bmershon/geoid-height#tests) and further documentation to validate the accuracy of this calculator. `48:[{"id":"6e95cb17aaefc544c9c7d7fe8afc92cd79df09fdf32bd2788cb7075f2baa1da257ccf9091b239176fbe2b62d926f76227883f55b0649a1657969b1fc9b30a20f","href":"https://static.observableusercontent.com/files/6e95cb17aaefc544c9c7d7fe8afc92cd79df09fdf32bd2788cb7075f2baa1da257ccf9091b239176fbe2b62d926f76227883f55b0649a1657969b1fc9b30a20f","name":"unav_50_real-time_stations@1.csv","type":"text/csv","lastModified":1674213199942.448,"size":237},{"id":"0ca9148938fe656b24d3cd9474fc7190de67f0c2fa0c6940f93f874da1572341e3691665fd40b708cdd5573317e4b18f96bfc1d3617464cb0dc2d8b607c3bddd","href":"https://static.observableusercontent.com/files/0ca9148938fe656b24d3cd9474fc7190de67f0c2fa0c6940f93f874da1572341e3691665fd40b708cdd5573317e4b18f96bfc1d3617464cb0dc2d8b607c3bddd","name":"world-atlas-110m.json","type":"application/json","lastModified":1674213199942.448,"size":102116}] 43:{"id":"9ea11b117bc40faa","slug":null,"title":"Geoid Height Calculator","thumbnail":"57c2be890cfaa83feef3a7e404dfee576897095736b1f695f9491297922ff51a","access_level":"public","create_time":"$D2023-01-20T11:13:19.942Z","update_time":"$D2023-01-20T11:13:19.942Z","view_time":null,"first_public_time":"$D2023-01-20T11:13:19.942Z","has_unpublished_edits":null,"fork":{"id":"6388e8aaf9816688","slug":"geoid-height-calculator/2","title":"Geoid Height Calculator","owner":{"id":"a505e42d43acc70e","login":"earthscope","name":"EarthScope Consortium"}},"stars":0,"starred":false,"owner":{"type":"team","id":"17521a73b4bf5369","login":"metaclass","name":"Fred Lu","avatar_url":"https://avatars-next.observableusercontent.com/74842e3449a16eaa8dc29f8685b5abd7f6e2a5bbb81c99ab6866780ea41c1981","tier":"starter_2024","bio":"","following":false},"version":2567,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"92c6c0b7fc90056e","login":"metaclass","name":"Fred Lu","avatar_url":"https://avatars-next.observableusercontent.com/74842e3449a16eaa8dc29f8685b5abd7f6e2a5bbb81c99ab6866780ea41c1981","tier":null,"bio":"","following":false}],"members":[{"type":"individual","id":"92c6c0b7fc90056e","login":"metaclass","name":"Fred Lu","avatar_url":"https://avatars-next.observableusercontent.com/74842e3449a16eaa8dc29f8685b5abd7f6e2a5bbb81c99ab6866780ea41c1981","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Geoid Height Calculator","cells":[{"id":0,"value":"introtxt = md`# Geoid Height Calculator\n\n© [UNAVCO](https://www.unavco.org/) by Cassie Hanagan & Brooks Mershon\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2474,"value":"md`***Launch the latest stable verion*** by clicking the button below to copy a link, then paste it in a new browser window: ${Copier(\n \"Copy link\",\n {\n value: `https://observablehq.com/embed/@cehanagan/geoid-height-calculator?cells=introtxt%2Ctoctxt%2Ccalc%2Cviewof+modelSelection%2Cviewof+cubic%2Cinstrtxt%2Cviewof+csvData%2Cviewof+coordinatesInput%2Cinstr2txt%2CcolorLegend%2Cearth%2Cviewof+solutionTable%2Csavemetxt%2Cdownloadzip%2Coverviewtxt%2Cheightstxt%2Ccalculationtxt%2Corigintxt%2Creftxt`\n }\n)}\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":412,"value":"toctxt = toc()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1262,"value":"calc = md`## Calculator: Input and output\n\n**Select the geoid model to use and choose whether you want cubic interpolation between grid points:**`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":345,"value":"viewof modelSelection = Inputs.select(models, {\n value: models[0],\n label: html`1. Geoid Model`\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":331,"value":"viewof cubic = Inputs.toggle({\n label: html`2. Cubic interpolation`,\n value: true\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1145,"value":"instrtxt = md`**Import CSV or copy & paste point data**\n\n(1) Upload a comma-separated file with latitude (decimal degrees), longitude (decimal degrees), and elevation (m) column headers. \n\n**or**\n\n(2) Copy and paste comma-separated latitude (decimal degrees), longitude (decimal degrees), and elevation (m) values without headers.\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1065,"value":"viewof csvData = csvInput({\n initialUrl: await FileAttachment(\"unav_50_real-time_stations@1.csv\").url(),\n label: \"CSV File:\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2509,"value":"coordinatesInput","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":513,"value":"viewof coordinatesInput = textarea({\n title: \"Coordinates (Latitude, Longitude, Elevation)\",\n value: d3\n .csvFormat(csvData)\n .split('\\n')\n .slice(1)\n .join(\"\\n\"),\n rows: 10,\n cols: 60,\n submit: true\n})\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1256,"value":"instr2txt = md`**Your coordinates and results**`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2453,"value":"colorLegend = html`\n

\n ${legend({\n color: d3.scaleDiverging(\n [d3.min(geoid_heights), 0, d3.max(geoid_heights)],\n d3.interpolateRdBu\n ),\n title: \"Geoid Height\"\n })}\n

\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":480,"value":"earth = {\n const context = DOM.context2d(width, width / 1.8);\n const path = d3.geoPath(project, context).pointRadius(3);\n (context.fillStyle = \"#fff\"), context.fillRect(0, 0, width, width / 1.8);\n // Plot the gratucule, land, country borders\n context.beginPath(),\n path(graticule),\n (context.lineWidth = 0.75),\n (context.strokeStyle = \"#dddddd\"),\n context.stroke();\n context.beginPath(),\n path(land),\n (context.fillStyle = \"#f4f4f4\"),\n context.fill();\n context.beginPath(),\n path(countries),\n (context.strokeStyle = \"#aaaaaa\"),\n context.stroke();\n map_coords.forEach((d, i) => {\n const pointPath = { type: \"Point\", coordinates: d };\n context.beginPath(),\n path(pointPath),\n (context.fillStyle = colorscale(geoid_heights[i])),\n context.fill(),\n (context.strokeStyle = \"#000000\"),\n context.stroke();\n });\n\n return context.canvas;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1678,"value":"viewof solutionTable = Inputs.table(csvOut, {\n format: {\n Latitude: x => html`${d3.format(\"D\")(x)}`,\n Longitude: x => html`${d3.format(\"D\")(x)}`,\n \"Ellps Height (m)\": x => html`${d3.format(\"D\")(x)}`,\n \"Geoid Height (m)\": x =>\n html`${x}`,\n \"Ortho Height (m)\": x =>\n html`${x}`\n }\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1244,"value":"savemetxt = md`Click the button below to save and download a zip file with the table in CSV format and a README describing the calculation input parameters.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1922,"value":"downloadzip = download(\n zip,\n 'GeoidHeight_' + d3.timeFormat(\"%Y-%m-%d\")(new Date())\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":4,"value":"overviewtxt = md`## Overview\n\nThis tool computes the geoid height and orthometric height of a point (or points). \n\nUser-specified inputs include:\n 1. The [Earth Gravitational Model](https://earth-info.nga.mil/index.php?dir=wgs84&action=wgs84) to compute the geoid. The number following EGM represents the model year, the number following the dash denotes the model grid spacing in minutes of a degree.\n 2. The option for cubic interpolation between grid points. Otherwise no interpolation is performed. *See the [GeographicLib](https://geographiclib.sourceforge.io/html/geoid.html#geoidinterp) information pages for more info on the interpolation method.* \n 3. The latitude, longitude, and height of a point(s) above the WGS84 reference ellipsoid.\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":10,"value":"$45","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":407,"value":"$46","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":297,"value":"$47","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":372,"value":"reftxt = md`## References \n\nC. F. F. Karney, GeographicLib, Version 1.51 (2019-09-24), https://geographiclib.sourceforge.io/1.51\n\nRapp, R. H. (1997). Use of potential coefficient models for geoid undulation determinations using a spherical harmonic representation of the height anomaly/geoid undulation difference. *Journal of Geodesy, 71(5)*, 282-289.\n\nSmith, D. A. (1998). There is no such thing as \"The\" EGM96 geoid: Subtle points on the use of a global geopotential model. *IGeS Bulletin N. 8*, Int. Geoid Service, 17-27.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":310,"value":"md`### Appendix`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":357,"value":"md`** I. Code Imports**`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2496,"value":"import { Copier } from \"@mbostock/copier\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":311,"value":"import { models, geoid } from \"@unavco/geoid-height-function/2\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":518,"value":"import { select, textarea, slider, color } from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1059,"value":"import { csvInput } from \"@unavco/file-input-with-csv-support\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1241,"value":"import { download } from \"@mbostock/lazy-download\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2344,"value":"import { legend, swatches } from \"@d3/color-legend\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1271,"value":"md` ** II. Non-geoid calculation variables and functions**\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2559,"value":"function toc(selector = \"h2\", heading = \"Jump to:\") {\n return Generators.observe((notify) => {\n let headings = [];\n\n function observed() {\n const h = Array.from(document.querySelectorAll(selector));\n if (h.length !== headings.length || h.some((h, i) => headings[i] !== h)) {\n notify(\n html`${heading} ${Array.from((headings = h), (h) => {\n return Object.assign(\n html`${DOM.text(\n h.textContent\n )} `,\n { onclick: (e) => (e.preventDefault(), h.scrollIntoView()) }\n );\n })}`\n );\n }\n }\n\n const observer = new MutationObserver(observed);\n observer.observe(document.body, { childList: true, subtree: true });\n observed();\n return () => observer.disconnect();\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":491,"value":"graticule = d3.geoGraticule10()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":575,"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","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":494,"value":"land = topojson.feature(world, world.objects.land)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":496,"value":"world = FileAttachment(\"world-atlas-110m.json\").json()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":498,"value":"topojson = require(\"topojson@3\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":499,"value":"d3 = require(\"d3@5\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":593,"value":"countries = topojson.feature(world, world.objects.countries)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1697,"value":"function rowsToObjects(rows, headers) {\n return rows.map(r =>\n r.reduce((o, c, i) => Object.assign(o, { [headers[i]]: c }), {})\n );\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1866,"value":"JSZip = require(\"jszip@3/dist/jszip.min.js\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2365,"value":"colorscale = d3.scaleDiverging(\n [d3.min(geoid_heights), 0, d3.max(geoid_heights)],\n d3.interpolateRdBu\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":380,"value":"md`**III. Geoid calculator variables and functions**\n\nThe user-specified inputs are run through the geoid function in the following cells.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1123,"value":"// lon, lat\ncoords = coordinatesInput\n .trim()\n .split(/\\n/)\n .map(\n line =>\n line\n .split(/,\\s*/)\n .slice(0, 2) // elevation discarded\n .map(n => +n) // number\n )","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1294,"value":"heights = coordinatesInput\n .trim()\n .split(/\\n/)\n .map(\n line =>\n line\n .split(/,\\s*/)\n .slice(-1) // lon, lat discarded\n .map(n => +n) // number\n )","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1280,"value":"geoid_heights = {\n let gheight = [];\n for (var i = 0; i < coords.length; i++) {\n gheight.push(await new geoidHeight(coords[i][0], coords[i][1], cubic));\n }\n return gheight;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1278,"value":"ortho_heights = {\n let oheight = []; //; var oheight = [];\n for (var i = 0; i < coords.length; i++) {\n oheight.push(heights[i] - geoid_heights[i]);\n }\n return oheight;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2312,"value":"// reverse coordinates for mapping\nmap_coords = {\n let n = [];\n for (var i = 0; i < coords.length; i++) {\n n.push([coords[i][0], coords[i][1], geoid_heights[i]]);\n }\n return n.map(line => line.slice(0, 2).reverse());\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1527,"value":"// filter coordinates based on whether the geoid is above the ellipsoid\nabove_coords = {\n let n = [];\n for (var i = 0; i < coords.length; i++) {\n n.push([coords[i][0], coords[i][1], geoid_heights[i]]);\n }\n return n\n .filter(function(arr) {\n return arr[2] > 0;\n })\n .map(line => line.slice(0, 2).reverse());\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1435,"value":"below_coords = {\n let n = [];\n for (var i = 0; i < coords.length; i++) {\n n.push([coords[i][0], coords[i][1], geoid_heights[i]]);\n }\n return n\n .filter(function(arr) {\n return arr[2] <= 0;\n })\n .map(line => line.slice(0, 2).reverse());\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1650,"value":"// Maps the height, ortho height, and geoid height to the coordinates,\n// and turns the array into an object with column headers\ncsvOut = rowsToObjects(\n coordinatesInput\n .trim()\n .split(/\\n/)\n .map(\n line =>\n line\n .split(/,\\s*/)\n .slice(0, 2) // elevation discarded\n .map(n => +n)\n .reverse() // number\n ) // Left with lat, lon. Next: add heights\n .map(line => line.reverse())\n .map((d, i) => {\n (d[2] = heights[i][0]),\n (d[3] = Number(geoid_heights[i].toFixed(2))),\n (d[4] = Number(ortho_heights[i].toFixed(2)));\n return d;\n }),\n [\n 'Latitude',\n 'Longitude',\n 'Ellps Height (m)',\n 'Geoid Height (m)',\n 'Ortho Height (m)'\n ]\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1869,"value":"function readmeText() {\n return `© ${d3.timeFormat(\"%Y\")(new Date())} UNAVCO\n\n Created with the Geoid Height Calculator at:\n\n https://observablehq.com/@cehanagan/geoid-height-calculator\n\n The file \"geoid_height_calculator_${d3.timeFormat(\"%Y-%m-%d\")(\n new Date()\n )}.csv\"\n contains the user-input latitudes, longitudes, and heights (above the WGS84 ellipsoid), \n and calculated geoid and orthometric heights above the ${modelSelection} geoid.\n\n Cubic interpolation was set to ${cubic}.\n\n Contact brooks.mershon@unavco.org or @bmershon on GitHub with questions, concerns, or 🐛 reports.\n \n `;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1880,"value":"zip = {\n const zip = new JSZip();\n const folder = zip.folder(\n 'GeoidHeight' + d3.timeFormat(\"%Y-%m-%d\")(new Date())\n );\n folder.file('README.txt', readmeText());\n folder.file(\n 'geoid_height_' + d3.timeFormat(\"%Y-%m-%d\")(new Date()) + '.csv',\n d3.csvFormat(solutionTable)\n );\n return zip.generateAsync({ type: 'blob' });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1015,"value":"function geoidHeight(lat, lon, cubic = false) {\n return geoid(modelSelection).then(\n // This function is called when the dataset is loaded (a promise resolves).\n function (calculate) {\n // The parameter to this function is a function that takes a lat/long and provides a\n // height using the loaded dataset.\n return calculate(\n lat, // latitude\n lon, // longitude (be careful about the order of the arguments!)\n cubic // true or false\n );\n }\n );\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W48","stdlib":"1"}} 44:"$43:body"