validation.md

Validation

The heat1d model is validated against lunar temperature data from Hayne et al. (2017), Table A2, using constraints from Diviner observations and Apollo heat flow experiments.

Validation Constraints

The following constraints are used (Table A2 of Hayne et al., 2017):

Equatorial temperatures (latitude = 0, highland albedo $A_0$ = 0.12):

Constraint	Value (K)	Tolerance
Peak noon temperature	385	±5
Midnight temperature	101	±5
Minimum nighttime temperature	95	±5

Apollo site mean temperatures (mare albedo $A_0$ = 0.06):

Constraint	Latitude	Value (K)	Tolerance
Apollo 15 surface mean T	26°N	211	±5
Apollo 15 subsurface (0.83 m) mean T	26°N	252	±5
Apollo 17 surface mean T	20°N	216	±5
Apollo 17 subsurface (0.13 m) mean T	20°N	256	±5

Mare vs. Highland Albedo

The equator checks use the default Moon highland normal bolometric Bond albedo ($A_0$ = 0.12). The Apollo landing sites are in dark mare regions with significantly lower albedo. Following Hayne et al. (2017), which reports $A_0$ = 0.12 for highland and $A_0$ = 0.07 for mare, the Apollo checks use a mare albedo of $A_0$ = 0.06 appropriate for the particularly dark basaltic floors at Hadley Rille (Apollo 15) and Taurus-Littrow (Apollo 17).

Density/Conductivity Scale Depth

The validation suite uses the Hayne et al. (2017) Table A1 standard value for the density and conductivity e-folding scale depth (H = 0.06 m), overriding the planets package default of H = 0.07 m. This improves the fit to Diviner nighttime cooling observations at all latitudes (RMS residual drops from ~1 K to ~0.3 K).

Energy Conservation

In addition to temperature comparisons, the validation suite checks energy conservation by computing the stored energy change over one diurnal cycle. For a well-equilibrated model, the relative energy imbalance should be < 1%.

Running the Validation Suite

From the command line:

heat1d --validate

Or from Python:

from heat1d.validation import run_validation_suite
results = run_validation_suite(solver="explicit", nyearseq=5)

Validation Plots

The validation suite generates four diagnostic plots, shown below using the Fourier-matrix solver with Hayne et al. (2017) standard parameters.

Diurnal Equator Curve

Surface temperature vs. local time at the equator, with Table A2 reference values and tolerance bands marked. The model closely matches the peak noon temperature (385 K), midnight temperature (101 K), and minimum nighttime temperature (95 K).

Multi-Latitude Diurnal Curves

Surface temperature at 0, 15, 30, 45, 60, and 75 degrees latitude. Peak daytime temperatures decrease with latitude due to lower solar incidence angles, while nighttime temperatures converge as all surfaces radiate to the same cold sky.

Nighttime Cooling Curves

Surface temperature during the lunar night at multiple latitudes, overlaid with Diviner Lunar Radiometer regolith temperature observations; note that these represent the rock-free regolith temperature (Bandfield et al., 2011). The model reproduces the observed nighttime cooling behavior across all available latitudes (similar to Figure A2 of Hayne et al., 2017).

Mean Temperature vs. Latitude

Diurnal mean surface and subsurface temperature vs. latitude using mare albedo, with Apollo 15 and 17 heat flow experiment data shown as points with error bars. Surface measurements (squares) and subsurface measurements at 0.13 m and 0.83 m depth (triangles) all fall within the published uncertainties.

Validation Results

With the Hayne et al. (2017) Table A1 standard properties (highland albedo for equator, mare albedo for Apollo sites, H = 0.06 m), all 8 validation checks pass. The Apollo checks use a finer grid (m=20, b=30) and longer equilibration (25 orbits) to ensure the 0.83 m subsurface temperature is well converged:

[PASS] equator_peak_noon_T: 388.5 K (ref: 385.0 +/- 5.0 K)
[PASS] equator_midnight_T: 100.2 K (ref: 101.0 +/- 5.0 K)
[PASS] equator_min_night_T: 93.7 K (ref: 95.0 +/- 5.0 K)
[PASS] energy_conservation: relative error = 0.0000
[PASS] apollo15_surface_mean_T: 209.1 K (ref: 211.0 +/- 5.0 K)
[PASS] apollo15_subsurface_mean_T: 252.9 K (ref: 252.0 +/- 5.0 K)
[PASS] apollo17_surface_mean_T: 211.7 K (ref: 216.0 +/- 5.0 K)
[PASS] apollo17_subsurface_mean_T: 255.4 K (ref: 256.0 +/- 5.0 K)
8/8 checks passed

Regenerating Plots

To regenerate the validation plots for the documentation:

python docs/generate_validation_plots.py

This produces four PNG files in docs/images/ using the Fourier-matrix solver (fastest). The full validation suite (heat1d --validate) generates additional comparison plots across all four solvers.

References

Bandfield, J. L., Ghent, R. R., Vasavada, A. R., Paige, D. A., Lawrence, S. J., & Robinson, M. S. (2011). Lunar surface rock abundance and regolith fines temperatures derived from LRO Diviner Radiometer data. Journal of Geophysical Research: Planets, 116(E12). https://doi.org/10.1029/2011JE003866