2c:null 2d:["$","title",null,{"children":"🧭 Earthʼs Magnetic Field Declination | Christophe Yamahata | Observable"}] 32:T68f,IGRF_magnetic_declination = Plot.plot({ width: width, height: width/selected_projection.height_factor_1, marginTop: selected_projection.marginTop, projection: ({width, height}) => selected_projection.value .translate([width / 2 - 20, height / selected_projection.height_factor_2]), color: { type: "linear", scheme: "BuYlRd", domain: [-50, 50], legend: true, label: "Year "+Year+": Main Field Declination (°)" }, marks: [ Plot.contour(data, { thresholds: 100, fill: Plot.identity, fillOpacity: 1, width: 360, height: 180, x1: -180, y1: -90, x2: 180, y2: 90, blur: blur, stroke: "white", strokeWidth: 0.5, clip: "sphere" }), Plot.contour(data, { thresholds: [0], width: 360, height: 180, x1: -180, y1: -90, x2: 180, y2: 90, blur: blur, stroke: "mediumseagreen", strokeDasharray: "8,3", strokeWidth: 2.2, clip: "sphere" }), Plot.contour(data, { thresholds: [-180,-160,-140,-120,-100,-80,-60,-40,-20,20,40,60,80,100,120,140,160,180], width: 360, height: 180, x1: -180, y1: -90, x2: 180, y2: 90, blur: blur, stroke: "black", strokeWidth: 0.8, clip: "sphere" }), Plot.geo(land, { fill: "#000", fillOpacity: 0.2, }), Plot.text([{ x: -130 + selected_projection.text_Dx, y: -10, label: String(Year) }], { x: "x", y: "y", text: "label", fill: "white", fontSize: 70, fontWeight: "600", }), Plot.sphere({stroke: "#c0c0c0"}) ], })33:T60b,
## Magnetic Declination Angle The Earth's magnetic field is generated by various sources, primarily molten iron in the Earth's outer core. At every point on the Earth's surface, the magnetic field has a well-defined direction. A magnetic compass needle aligns with this direction but does not necessarily point toward true north. The angular difference between true north and the magnetic field direction is known as **magnetic declination**. By convention, areas shaded in blue indicate negative declination, meaning compass needles point westward of true north. In contrast, red regions indicate positive declination, where the compass points eastward of true north. On the green dashed contour, the compass aligns with true north. Our understanding of changes in the magnetic field is limited, making future predictions challenging. Consequently, the IGRF model maintained by the IAGA needs regular updates. Notably, since around the year 2000, these changes have accelerated rapidly. Some scientists suggest we may be in the early stages of a pole reversal, a phenomenon in which the magnetic north and south poles switch places. 34:T870,md`
## Source Data The data were obtained using the Python package PyIGRF (IGRF-13 model). A script was utilized to extract only the magnetic declination for a specific year, and the distance was set to *R = ${R} km* (Earth's mean radius). The resulting CSV files (see ᥫ files pane) contain comma-separated values representing the magnetic declination, starting with the value ${tex`D_{0,0}`}, corresponding to Latitude -90° and Longitude -180° (as shown in the table below). The grid was filled by acquiring data in 1° increments, resulting in a total of 180 rows × 360 columns = 64'800 values per CSV file. | Lat. \\ Long. | -180° | -179° | ... | +178° | +179° | | :-----------: | :----------------: | :----------------: | :----------------: | :-------------------:| :------------------: | | **-90°** | ${tex`D_{0,0}`} | ${tex`D_{0,1}`} | ... | ${tex`D_{0,358}`} | ${tex`D_{0,359}`} | | **-89°** | ${tex`D_{1,0}`} | ${tex`D_{1,1}`} | ... | ${tex`D_{1,358}`} | ${tex`D_{1,359}`} | | ... | ... | ... | ... | ... | ... | | **88°** | ${tex`D_{178,0}`} | ${tex`D_{178,1}`} | ... | ${tex`D_{178,358}`} | ${tex`D_{178,359}`} | | **89°** | ${tex`D_{179,0}`} | ${tex`D_{179,1}`} | ... | ${tex`D_{179,358}`} | ${tex`D_{179,359}`} | To visualize these data as **contour** plots on a map, one can simply use an **Observable Plot** (refer to the forked notebook). In the Obervable plot displayed above, note that the *y*‑axis for the contour is configured with limits set at y1 = -90 and y2 = 90. `35:T764,projections = [ {name: "Aitoff", value: d3.geoAitoff(), marginTop: 0, height_factor_1: 2, height_factor_2: 2, text_Dx: 0}, {name: "August", value: d3.geoAugust(), marginTop: 10, height_factor_1: 1.9, height_factor_2: 2, text_Dx: -20}, {name: "Azimuthal equal-area", value: d3.geoAzimuthalEqualArea(), marginTop: 0, height_factor_1: 1.9, height_factor_2: 2, text_Dx: 50}, {name: "Bertin’s 1953", value: d3.geoBertin1953(), marginTop: 0, height_factor_1: 1.9, height_factor_2: 2, text_Dx: 30}, {name: "Bonne", value: d3.geoBonne(), marginTop: 0, height_factor_1: 1.9, height_factor_2: 2, text_Dx: 50}, {name: "Eisenlohr conformal", value: d3.geoEisenlohr(), marginTop: 10, height_factor_1: 1.9, height_factor_2: 2, text_Dx: -20}, {name: "Eckert V", value: d3.geoEckert5(), marginTop: 0, height_factor_1: 2, height_factor_2: 2, text_Dx: 0}, {name: "Flat-polar sinusoidal", value: d3.geoMtFlatPolarSinusoidal(), marginTop: 0, height_factor_1: 2, height_factor_2: 2, text_Dx: 0}, {name: "Ginzburg V", value: d3.geoGinzburg5(), marginTop: 0, height_factor_1: 1.9, height_factor_2: 2, text_Dx: 0}, {name: "Gringorten quincuncial", value: d3.geoGringortenQuincuncial(), marginTop: 0, height_factor_1: 1.8, height_factor_2: 2, text_Dx: -10}, {name: "Lagrange conformal", value: d3.geoLagrange(), marginTop: 0, height_factor_1: 2, height_factor_2: 2, text_Dx: 10}, {name: "Mercator", value: d3.geoMercator(), marginTop: 10, height_factor_1: 1.25, height_factor_2: 1.6, text_Dx: 0}, {name: "Peirce quincuncial", value: d3.geoPeirceQuincuncial(), marginTop: 0, height_factor_1: 1.8, height_factor_2: 2, text_Dx: -10}, {name: "Transverse Mercator", value: d3.geoTransverseMercator(), marginTop: 0, height_factor_1: 0.8, height_factor_2: 2.4, text_Dx: 30}, {name: "Wiechel", value: d3.geoWiechel(), marginTop: 0, height_factor_1: 1.9, height_factor_2: 2, text_Dx: -45}, ]36:T764,fileMap = [ { year: 2025, file: FileAttachment("IGRF-13_declination_2025.csv") }, { year: 2020, file: FileAttachment("IGRF-13_declination_2020.csv") }, { year: 2015, file: FileAttachment("IGRF-13_declination_2015.csv") }, { year: 2010, file: FileAttachment("IGRF-13_declination_2010.csv") }, { year: 2005, file: FileAttachment("IGRF-13_declination_2005.csv") }, { year: 2000, file: FileAttachment("IGRF-13_declination_2000.csv") }, { year: 1995, file: FileAttachment("IGRF-13_declination_1995.csv") }, { year: 1990, file: FileAttachment("IGRF-13_declination_1990.csv") }, { year: 1985, file: FileAttachment("IGRF-13_declination_1985.csv") }, { year: 1980, file: FileAttachment("IGRF-13_declination_1980.csv") }, { year: 1975, file: FileAttachment("IGRF-13_declination_1975.csv") }, { year: 1970, file: FileAttachment("IGRF-13_declination_1970.csv") }, { year: 1965, file: FileAttachment("IGRF-13_declination_1965.csv") }, { year: 1960, file: FileAttachment("IGRF-13_declination_1960.csv") }, { year: 1955, file: FileAttachment("IGRF-13_declination_1955.csv") }, { year: 1950, file: FileAttachment("IGRF-13_declination_1950.csv") }, { year: 1945, file: FileAttachment("IGRF-13_declination_1945.csv") }, { year: 1940, file: FileAttachment("IGRF-13_declination_1940@1.csv") }, { year: 1935, file: FileAttachment("IGRF-13_declination_1935.csv") }, { year: 1930, file: FileAttachment("IGRF-13_declination_1930.csv") }, { year: 1925, file: FileAttachment("IGRF-13_declination_1925.csv") }, { year: 1920, file: FileAttachment("IGRF-13_declination_1920.csv") }, { year: 1915, file: FileAttachment("IGRF-13_declination_1915.csv") }, { year: 1910, file: FileAttachment("IGRF-13_declination_1910.csv") }, { year: 1905, file: FileAttachment("IGRF-13_declination_1905.csv") }, { year: 1900, file: FileAttachment("IGRF-13_declination_1900.csv") }, ];37:Ta6a,// https://observablehq.com/@mbostock/scrubber function Scrubber(values, { format = value => value, initial = 0, direction = 1, delay = null, autoplay = true, loop = true, loopDelay = null, alternate = false } = {}) { values = Array.from(values); const form = html``; let frame = null; let timer = null; let interval = null; function start() { form.b.textContent = "Pause"; if (delay === null) frame = requestAnimationFrame(tick); else interval = setInterval(tick, delay); } function stop() { form.b.textContent = "Play"; if (frame !== null) cancelAnimationFrame(frame), frame = null; if (timer !== null) clearTimeout(timer), timer = null; if (interval !== null) clearInterval(interval), interval = null; } function running() { return frame !== null || timer !== null || interval !== null; } function tick() { if (form.i.valueAsNumber === (direction > 0 ? values.length - 1 : direction < 0 ? 0 : NaN)) { if (!loop) return stop(); if (alternate) direction = -direction; if (loopDelay !== null) { if (frame !== null) cancelAnimationFrame(frame), frame = null; if (interval !== null) clearInterval(interval), interval = null; timer = setTimeout(() => (step(), start()), loopDelay); return; } } if (delay === null) frame = requestAnimationFrame(tick); step(); } function step() { form.i.valueAsNumber = (form.i.valueAsNumber + direction + values.length) % values.length; form.i.dispatchEvent(new CustomEvent("input", {bubbles: true})); } form.i.oninput = event => { if (event && event.isTrusted && running()) stop(); form.value = values[form.i.valueAsNumber]; form.o.value = format(form.value, form.i.valueAsNumber, values); }; form.b.onclick = () => { if (running()) return stop(); direction = alternate && form.i.valueAsNumber === values.length - 1 ? -1 : 1; form.i.valueAsNumber = (form.i.valueAsNumber + direction) % values.length; form.i.dispatchEvent(new CustomEvent("input", {bubbles: true})); start(); }; form.i.oninput(); if (autoplay) start(); else stop(); Inputs.disposal(form).then(stop); return form; 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30:{"id":"b32cb85ab0eb827b","slug":"igrf-13-magnetic-field-declination","title":"🧭 Earthʼs Magnetic Field Declination","thumbnail":"474a90525a18a85aa6f1cf9a10a723875f170f252e4e5c868b69ea94a0139653","access_level":"public","create_time":"$D2024-09-23T10:06:35.713Z","update_time":"$D2026-09-05T14:40:04.674Z","view_time":null,"first_public_time":"$D2024-09-23T20:08:54.957Z","fork":{"id":"2aba1ff1101ae1a6","slug":"plot-contours-projection","title":"Plot: Contours & projection","owner":{"id":"f35c755083683fe5","login":"observablehq","name":"Observable"}},"stars":1,"starred":false,"owner":{"type":"team","id":"dd67891d326bcfb1","login":"christophe-yamahata","name":"Christophe 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level.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":338,"value":"viewof Year = Scrubber(years, { initial: years.length-1, loop: false, alternate: true, autoplay: false, delay: 300, format: d => `Year ${d.toFixed(0)}`})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":889,"value":"viewof selected_projection = Inputs.select(projections, {\n label: \"Select a projection\",\n format: d => d.name,\n value: projections.find(p => p.name === \"Aitoff\")\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1069,"value":"viewof blur = Inputs.range([0, 6], {value: 1.5, step: 0.5, label: \"Blur level\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":3,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":754,"value":"DOM.download(() => serialize(IGRF_magnetic_declination), \"IGRF-13_Earth_magnetic_declination_\"+Year, \"Save as SVG\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":483,"value":"$33","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":504,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":761,"value":"---","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":763,"value":"viewof display_inspect = Inputs.toggle({label: \"⇣ Check to inspect variables and functions used in this notebook\", values: [\"true\", \"none\"], value: \"none\" })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":286,"value":"\n
\n${display_inspect == \"none\"? html`

⇣ Appendix is hidden ...

` : html`

Appendix

`}","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined"},{"id":261,"value":"width = 1000","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":508,"value":"R = 6371","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":74,"value":"world = FileAttachment(\"land-50m.json\").json()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":76,"value":"land = topojson.feature(world, world.objects.land)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":891,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":294,"value":"years = [1900,1905,1910,1915,1920,1925,1930,1935,1940,1945,1950,1955,1960,1965,1970,1975,1980,1985,1990,1995,2000,2005,2010,2015,2020,2025]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":309,"value":"$36","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":323,"value":"fileInfo = fileMap.find(d => d.year === Year);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":8,"value":"data = fileInfo.file.csv({ array: true }).then(rows => \n rows.flat().map(x => parseFloat(x))\n);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":119,"value":"d3 = require(\"d3@7\", \"d3-geo-projection@4\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":341,"value":"$37","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":751,"value":"// https://observablehq.com/@mbostock/saving-svg\nserialize = {\n const xmlns = \"http://www.w3.org/2000/xmlns/\";\n const xlinkns = \"http://www.w3.org/1999/xlink\";\n const svgns = \"http://www.w3.org/2000/svg\";\n return function serialize(svg) {\n svg = svg.cloneNode(true);\n const fragment = window.location.href + \"#\";\n const walker = document.createTreeWalker(svg, NodeFilter.SHOW_ELEMENT);\n while (walker.nextNode()) {\n for (const attr of walker.currentNode.attributes) {\n if (attr.value.includes(fragment)) {\n attr.value = attr.value.replace(fragment, \"#\");\n }\n }\n }\n svg.setAttributeNS(xmlns, \"xmlns\", svgns);\n svg.setAttributeNS(xmlns, \"xmlns:xlink\", xlinkns);\n const serializer = new window.XMLSerializer;\n const string = serializer.serializeToString(svg);\n return new Blob([string], {type: \"image/svg+xml\"});\n };\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W38","stdlib":"1","titling":"auto"}} 31:"$30:body"