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ArtemisThermalBase — Assumptions & Limitations

Academic Transparency Document

This document explicitly states every assumption, simplification, and known limitation of the ArtemisThermalBase thermal simulation engine. Scientific credibility requires honest disclosure of what the model can and cannot do.

1. Registered Model Assumptions

The following 10 assumptions are programmatically registered in core_engine/constants.py and logged at the start of every simulation run.

# Parameter Value Source Uncertainty
1 Bond Albedo 0.12 Vasavada et al., 2012 ±0.03
2 Thermal Emissivity 0.95 Bandfield et al., 2015 ±0.02
3 Geothermal Flux 0.018 W/m² Langseth et al., 1976 (Apollo 15/17) ±50%
4 Surface Density 1100 kg/m³ Hayne et al., 2017 ±200 kg/m³
5 Deep Density 1800 kg/m³ Hayne et al., 2017 ±200 kg/m³
6 Surface k_contact 7.4×10⁻⁴ W/m/K Hayne et al., 2017 ±50%
7 Reflectance Model Lambertian User requirement N/A
8 No Dust Levitation Excluded User requirement N/A
9 No Sub-pixel Roughness Excluded User requirement N/A
10 Spatially Uniform Regolith Depth-dependent only Simplification Unknown

2. Known Limitations

2.1 No Multi-Bounce IR Scattering

Impact: HIGH — PSR temperatures may be underestimated by ~10–20 K

The current model computes only direct solar illumination and does not include infrared thermal radiation exchange between terrain facets. In deep craters like Shackleton, sunlit rim surfaces emit thermal IR that illuminates/warms the permanently shadowed floor. Without this term, cold trap temperatures are biased low.

This is a planned Milestone 4 feature requiring view-factor computation between all $N^2$ face pairs.

2.2 No Temperature-Dependent Albedo

Impact: LOW–MEDIUM

The Bond albedo is treated as spatially and thermally uniform (A = 0.12). In reality, albedo varies with:

  • Composition (highlands vs. mare)
  • Solar incidence angle (opposition surge)
  • Temperature (minor effect)

A future Hapke reflectance model would address direction-dependent effects (Milestone 5).

2.3 1D Heat Flow Assumption (Lateral Conduction Ignored)

Impact: LOW for most surfaces; MEDIUM at sharp shadow boundaries

Each DEM facet is treated as an independent 1D thermal column with no lateral heat conduction. This is valid when:

$$ L_{\text{face}} \gg d_{\text{skin}} \approx \sqrt{\frac{k P}{\pi \rho c_p}} $$

For typical regolith properties and a 29.5-day lunar period, $d_{\text{skin}} \approx 0.3$ m. At 20 m/px DEM resolution, each face is ~20 m wide, so $L/d \approx 67$ — lateral conduction is negligible.

Exception: At sharp PSR boundaries where temperature gradients exceed ~100 K/m, 3D effects may become significant.

2.4 Equatorial Geothermal Flux Applied to Polar Region

Impact: MEDIUM for deep temperatures

The geothermal heat flux (0.018 W/m²) was measured at the Apollo 15 and 17 equatorial landing sites. Polar regions may have different internal heat distribution due to:

  • Crustal thickness variations
  • Tidal heating anisotropy
  • Compositional differences

The ±50% uncertainty partially accounts for this.

2.5 No Dust Levitation or Electrostatic Transport

Impact: LOW

Electrostatically charged dust particles can be lofted from the surface at the terminator (Day/night boundary) due to photoelectric charging. This may affect local albedo and surface thermal properties. The effect is excluded as it requires particle transport modeling.

2.6 No Sub-pixel Roughness

Impact: MEDIUM for thermal emission models

Surface roughness at scales smaller than the DEM resolution (< 20 m) affects:

  • Thermal inradiance at grazing solar angles
  • Effective emissivity (cavity effect)
  • Shadow fraction near the terminator

Roughness could be parameterized using a Gaussian surface model (Bandfield et al., 2015).

2.7 Spatially Uniform Regolith

Impact: MEDIUM

Regolith properties (k, ρ, cₚ) vary only with depth, not laterally. In reality:

  • Highland regolith differs from mare regolith
  • Rocky ejecta near craters has different thermal inertia
  • PSR regolith may contain water ice (higher thermal conductivity)

2.8 No Orbital Eccentricity / Distance Correction

Impact: LOW

The solar constant is fixed at 1361 W/m² (1 AU). Earth-Moon distance variation (~±1.7%) causes ~±3.4% flux variation throughout the year. This is currently not modeled.

2.9 No Atmospheric Effects

Impact: NONE

The Moon has no significant atmosphere. This is correctly handled — no atmospheric scattering, absorption, or convection is included.

2.10 No Spacecraft/Instrument Self-Heating

Impact: N/A

The simulation models the natural thermal environment only. Spacecraft thermal interactions are out of scope for this version.

3. Numerical Approximations

Approximation Details Error Bound
Crank-Nicolson temporal discretization $O(\Delta t^2)$ < 0.1 K at dt = 120 s
Non-uniform FD spatial discretization $O(\Delta z^2)$ < 0.05 K with geometric grid
Newton linearization of $T^4$ Converges in 2–4 iterations $10^{-4}$ K tolerance
Fibonacci disk sampling (64 points) ~1.5% noise at shadow edges < 0.02 illumination fraction
Harmonic mean for interface conductivity Exact for piecewise-constant k N/A (exact)
Thomas algorithm (TDMA) Exact for tridiagonal systems Machine precision

4. Validation Status

Against Status Reference
LRO Diviner surface temperatures Planned (Milestone 5) Paige et al. (2010)
Analytical solutions (flat surface) Partial — initial testing Spencer et al. (1989)
Energy conservation (internal check) ✅ Implemented compute_internal_energy()

5. Improvement Roadmap

Milestone Feature Impact on Accuracy
3 C++ BVH raytracer (pybind11) Performance only (no accuracy change)
4 Multi-bounce IR view factors +10–20 K in PSRs
5 Diviner validation + Hapke reflectance Quantified error bars
Future 3D heat conduction ±1–3 K at shadow boundaries
Future Orbital eccentricity correction ±3% flux
Future Water ice thermal properties Critical for volatile stability