Analytical Models
Terranoetis ships 150 scientific equation engines organized across 7 parts and 26 domains. Every model is grounded in primary literature and math-verified against its source — no machine learning, no black boxes. Each of the 150 catalog entries carries a full citation: 80 reference strings contain a DOI, 12 cite books by ISBN, 4 are explicitly flagged NO-DOI, and the remainder are pre-DOI classics, government/standards documents, or conference papers (counts produced by programmatic scan of src/data/analyticalModels.ts). Spot-checked DOI resolvability: doi.org/10.1785/0120130065 → HTTP 302.
Verified site view (counts, workflow, measured sample computations): Analytical equation engine.
Table of Contents
Architecture
Before execution, the context engine (contextEngine.ts) enriches inputs from live data feeds (weather, terrain, ocean, seismic, air quality, satellite thermal). Each tool then runs through the 7-stage workflow defined in toolWorkflows.ts:
- Input validation — range, type, and physical-plausibility checks
- Preprocessing — unit conversion, derived-parameter computation
- Computation — the source equation (
engine.ts) - Post-processing — classification, unit normalisation
- Quality control — result sanity checks, outlier detection
- Uncertainty estimation — error propagation / empirical RMSE
- Interpretation — contextual analysis + scientific recommendations
Visualization Types
Each tool declares a vizType; the client renders it via Recharts (charts) or Cesium (field surfaces):
| Type | Description |
|---|---|
| scalar | Single computed value with unit + interpretation |
| timeseries / bar / histogram / scatter / distribution / gauge / profile / spectrum | Recharts visualizations |
| heatmap / contour / vector | Field surfaces over the study area (Cesium) — direct per-cell equation sweeps, or IDW interpolation for point-sampled surfaces |
| (derived) | Structured grids feed downstream GIS fusion; PDF "report" export (charts + methodology) is a client-side composition of any tool's result, not a declared vizType |
Parts & Domains
Part I — Earth System Core (Tools 1–50) · 6 Domains
| Domain | Tools | Topics |
|---|---|---|
| Atmospheric Science | 1–8 | Land surface temperature, brightness temperature, saturation vapor pressure, atmospheric pressure profile, geostrophic wind, pollutant transport, atmospheric stability, turbulent energy spectrum |
| Hydrology & Oceanography | 9–18 | Evapotranspiration, runoff (SCS-CN), open channel flow, peak discharge, flood wave routing, tide prediction, wind-driven current, ocean current, marine heat budget, infiltration |
| Geophysics & Seismology | 19–25 | Earthquake frequency (Gutenberg-Richter), aftershock decay (Omori), ground motion prediction (GMPE), shear strength, moment magnitude, stress drop, fault rupture scaling |
| Remote Sensing & Cryosphere | 26–35 | Vegetation health index, surface water detection, vegetation water content, enhanced vegetation index, snow cover, burn severity (NBR), fire radiative power, crop water stress, snowmelt runoff, sea ice analysis |
| Spatial Analysis & Extreme Events | 36–42 | Great circle distance, kriging, IDW interpolation, Gaussian plume dispersion, Gumbel extreme value analysis, Pareto peaks-over-threshold, semivariogram analysis |
| Soil Science & Land Surface | 43–50 | Soil water retention (van Genuchten), soil hydraulic model, universal soil loss equation (USLE), soil respiration (Q₁₀), soil thermal conductivity, surface layer stability (Monin-Obukhov), logarithmic wind profile, stomatal conductance |
Part II — Biosphere, Agriculture & Chemistry (Tools 51–65) · 3 Domains
| Domain | Tools | Topics |
|---|---|---|
| Biosphere & Carbon Cycle | 51–57 | Gross primary production (LUE model), canopy light extinction (Beer-Lambert), net carbon flux, C3 photosynthesis (Farquhar), forest biomass estimation, ocean CO₂ uptake, ocean nutrient ratios |
| Agriculture & Crop Science | 58–63 | Growing degree days, Priestley-Taylor evapotranspiration, Hargreaves-Samani ET, FAO yield-water response, phytoplankton temperature growth, Bigleaf Penman-Monteith |
| Atmospheric Chemistry & Aerosols | 64–65 | Stratospheric ozone equilibrium, pollutant lifetime estimation |
Part III — Ocean & Coastal Advanced (Tools 66–80) · 2 Domains
| Domain | Tools | Topics |
|---|---|---|
| Ocean Dynamics & Circulation | 66–73 | Wind-driven ocean transport, westward-intensified gyre flow (Stommel), western boundary current structure, thermohaline flow, seawater density (TEOS-10), ocean mixing diffusivity, mixed layer deepening, fully developed sea state |
| Coastal & Wave Mechanics | 74–80 | Coastal wave runup, shoreline retreat (Bruun Rule), breaking wave height (McCowan), longshore sediment transport (CERC), wave dispersion (Airy), Stokes drift, JONSWAP wave spectrum |
Part IV — Geomorphology, Limnology & Cryosphere (Tools 81–95) · 3 Domains
| Domain | Tools | Topics |
|---|---|---|
| Geomorphology & Mass Wasting | 81–87 | Erosion from stream power, river network scaling (Hack's law), fractal coastline dimension, slope stability (infinite slope), avalanche runout distance, stream power index, topographic wetness index |
| Limnology & Freshwater | 88–90 | Lake evaporation, lake thermal stability, unit hydrograph (linear reservoir) |
| Cryosphere Advanced & Volcanology | 91–95 | Glacier ablation (temperature-index), permafrost active layer depth (Stefan), firn densification, eruption volume from VEI, volcanic plume rise height |
Part V — Climate & Atmosphere Advanced (Tools 96–110) · 3 Domains
| Domain | Tools | Topics |
|---|---|---|
| Climate Dynamics & Feedback | 96–101 | Global energy balance model, equilibrium climate sensitivity, Planck feedback parameter, Rossby wave phase speed, baroclinic instability condition, baroclinic growth rate (Eady) |
| Atmospheric Dynamics & Turbulence | 102–107 | Quasi-geostrophic potential vorticity, turbulent velocity field decomposition (Reynolds), Ekman layer depth, convective velocity scale (Deardorff), frontogenesis rate, vorticity tendency |
| Cloud Physics & Precipitation | 108–110 | Equilibrium saturation over droplet (Köhler), drop size distribution, radar reflectivity → rain rate (Z-R) |
Part VI — Space Environment & Satellite (Tools 111–130) · 4 Domains
| Domain | Tools | Topics |
|---|---|---|
| Geodesy & Reference Frames | 111–115 | Earth rotation matrix (IAU-2006), solid earth tide displacement, geopotential from spherical harmonics, 7-parameter Helmert transform, orthometric height from GPS |
| Thermosphere, Ionosphere & Magnetosphere | 116–122 | Thermospheric density profile (NRLMSISE-00), ionospheric electron density (IRI-2016), Joule heating rate, scintillation index S4, magnetopause standoff distance, pressure-corrected Dst, plasma Debye length |
| Satellite Dynamics & Space Debris | 123–127 | Satellite drag acceleration, orbital decay from drag, conjunction collision probability, Kessler debris cascade, relative orbit motion (Clohessy-Wiltshire) |
| Solar-Terrestrial & GNSS | 128–130 | Kp geomagnetic index, GNSS dilution of precision (DOP), tropospheric delay for GNSS |
Part VII — Advanced Engineering & Risk (Tools 131–150) · 5 Domains
| Domain | Tools | Topics |
|---|---|---|
| Groundwater & Subsurface | 131–134 | Steady-state well discharge (Thiem), transient well drawdown (Theis), straight-line well test (Jacob), infiltration capacity over time (Horton) |
| Hazard, Risk & Disaster Engineering | 135–140 | Disaster risk index, expected annual flood damage, air quality index, probable maximum precipitation (PMP), Palmer drought severity index (PDSI), dam breach parameters |
| Data Assimilation & State Estimation | 141–144 | Ensemble Kalman filter (EnKF), optimal interpolation, 4D-Var assimilation cost, Shannon information entropy |
| Signal Processing & Communications | 145–147 | Free-space RF path loss (Friis), ionospheric delay (Klobuchar), frequency shift from relative velocity (Doppler) |
| Mathematical Frameworks | 148–150 | Hohmann transfer Δv, Lagrange point positions, mutual information between variables |
Key Features
- 150 non-ML equations — every model is derived from a peer-reviewed paper, textbook, or authoritative standard
- 26 domains — atmospheric, oceanic, seismic, cryospheric, space, and beyond
- 7-part structure — logically grouped from Earth system core to advanced engineering
- 7-stage workflow — input validation → preprocessing → computation → post-processing → quality control → uncertainty estimation → interpretation
- Real-data context — every model receives live context (weather, terrain, ocean, seismic) from 30+ data feeds
- Literature-indexed — 80 models carry a DOI in their citation (12 ISBN, 4 explicit NO-DOI; remainder pre-DOI/standards)
7-Stage Workflow
Defined in server/analytical-models/toolWorkflows.ts (preceded by live-data context enrichment in contextEngine.ts):
| Stage | Description |
|---|---|
| 1. Input validation | Range, type, and physical-plausibility checks |
| 2. Preprocessing | Unit conversion, derived-parameter computation |
| 3. Computation | The source equation (engine.ts) |
| 4. Post-processing | Classification, unit normalisation |
| 5. Quality control | Result sanity checks, outlier detection |
| 6. Uncertainty estimation | Error propagation / empirical RMSE |
| 7. Interpretation | Contextual analysis + scientific recommendations |