Developing an Integrative Astronomy, Geography, Oceanography and Meteorology Research and Application Platform

Posted on 2026-10-22 In Research Views: Disqus: Word count in article: 3.4k Reading time ≈ 12 mins.

A long-term platform for learning, using and researching astronomy, geography, oceanography and meteorology as one connected body of knowledge, with geometry, mathematics and physics as the shared foundation. Its first two applications, the Earth Atlas and the Celestial Atlas, already work. This post introduces the project and shows their gallery.

Source code: Integrative Astronomy, Geography, Oceanography Laboratory on GitHub (MIT License).

Abstract

English. This project studies astronomy, geography, oceanography and meteorology as one connected body of knowledge, in theory and in practice. Geometry, mathematics and physics form their shared foundation. The fields share spherical geometry, coordinate systems, the rotation group, potential theory, harmonic analysis and the dynamics of rotating, stratified fluids. They meet in concrete phenomena: tides, navigation, the figure and mapping of the Earth, the coupled exchange between ocean and atmosphere, and the astronomical forcing of climate. New ideas will keep emerging and evolving, so the project is designed throughout to be modular, extensible and revisable.

中文. 本项目是一个长期的综合计划，以几何学、数学与物理学为共同基础，把天文学、地理学、海洋学与气象学作为一个相互联系的知识整体，从理论与实践两方面加以学习、应用和研究。这些领域共享球面几何、坐标系、旋转群、位势理论、调和分析以及旋转层结流体动力学，并在潮汐、导航、地球的形状与测绘、海洋与大气的耦合交换以及气候的天文强迫等现象中交汇。由于新的想法会不断涌现和演化，本项目以模块化、可扩展、可修订为总体设计原则。

日本語. 本プロジェクトは、幾何学・数学・物理学を共通の基盤として、天文学・地理学・海洋学・気象学を一つのつながった知識体系として、理論と実践の両面から学び、使い、研究するための長期的な総合プログラムである。これらの分野は球面幾何学、座標系、回転群、ポテンシャル論、調和解析、回転成層流体の力学を共有し、潮汐、航法、地球の形状と地図化、海洋と大気の結合した交換、気候の天文学的強制といった現象において交わる。新しい着想が絶えず生まれ発展していくことを前提に、モジュール性・拡張性・改訂可能性を全体の設計原則とする。

Why One Platform

These subjects are usually taught apart, yet shared structure binds them together.

Spheres and rotations. The celestial sphere, the figure of the Earth, and the ocean and atmosphere (thin fluid shells on a rotating sphere) are all described by the geometry of the sphere. Changes of reference frame are elements of SO(3), and fields on the sphere expand in spherical harmonics.
Tides join astronomy to oceanography. The Moon and the Sun set up a tide-generating potential, and the ocean responds to it. Each tidal constituent oscillates at an integer combination of six fundamental astronomical frequencies (Doodson’s expansion).
Navigation joins astronomy to geography. A position at sea is fixed from star sights by solving a spherical triangle, with an almanac computed by positional astronomy.
Ocean and atmosphere form one coupled fluid system. Both obey the equations of rotating, stratified flow and exchange momentum, heat, freshwater and gases at the sea surface. ENSO and the monsoons exist only in the coupled system.
Astronomy sets the sunlight. It decides how sunlight is distributed over the Earth, and how that distribution changes slowly over millennia (the Milankovitch cycles).
Geography maps the surface where all of these meet, resting on geodesy and map projections.

How It Is Built

The project spans four repositories. The laboratory composes three independent C++ libraries, and its dependencies point only downward:

Edges        applications · visualization · observation · data
                    │
core/        inference · domains · metrology            (the laboratory's own library)
                    │
lib/         physis ──► calx
                └─────► morphe                          (calx and morphe are independent)

Library	Scope
calx	A retargetable computation stack with numerical methods. A computation is written once and runs on the CPU (the reference backend) and on any device with a backend.
morphe	Mathematical structures and their equivalences: exact arithmetic, algebra, category theory, topology, algebraic geometry and formal structures.
physis	Geometry and theoretical physics: units, differential geometry, structure-preserving discretisation, mechanics, gravitation, thermodynamics, geophysical fluid dynamics, chemistry and radiation.

Five principles guide the construction:

Modularity. Libraries and core are pure computation; data, instruments and interfaces sit at the edges.
Extensibility. A new field, method, device or presentation technique is added as a module, leaving existing ones intact.
Revisability. Every module carries a status (planned, seed, draft, stable, deprecated), and decisions are recorded with their alternatives.
Unity of theory and computation. Every formula cites its derivation, and every checkable result is checked by code.
Verifiability. Results are validated against references such as IAU SOFA/ERFA, JPL Horizons, the IERS Conventions and NOAA tide predictions.

Gallery

These screenshots of the two applications were taken on 22 October 2026 with the data of that day. Both are web applications without a build step. Their computations are provisional, tested against published references: 105 checks for the Earth Atlas and 61 for the Celestial Atlas. Click an image to see it at full size.

The Earth Atlas

The atmosphere, the ocean, the land and its people on one globe, or on equal-area and equirectangular maps, at one instant. Each kind of data comes from its own dataset and is joined to the map only in the application.

Weather and the Ocean

Wind at 10 m over the North Atlantic on the globe, with moving particles — **Wind at 10 m** from the GFS forecast for 22 October 2026, 12:00 UTC. Colour gives the speed, and moving particles trace the flow. Two cyclones turn in the North Atlantic.

Pressure at sea level and isobars on the Equal Earth projection — **Pressure at sea level** and isobars every 4 hPa, with highs and lows, on the equal-area Equal Earth projection. Lows near 950 hPa follow the Southern Ocean's storm track, and a typhoon of 932 hPa lies east of the Philippines.

Significant wave height over the South Atlantic, with wave energy as particles — **Waves** from WaveWatch III. Colour gives the significant wave height. Particles travel along the peak direction at the deep-water group speed, gT/4π. Swell from the Southern Ocean spreads north into the Atlantic.

Sea-surface temperature anomaly on the Equal Earth projection — **Sea-surface temperature anomaly** from NOAA's OISST v2.1, 20 October 2026. A warm tongue lies along the equator in the eastern Pacific, the pattern of El Niño.

Models Compared, and the Laboratory’s Own

AIGFS minus GFS, air temperature at 2 m — **Two models compared.** NOAA's AI model AIGFS minus the GFS, air temperature at 2 m, on a diverging scale fitted to the whole forecast. Any two models of the same quantity can be differenced this way.

The shallow-water model's 500 hPa heights after 48 hours, with its verification table — **A model of our own.** The laboratory's shallow-water model, 48 hours after starting from the GFS analysis of 19 October 2026: heights at 500 hPa, contours every 60 m, and the wind.

The laboratory’s two models run in the page by the spectral transform method at T42. Their errors, compared with persistence (the forecast that nothing changes):

Lead	Barotropic model (1950)	Shallow-water model	Persistence
+24 h	58 m	43 m	81 m
+48 h	85 m	74 m	108 m
+72 h	108 m	100 m	127 m

These are root-mean-square errors of the height of the 500 hPa surface over 20–80° N, against the GFS’s own analyses. The theory is in the notes on the barotropic model and the shallow-water model.

Climate

Mumbai's climate class and Walter–Lieth climate diagram — **A climate diagram.** Mumbai, class Am (tropical monsoon), and its normal year from TerraClimate, drawn after Walter and Lieth (1960). The dry season, from November to May, is dotted. The monsoon, above 100 mm a month from June to September, is filled.

July precipitation normal on the Equal Earth projection — **The normal July.** Precipitation in July, the normal of 1991–2020 from TerraClimate. The monsoons of South Asia and the Sahel are wet, and the Mediterranean summer is dry. Normals follow the month of the time shown.

The atlas also classifies the TerraClimate normals itself, by the rules of Beck et al. (2018). Its classes agree with the published map in 89 % of land cells. The classification is invariant under a group of order 2·(6!)⁴: permutations of the months within each half-year, and the exchange of the halves. See the theory note.

The Earth from Space, and Its Relief

The Blue Marble by day and city lights by night over Europe and Africa — **Day and night.** NASA's Blue Marble by day, and the Black Marble's city lights where the Sun has set, at 17:40 UTC. Sunset and the ends of civil, nautical and astronomical twilight are drawn as steps.

VIIRS true-colour mosaic over Africa and Europe — **The Earth from space** on 20 October 2026: the VIIRS true-colour mosaic from NASA GIBS. A gap between two orbits crosses the Sahara.

The Alps at close range with fine shaded relief — **The Alps at close range.** Shaded relief from 30 m elevations (ASTER GDEM, through NASA GIBS), fetched for the region in view. It is drawn over hypsometric tints from ETOPO 2022, with Lake Geneva on the left.

The Himalaya around Everest at close range — **The Himalaya** around Everest, at the centre of the view, in the same way. The Tibetan Plateau lies above, and the valleys descend toward the Ganges plain below.

Earthquakes and People

A month of earthquakes in the western Pacific — **Earthquakes** of magnitude 4.5 and above over a month, from the USGS. Colour gives the depth and size the magnitude. They trace the subduction zones of the western Pacific.

Population density by country on the Equal Earth projection — **People.** Population density by country, 2024, from the World Bank. It is joined to Natural Earth's countries by stated codes; the base map itself carries no values.

The Celestial Atlas

The Sun, the Moon, the planets, the stars and the galaxies, at any instant from 1849 to 2150 or live. Positions come from JPL’s DE440 ephemeris, read directly from its kernel.

The Solar System

Saturn and its rings — **Saturn** and its rings, which lie in its equatorial plane. Each body's map is turned to the instant shown by the IAU rotation models, which agree with JPL Horizons to within 0.011°.

**Jupiter**, lit by the Sun from its direction at that instant.

The Earth's night side with city lights — **The Earth at night.** The Blue Marble by day, and the Black Marble's lights where the Sun is below the horizon: the same imagery products as the Earth Atlas.

Close to the Moon and Mars, and Beyond the Sun

The Moon at close range — **The Moon** at close range. When a body fills the view, the part in view is fetched from NASA's Trek tiles (here the LRO wide-angle camera mosaic) at the screen's resolution.

Lunar craters and a rille at close range — **Closer still:** craters and a winding rille, lit by the Sun from its direction at that instant.

Mars at close range — **Mars** from the Viking MDIM 2.1 colour mosaic, turned by Mars's IAU rotation model, periodic terms included.

Stars within 20 parsecs — **The stellar neighbourhood:** 1,900 stars within 20 parsecs from HYG v4.1, at their measured distances, in galactic coordinates, against the Milky Way.

Galaxies, the Sky and the Orbits

Galaxies of the Local Volume linked to their main disturbers — **The Local Volume.** 869 galaxies of the Updated Nearby Galaxy Catalog (Karachentsev et al. 2013), in supergalactic coordinates. Each is linked to its main disturber, and the tidal groups are named. The atlas recomputes the disturbers; they agree with the published ones for 99.2 % of galaxies.

Velocity against distance for the Local Volume — **The Hubble flow** of the Local Volume: velocity against distance, coloured by tidal index, with v = H₀d for H₀ = 73 km s⁻¹ Mpc⁻¹.

Galaxies of the 2MASS Redshift Survey linked into groups — **The Local Universe.** 43,037 galaxies of the 2MASS Redshift Survey in 25,474 groups (Tully 2015), linked to their group centres. Clusters are named through SIMBAD.

Sky chart for Tokyo — **The sky** over Tokyo on the morning of 22 October 2026, drawn as a star atlas. It shows the constellations, the bright stars and the planets, with refraction applied.

The inner planets seen from the north ecliptic pole — **The orbits** of the inner planets seen from the north ecliptic pole, with the lines of sight from the Earth and each planet's elongation.

Status and Next Steps

Early working stage (22 October 2026). The architecture is designed, and the four repositories are scaffolded and published. Two applications work, and their computation is provisional JavaScript tested against published references. There is no C++ code yet. The next step is Phase 0 of the roadmap: the toolchain and the build.

New fields such as geophysics and the cryosphere may join as the work grows.

Credits

The screenshots are the laboratory’s, under its MIT licence. The data in them keep their own licences.

Data	Source	Licence
Base map	Natural Earth	Public domain
Relief	ETOPO 2022 (NOAA NCEI); ASTER GDEM (METI and NASA), shaded by NASA GIBS	Public domain; NASA, acknowledge
Forecasts and analyses	GFS and WaveWatch III (NOAA NCEP, via PacIOOS ERDDAP); AIGFS (NOAA NCEP and EPIC, via Unidata THREDDS); OISST v2.1 (NOAA NCEI)	Public domain
Climate classes	Beck et al. (2023), Scientific Data 10, 724	CC BY 4.0
Climate normals	TerraClimate (Abatzoglou et al. 2018)	CC0
Imagery of the Earth	VIIRS true colour, Blue Marble and Black Marble (NASA, via GIBS)	NASA, acknowledge
Country indicators	World Bank, World Development Indicators	CC BY 4.0
Earthquakes	USGS ComCat	Public domain
Ephemeris	JPL DE440 (Park et al. 2021)	Freely distributed
Maps of the bodies and the sky	Solar System Scope (INOVE), from NASA, JPL and ESA data	CC BY 4.0
Detail of the Moon and Mars	LRO WAC (NASA/GSFC/ASU), Viking MDIM 2.1 (NASA/USGS), via NASA Trek	NASA, acknowledge
Stars	HYG v4.1	CC BY-SA 4.0
Galaxies	Karachentsev et al. (2013); Tully (2015); names from SIMBAD (CDS)	Published catalogues; cite