Benchmarks
vSmartMOM is validated against two distinct kinds of references with very different epistemic standing. This page is regenerated by docs/build_benchmarks.jl whenever reference data, model parameters, or the RT solver itself change. Last regenerated: 2026-05-07, on Float64 + Float32 CPU.
Two kinds of references
📚 Published benchmarks — Natraj 2009 polarised Rayleigh tables and Siewert 2000 PROBLEM IIA — are theoretically-derived, high- accuracy references. The numerical procedures used to compute them are documented in the original papers and have themselves been independently cross-validated. Treat any disagreement as a vSmartMOM defect to track down.
🧪 VLIDORT 2.8.3 regression tables — solar_tester scalar (Case B, Stokes-I only) and solar_tester vector (Case C, Stokes-IQU) — are saved_results tables shipped with the VLIDORT 2.8.3 distribution. These compare two independently-implemented RT codes against each other, not against an analytic ground truth. Disagreement at the level of 10⁻³–10⁻² could be either code's numerical behavior at the chosen NSTREAMS / convergence settings; we report it for transparency, not as a correctness benchmark.
Error metric
Each row reports the modeled value, the truth value, the absolute error |Δ| = |modeled − truth|, and the relative error |Δ|/|truth|·100%. Cells where |truth| falls below a per-case near-zero threshold are reported as — for the relative error and excluded from the median/max in the summary line — at small |truth| the relative error is dominated by the absolute noise floor and is not a meaningful accuracy measure. The threshold and the number of excluded cells are stated in each summary line.
Where applicable, thresholds match the in-tree regression tests: for Natraj Q/U we use |truth| < 0.01, the same filter applied in test/test_CoreRT.jl (@test maximum(Q_deltas[Q_modeled .≥ 0.01]) < 0.008).
Case A — Siewert 2000 PROBLEM IIA
📚 published benchmark
A single-layer aerosol slab (τ = 1.0, ω̃ = 0.973527) with the PROBLEM IIA Greek phase-matrix coefficients shipped with VLIDORT 2.8.3. TOA upwelling Stokes vector at 11 viewing-zenith cosines and 3 azimuths (0°, 90°, 180°). Q/U/V truth signs flipped to vSmartMOM's Hovenier convention.
Float64
Stokes I n=33 median rel = 0.01% max rel = 0.01% median |Δ| = 6.133e-06 max |Δ| = 2.691e-05
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| vza=0.0°, az=0° | 0.0507 | 0.0507 | 2.996e-06 | 0.01% |
| vza=25.8°, az=0° | 0.0931 | 0.0931 | 5.354e-06 | 0.01% |
| vza=36.9°, az=0° | 0.1342 | 0.1342 | 8.005e-06 | 0.01% |
| vza=45.6°, az=0° | 0.1859 | 0.1859 | 1.030e-05 | 0.01% |
| vza=53.1°, az=0° | 0.2526 | 0.2526 | 1.395e-05 | 0.01% |
| vza=60.0°, az=0° | 0.3391 | 0.3391 | 1.703e-05 | 0.01% |
| vza=66.4°, az=0° | 0.4500 | 0.4500 | 2.057e-05 | 0.00% |
| vza=72.5°, az=0° | 0.5883 | 0.5883 | 2.443e-05 | 0.00% |
| vza=78.5°, az=0° | 0.7513 | 0.7513 | 2.657e-05 | 0.00% |
| vza=84.3°, az=0° | 0.9268 | 0.9268 | 2.691e-05 | 0.00% |
| vza=90.0°, az=0° | 1.0631 | 1.0631 | 2.216e-05 | 0.00% |
| vza=0.0°, az=90° | 0.0507 | 0.0507 | 2.974e-06 | 0.01% |
| vza=25.8°, az=90° | 0.0619 | 0.0619 | 3.802e-06 | 0.01% |
| vza=36.9°, az=90° | 0.0750 | 0.0750 | 4.818e-06 | 0.01% |
| vza=45.6°, az=90° | 0.0900 | 0.0900 | 5.964e-06 | 0.01% |
| vza=53.1°, az=90° | 0.1066 | 0.1066 | 6.783e-06 | 0.01% |
| vza=60.0°, az=90° | 0.1246 | 0.1246 | 8.647e-06 | 0.01% |
| vza=66.4°, az=90° | 0.1430 | 0.1430 | 1.008e-05 | 0.01% |
| vza=72.5°, az=90° | 0.1594 | 0.1594 | 1.070e-05 | 0.01% |
| vza=78.5°, az=90° | 0.1692 | 0.1692 | 1.165e-05 | 0.01% |
| vza=84.3°, az=90° | 0.1645 | 0.1645 | 1.094e-05 | 0.01% |
| vza=90.0°, az=90° | 0.1298 | 0.1298 | 9.274e-06 | 0.01% |
| vza=0.0°, az=180° | 0.0507 | 0.0507 | 2.951e-06 | 0.01% |
| vza=25.8°, az=180° | 0.0449 | 0.0449 | 2.825e-06 | 0.01% |
| vza=36.9°, az=180° | 0.0496 | 0.0496 | 3.140e-06 | 0.01% |
| vza=45.6°, az=180° | 0.0555 | 0.0555 | 3.648e-06 | 0.01% |
| vza=53.1°, az=180° | 0.0619 | 0.0619 | 4.300e-06 | 0.01% |
| vza=60.0°, az=180° | 0.0684 | 0.0684 | 4.855e-06 | 0.01% |
| vza=66.4°, az=180° | 0.0744 | 0.0744 | 5.541e-06 | 0.01% |
| vza=72.5°, az=180° | 0.0790 | 0.0790 | 5.975e-06 | 0.01% |
| vza=78.5°, az=180° | 0.0801 | 0.0802 | 6.133e-06 | 0.01% |
| vza=84.3°, az=180° | 0.0752 | 0.0752 | 5.738e-06 | 0.01% |
| vza=90.0°, az=180° | 0.0594 | 0.0594 | 4.515e-06 | 0.01% |
Stokes Q n=33 median rel = 0.01% max rel = 0.03% median |Δ| = 3.518e-07 max |Δ| = 8.066e-07
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| vza=0.0°, az=0° | 0.0026 | 0.0026 | 1.018e-07 | 0.00% |
| vza=25.8°, az=0° | 0.0062 | 0.0062 | 3.419e-07 | 0.01% |
| vza=36.9°, az=0° | 0.0092 | 0.0092 | 4.860e-07 | 0.01% |
| vza=45.6°, az=0° | 0.0135 | 0.0135 | 6.084e-07 | 0.00% |
| vza=53.1°, az=0° | 0.0198 | 0.0198 | 6.107e-07 | 0.00% |
| vza=60.0°, az=0° | 0.0282 | 0.0282 | 5.480e-07 | 0.00% |
| vza=66.4°, az=0° | 0.0388 | 0.0388 | 4.458e-07 | 0.00% |
| vza=72.5°, az=0° | 0.0509 | 0.0509 | 2.898e-07 | 0.00% |
| vza=78.5°, az=0° | 0.0639 | 0.0639 | 2.234e-07 | 0.00% |
| vza=84.3°, az=0° | 0.0764 | 0.0764 | 1.765e-07 | 0.00% |
| vza=90.0°, az=0° | 0.0868 | 0.0868 | 4.789e-07 | 0.00% |
| vza=0.0°, az=90° | -0.0026 | -0.0026 | 1.028e-07 | 0.00% |
| vza=25.8°, az=90° | -0.0028 | -0.0028 | 1.217e-07 | 0.00% |
| vza=36.9°, az=90° | -0.0031 | -0.0031 | 1.718e-07 | 0.01% |
| vza=45.6°, az=90° | -0.0036 | -0.0036 | 2.496e-07 | 0.01% |
| vza=53.1°, az=90° | -0.0043 | -0.0043 | 3.580e-07 | 0.01% |
| vza=60.0°, az=90° | -0.0051 | -0.0051 | 4.786e-07 | 0.01% |
| vza=66.4°, az=90° | -0.0060 | -0.0060 | 6.164e-07 | 0.01% |
| vza=72.5°, az=90° | -0.0067 | -0.0067 | 7.376e-07 | 0.01% |
| vza=78.5°, az=90° | -0.0070 | -0.0070 | 8.066e-07 | 0.01% |
| vza=84.3°, az=90° | -0.0062 | -0.0062 | 7.663e-07 | 0.01% |
| vza=90.0°, az=90° | -0.0033 | -0.0033 | 5.513e-07 | 0.02% |
| vza=0.0°, az=180° | 0.0026 | 0.0026 | 1.039e-07 | 0.00% |
| vza=25.8°, az=180° | 0.0003 | 0.0003 | 1.619e-08 | 0.01% |
| vza=36.9°, az=180° | -0.0005 | -0.0005 | 7.591e-08 | 0.02% |
| vza=45.6°, az=180° | -0.0011 | -0.0011 | 1.450e-07 | 0.01% |
| vza=53.1°, az=180° | -0.0015 | -0.0015 | 2.068e-07 | 0.01% |
| vza=60.0°, az=180° | -0.0020 | -0.0020 | 2.842e-07 | 0.01% |
| vza=66.4°, az=180° | -0.0023 | -0.0023 | 3.518e-07 | 0.02% |
| vza=72.5°, az=180° | -0.0025 | -0.0025 | 4.163e-07 | 0.02% |
| vza=78.5°, az=180° | -0.0024 | -0.0024 | 4.476e-07 | 0.02% |
| vza=84.3°, az=180° | -0.0020 | -0.0020 | 4.047e-07 | 0.02% |
| vza=90.0°, az=180° | -0.0009 | -0.0009 | 2.874e-07 | 0.03% |
Stokes U n=11 median rel = 0.01% max rel = 0.01% median |Δ| = 4.522e-07 max |Δ| = 6.789e-07
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| vza=0.0°, az=90° | 0.0000 | 0.0000 | 4.997e-13 | 0.01% |
| vza=25.8°, az=90° | 0.0027 | 0.0027 | 1.506e-07 | 0.01% |
| vza=36.9°, az=90° | 0.0042 | 0.0042 | 2.606e-07 | 0.01% |
| vza=45.6°, az=90° | 0.0056 | 0.0056 | 3.606e-07 | 0.01% |
| vza=53.1°, az=90° | 0.0069 | 0.0069 | 4.522e-07 | 0.01% |
| vza=60.0°, az=90° | 0.0080 | 0.0080 | 5.494e-07 | 0.01% |
| vza=66.4°, az=90° | 0.0090 | 0.0090 | 6.230e-07 | 0.01% |
| vza=72.5°, az=90° | 0.0095 | 0.0095 | 6.750e-07 | 0.01% |
| vza=78.5°, az=90° | 0.0091 | 0.0091 | 6.789e-07 | 0.01% |
| vza=84.3°, az=90° | 0.0073 | 0.0073 | 6.090e-07 | 0.01% |
| vza=90.0°, az=90° | 0.0031 | 0.0031 | 4.279e-07 | 0.01% |
Stokes V n=11 median rel = 0.01% max rel = 0.02% median |Δ| = 9.773e-09 max |Δ| = 3.477e-08
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| vza=0.0°, az=90° | 0.0000 | 0.0000 | 9.148e-14 | 0.02% |
| vza=25.8°, az=90° | 0.0001 | 0.0001 | 9.773e-09 | 0.01% |
| vza=36.9°, az=90° | 0.0001 | 0.0001 | 9.386e-09 | 0.01% |
| vza=45.6°, az=90° | 0.0001 | 0.0001 | 5.596e-09 | 0.01% |
| vza=53.1°, az=90° | -0.0000 | -0.0000 | 5.078e-10 | 0.01% |
| vza=60.0°, az=90° | -0.0001 | -0.0001 | 8.288e-09 | 0.01% |
| vza=66.4°, az=90° | -0.0002 | -0.0002 | 1.676e-08 | 0.01% |
| vza=72.5°, az=90° | -0.0002 | -0.0002 | 2.565e-08 | 0.01% |
| vza=78.5°, az=90° | -0.0003 | -0.0003 | 3.227e-08 | 0.01% |
| vza=84.3°, az=90° | -0.0003 | -0.0003 | 3.477e-08 | 0.01% |
| vza=90.0°, az=90° | -0.0002 | -0.0002 | 3.097e-08 | 0.01% |
Float32
Stokes I n=33 median rel = 0.05% max rel = 0.30% median |Δ| = 6.352e-05 max |Δ| = 6.347e-04
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| vza=0.0°, az=0° | 0.0507 | 0.0507 | 8.506e-06 | 0.02% |
| vza=25.8°, az=0° | 0.0932 | 0.0931 | 3.058e-05 | 0.03% |
| vza=36.9°, az=0° | 0.1342 | 0.1342 | 2.948e-05 | 0.02% |
| vza=45.6°, az=0° | 0.1862 | 0.1859 | 3.658e-04 | 0.20% |
| vza=53.1°, az=0° | 0.2522 | 0.2526 | 4.542e-04 | 0.18% |
| vza=60.0°, az=0° | 0.3391 | 0.3391 | 7.373e-05 | 0.02% |
| vza=66.4°, az=0° | 0.4499 | 0.4500 | 9.684e-05 | 0.02% |
| vza=72.5°, az=0° | 0.5889 | 0.5883 | 6.347e-04 | 0.11% |
| vza=78.5°, az=0° | 0.7511 | 0.7513 | 1.550e-04 | 0.02% |
| vza=84.3°, az=0° | 0.9266 | 0.9268 | 1.790e-04 | 0.02% |
| vza=90.0°, az=0° | 1.0630 | 1.0631 | 5.071e-05 | 0.00% |
| vza=0.0°, az=90° | 0.0507 | 0.0507 | 8.406e-06 | 0.02% |
| vza=25.8°, az=90° | 0.0620 | 0.0619 | 2.976e-05 | 0.05% |
| vza=36.9°, az=90° | 0.0750 | 0.0750 | 2.324e-06 | 0.00% |
| vza=45.6°, az=90° | 0.0902 | 0.0900 | 1.977e-04 | 0.22% |
| vza=53.1°, az=90° | 0.1065 | 0.1066 | 1.738e-04 | 0.16% |
| vza=60.0°, az=90° | 0.1246 | 0.1246 | 4.408e-06 | 0.00% |
| vza=66.4°, az=90° | 0.1430 | 0.1430 | 8.277e-06 | 0.01% |
| vza=72.5°, az=90° | 0.1596 | 0.1594 | 2.106e-04 | 0.13% |
| vza=78.5°, az=90° | 0.1692 | 0.1692 | 1.898e-05 | 0.01% |
| vza=84.3°, az=90° | 0.1645 | 0.1645 | 2.056e-05 | 0.01% |
| vza=90.0°, az=90° | 0.1298 | 0.1298 | 3.070e-06 | 0.00% |
| vza=0.0°, az=180° | 0.0507 | 0.0507 | 8.306e-06 | 0.02% |
| vza=25.8°, az=180° | 0.0450 | 0.0449 | 3.879e-05 | 0.09% |
| vza=36.9°, az=180° | 0.0496 | 0.0496 | 2.883e-05 | 0.06% |
| vza=45.6°, az=180° | 0.0557 | 0.0555 | 1.655e-04 | 0.30% |
| vza=53.1°, az=180° | 0.0619 | 0.0619 | 4.263e-05 | 0.07% |
| vza=60.0°, az=180° | 0.0685 | 0.0684 | 6.930e-05 | 0.10% |
| vza=66.4°, az=180° | 0.0745 | 0.0744 | 7.981e-05 | 0.11% |
| vza=72.5°, az=180° | 0.0792 | 0.0790 | 1.951e-04 | 0.25% |
| vza=78.5°, az=180° | 0.0802 | 0.0802 | 8.326e-05 | 0.10% |
| vza=84.3°, az=180° | 0.0752 | 0.0752 | 7.007e-05 | 0.09% |
| vza=90.0°, az=180° | 0.0594 | 0.0594 | 6.352e-05 | 0.11% |
Stokes Q n=33 median rel = 0.04% max rel = 0.50% median |Δ| = 2.734e-06 max |Δ| = 5.077e-05
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| vza=0.0°, az=0° | 0.0026 | 0.0026 | 5.046e-08 | 0.00% |
| vza=25.8°, az=0° | 0.0062 | 0.0062 | 1.137e-06 | 0.02% |
| vza=36.9°, az=0° | 0.0092 | 0.0092 | 3.337e-06 | 0.04% |
| vza=45.6°, az=0° | 0.0135 | 0.0135 | 2.478e-05 | 0.18% |
| vza=53.1°, az=0° | 0.0197 | 0.0198 | 3.501e-05 | 0.18% |
| vza=60.0°, az=0° | 0.0282 | 0.0282 | 5.489e-06 | 0.02% |
| vza=66.4°, az=0° | 0.0388 | 0.0388 | 6.024e-06 | 0.02% |
| vza=72.5°, az=0° | 0.0510 | 0.0509 | 5.077e-05 | 0.10% |
| vza=78.5°, az=0° | 0.0638 | 0.0639 | 8.134e-06 | 0.01% |
| vza=84.3°, az=0° | 0.0764 | 0.0764 | 1.021e-05 | 0.01% |
| vza=90.0°, az=0° | 0.0868 | 0.0868 | 2.734e-06 | 0.00% |
| vza=0.0°, az=90° | -0.0026 | -0.0026 | 4.046e-08 | 0.00% |
| vza=25.8°, az=90° | -0.0028 | -0.0028 | 1.922e-06 | 0.07% |
| vza=36.9°, az=90° | -0.0031 | -0.0031 | 1.056e-06 | 0.03% |
| vza=45.6°, az=90° | -0.0036 | -0.0036 | 7.834e-06 | 0.22% |
| vza=53.1°, az=90° | -0.0043 | -0.0043 | 4.700e-06 | 0.11% |
| vza=60.0°, az=90° | -0.0051 | -0.0051 | 5.701e-07 | 0.01% |
| vza=66.4°, az=90° | -0.0060 | -0.0060 | 2.163e-07 | 0.00% |
| vza=72.5°, az=90° | -0.0067 | -0.0067 | 7.603e-06 | 0.11% |
| vza=78.5°, az=90° | -0.0070 | -0.0070 | 2.009e-06 | 0.03% |
| vza=84.3°, az=90° | -0.0062 | -0.0062 | 2.422e-06 | 0.04% |
| vza=90.0°, az=90° | -0.0033 | -0.0033 | 1.377e-06 | 0.04% |
| vza=0.0°, az=180° | 0.0026 | 0.0026 | 3.046e-08 | 0.00% |
| vza=25.8°, az=180° | 0.0003 | 0.0003 | 1.069e-06 | 0.41% |
| vza=36.9°, az=180° | -0.0005 | -0.0005 | 1.119e-06 | 0.23% |
| vza=45.6°, az=180° | -0.0011 | -0.0011 | 7.292e-07 | 0.07% |
| vza=53.1°, az=180° | -0.0015 | -0.0015 | 4.053e-06 | 0.26% |
| vza=60.0°, az=180° | -0.0020 | -0.0020 | 2.580e-06 | 0.13% |
| vza=66.4°, az=180° | -0.0023 | -0.0023 | 3.336e-06 | 0.15% |
| vza=72.5°, az=180° | -0.0025 | -0.0025 | 1.068e-06 | 0.04% |
| vza=78.5°, az=180° | -0.0024 | -0.0024 | 4.427e-06 | 0.18% |
| vza=84.3°, az=180° | -0.0020 | -0.0020 | 4.589e-06 | 0.23% |
| vza=90.0°, az=180° | -0.0009 | -0.0009 | 4.440e-06 | 0.50% |
Stokes U n=11 median rel = 0.05% max rel = 100.00% median |Δ| = 4.128e-06 max |Δ| = 1.527e-05
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| vza=0.0°, az=90° | 0.0000 | 0.0000 | 9.439e-09 | 100.00% |
| vza=25.8°, az=90° | 0.0027 | 0.0027 | 9.741e-08 | 0.00% |
| vza=36.9°, az=90° | 0.0042 | 0.0042 | 2.362e-06 | 0.06% |
| vza=45.6°, az=90° | 0.0056 | 0.0056 | 9.738e-06 | 0.17% |
| vza=53.1°, az=90° | 0.0069 | 0.0069 | 1.527e-05 | 0.22% |
| vza=60.0°, az=90° | 0.0080 | 0.0080 | 4.128e-06 | 0.05% |
| vza=66.4°, az=90° | 0.0090 | 0.0090 | 4.509e-06 | 0.05% |
| vza=72.5°, az=90° | 0.0095 | 0.0095 | 1.037e-05 | 0.11% |
| vza=78.5°, az=90° | 0.0091 | 0.0091 | 4.243e-06 | 0.05% |
| vza=84.3°, az=90° | 0.0073 | 0.0073 | 3.023e-06 | 0.04% |
| vza=90.0°, az=90° | 0.0031 | 0.0031 | 5.914e-07 | 0.02% |
Stokes V n=11 median rel = 0.04% max rel = 100.00% median |Δ| = 1.363e-08 max |Δ| = 2.670e-07
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| vza=0.0°, az=90° | 0.0000 | 0.0000 | 4.575e-10 | 100.00% |
| vza=25.8°, az=90° | 0.0001 | 0.0001 | 7.967e-08 | 0.09% |
| vza=36.9°, az=90° | 0.0001 | 0.0001 | 1.363e-08 | 0.02% |
| vza=45.6°, az=90° | 0.0001 | 0.0001 | 2.670e-07 | 0.52% |
| vza=53.1°, az=90° | -0.0000 | -0.0000 | 9.819e-08 | 2.57% |
| vza=60.0°, az=90° | -0.0001 | -0.0001 | 1.293e-08 | 0.02% |
| vza=66.4°, az=90° | -0.0002 | -0.0002 | 1.132e-08 | 0.01% |
| vza=72.5°, az=90° | -0.0002 | -0.0002 | 2.055e-07 | 0.09% |
| vza=78.5°, az=90° | -0.0003 | -0.0003 | 5.293e-09 | 0.00% |
| vza=84.3°, az=90° | -0.0003 | -0.0003 | 1.202e-08 | 0.00% |
| vza=90.0°, az=90° | -0.0002 | -0.0002 | 1.009e-07 | 0.04% |
Natraj 2009 — polarised Rayleigh τ=0.5
📚 published benchmark
Pure Rayleigh, optical depth τ = 0.5, sza = acos(0.2) ≈ 78.46°, depolarization 0 (Natraj's idealization). 16 viewing-zenith cosines from 0.02 to 1.00 across 7 azimuths from 0° to 180°. Modeled reflectance R = π · (I/F₀). GaussLegQuad + NoTruncation(): half-space Gauss-Legendre on [0, 1] (5–50× more accurate than RadauQuad on this Rayleigh-only setup) and Rayleigh has only β₀, β₁, β₂ non-zero so δ-fit forward-peak truncation is meaningless. Q/U use a near-zero filter of |truth| < 0.01 (mirrors the |modeled| ≥ 0.01 filter applied in test/test_CoreRT.jl).
Float64
Stokes I n=112 median rel = 0.00% max rel = 0.02% median |Δ| = 6.479e-06 max |Δ| = 5.528e-05
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| μ=0.02, ϕ=0° | 0.4412 | 0.4413 | 5.500e-05 | 0.01% |
| μ=0.02, ϕ=30° | 0.3944 | 0.3944 | 5.290e-05 | 0.01% |
| μ=0.02, ϕ=60° | 0.3009 | 0.3009 | 4.871e-05 | 0.02% |
| μ=0.02, ϕ=90° | 0.2546 | 0.2547 | 4.666e-05 | 0.02% |
| μ=0.02, ϕ=120° | 0.3025 | 0.3025 | 4.885e-05 | 0.02% |
| μ=0.02, ϕ=150° | 0.3972 | 0.3973 | 5.315e-05 | 0.01% |
| μ=0.02, ϕ=180° | 0.4445 | 0.4445 | 5.528e-05 | 0.01% |
| μ=0.06, ϕ=0° | 0.3925 | 0.3925 | 1.482e-05 | 0.00% |
| μ=0.06, ϕ=30° | 0.3522 | 0.3522 | 1.429e-05 | 0.00% |
| μ=0.06, ϕ=60° | 0.2721 | 0.2721 | 1.322e-05 | 0.00% |
| μ=0.06, ϕ=90° | 0.2334 | 0.2334 | 1.272e-05 | 0.01% |
| μ=0.06, ϕ=120° | 0.2764 | 0.2764 | 1.333e-05 | 0.00% |
| μ=0.06, ϕ=150° | 0.3597 | 0.3597 | 1.446e-05 | 0.00% |
| μ=0.06, ϕ=180° | 0.4011 | 0.4011 | 1.502e-05 | 0.00% |
| μ=0.1, ϕ=0° | 0.3508 | 0.3508 | 1.321e-05 | 0.00% |
| μ=0.1, ϕ=30° | 0.3157 | 0.3158 | 1.277e-05 | 0.00% |
| μ=0.1, ϕ=60° | 0.2462 | 0.2462 | 1.190e-05 | 0.00% |
| μ=0.1, ϕ=90° | 0.2135 | 0.2135 | 1.151e-05 | 0.01% |
| μ=0.1, ϕ=120° | 0.2526 | 0.2526 | 1.204e-05 | 0.00% |
| μ=0.1, ϕ=150° | 0.3268 | 0.3268 | 1.302e-05 | 0.00% |
| μ=0.1, ϕ=180° | 0.3635 | 0.3635 | 1.350e-05 | 0.00% |
| μ=0.16, ϕ=0° | 0.2986 | 0.2986 | 1.181e-05 | 0.00% |
| μ=0.16, ϕ=30° | 0.2697 | 0.2697 | 1.144e-05 | 0.00% |
| μ=0.16, ϕ=60° | 0.2128 | 0.2128 | 1.073e-05 | 0.01% |
| μ=0.16, ϕ=90° | 0.1870 | 0.1870 | 1.043e-05 | 0.01% |
| μ=0.16, ϕ=120° | 0.2214 | 0.2214 | 1.093e-05 | 0.00% |
| μ=0.16, ϕ=150° | 0.2847 | 0.2847 | 1.179e-05 | 0.00% |
| μ=0.16, ϕ=180° | 0.3159 | 0.3159 | 1.221e-05 | 0.00% |
| μ=0.2, ϕ=0° | 0.2694 | 0.2694 | 1.089e-05 | 0.00% |
| μ=0.2, ϕ=30° | 0.2438 | 0.2438 | 1.057e-05 | 0.00% |
| μ=0.2, ϕ=60° | 0.1937 | 0.1937 | 9.946e-06 | 0.01% |
| μ=0.2, ϕ=90° | 0.1717 | 0.1717 | 9.706e-06 | 0.01% |
| μ=0.2, ϕ=120° | 0.2034 | 0.2034 | 1.017e-05 | 0.01% |
| μ=0.2, ϕ=150° | 0.2607 | 0.2607 | 1.097e-05 | 0.00% |
| μ=0.2, ϕ=180° | 0.2889 | 0.2889 | 1.136e-05 | 0.00% |
| μ=0.28, ϕ=0° | 0.2215 | 0.2215 | 9.244e-06 | 0.00% |
| μ=0.28, ϕ=30° | 0.2014 | 0.2014 | 8.987e-06 | 0.00% |
| μ=0.28, ϕ=60° | 0.1622 | 0.1622 | 8.498e-06 | 0.01% |
| μ=0.28, ϕ=90° | 0.1461 | 0.1462 | 8.342e-06 | 0.01% |
| μ=0.28, ϕ=120° | 0.1734 | 0.1734 | 8.776e-06 | 0.01% |
| μ=0.28, ϕ=150° | 0.2209 | 0.2209 | 9.457e-06 | 0.00% |
| μ=0.28, ϕ=180° | 0.2441 | 0.2441 | 9.789e-06 | 0.00% |
| μ=0.32, ϕ=0° | 0.2018 | 0.2019 | 8.514e-06 | 0.00% |
| μ=0.32, ϕ=30° | 0.1839 | 0.1839 | 8.278e-06 | 0.00% |
| μ=0.32, ϕ=60° | 0.1492 | 0.1492 | 7.856e-06 | 0.01% |
| μ=0.32, ϕ=90° | 0.1356 | 0.1356 | 7.735e-06 | 0.01% |
| μ=0.32, ϕ=120° | 0.1610 | 0.1610 | 8.152e-06 | 0.01% |
| μ=0.32, ϕ=150° | 0.2043 | 0.2043 | 8.784e-06 | 0.00% |
| μ=0.32, ϕ=180° | 0.2254 | 0.2254 | 9.086e-06 | 0.00% |
| μ=0.4, ϕ=0° | 0.1689 | 0.1689 | 7.225e-06 | 0.00% |
| μ=0.4, ϕ=30° | 0.1547 | 0.1547 | 7.052e-06 | 0.00% |
| μ=0.4, ϕ=60° | 0.1275 | 0.1275 | 6.731e-06 | 0.01% |
| μ=0.4, ϕ=90° | 0.1179 | 0.1179 | 6.666e-06 | 0.01% |
| μ=0.4, ϕ=120° | 0.1399 | 0.1399 | 7.040e-06 | 0.01% |
| μ=0.4, ϕ=150° | 0.1761 | 0.1761 | 7.587e-06 | 0.00% |
| μ=0.4, ϕ=180° | 0.1936 | 0.1936 | 7.842e-06 | 0.00% |
| μ=0.52, ϕ=0° | 0.1310 | 0.1310 | 5.667e-06 | 0.00% |
| μ=0.52, ϕ=30° | 0.1212 | 0.1212 | 5.550e-06 | 0.00% |
| μ=0.52, ϕ=60° | 0.1028 | 0.1028 | 5.351e-06 | 0.01% |
| μ=0.52, ϕ=90° | 0.0976 | 0.0976 | 5.348e-06 | 0.01% |
| μ=0.52, ϕ=120° | 0.1153 | 0.1153 | 5.658e-06 | 0.00% |
| μ=0.52, ϕ=150° | 0.1428 | 0.1429 | 6.096e-06 | 0.00% |
| μ=0.52, ϕ=180° | 0.1560 | 0.1560 | 6.293e-06 | 0.00% |
| μ=0.64, ϕ=0° | 0.1023 | 0.1023 | 4.417e-06 | 0.00% |
| μ=0.64, ϕ=30° | 0.0960 | 0.0960 | 4.352e-06 | 0.00% |
| μ=0.64, ϕ=60° | 0.0844 | 0.0844 | 4.234e-06 | 0.01% |
| μ=0.64, ϕ=90° | 0.0824 | 0.0824 | 4.281e-06 | 0.01% |
| μ=0.64, ϕ=120° | 0.0963 | 0.0963 | 4.536e-06 | 0.00% |
| μ=0.64, ϕ=150° | 0.1165 | 0.1165 | 4.867e-06 | 0.00% |
| μ=0.64, ϕ=180° | 0.1261 | 0.1261 | 5.021e-06 | 0.00% |
| μ=0.72, ϕ=0° | 0.0868 | 0.0868 | 3.719e-06 | 0.00% |
| μ=0.72, ϕ=30° | 0.0824 | 0.0824 | 3.675e-06 | 0.00% |
| μ=0.72, ϕ=60° | 0.0746 | 0.0746 | 3.610e-06 | 0.00% |
| μ=0.72, ϕ=90° | 0.0742 | 0.0742 | 3.671e-06 | 0.00% |
| μ=0.72, ϕ=120° | 0.0856 | 0.0856 | 3.894e-06 | 0.00% |
| μ=0.72, ϕ=150° | 0.1015 | 0.1015 | 4.161e-06 | 0.00% |
| μ=0.72, ϕ=180° | 0.1089 | 0.1089 | 4.278e-06 | 0.00% |
| μ=0.84, ϕ=0° | 0.0678 | 0.0678 | 2.822e-06 | 0.00% |
| μ=0.84, ϕ=30° | 0.0658 | 0.0658 | 2.806e-06 | 0.00% |
| μ=0.84, ϕ=60° | 0.0627 | 0.0627 | 2.800e-06 | 0.00% |
| μ=0.84, ϕ=90° | 0.0639 | 0.0639 | 2.863e-06 | 0.00% |
| μ=0.84, ϕ=120° | 0.0716 | 0.0716 | 3.020e-06 | 0.00% |
| μ=0.84, ϕ=150° | 0.0812 | 0.0812 | 3.194e-06 | 0.00% |
| μ=0.84, ϕ=180° | 0.0856 | 0.0856 | 3.272e-06 | 0.00% |
| μ=0.92, ϕ=0° | 0.0578 | 0.0578 | 2.314e-06 | 0.00% |
| μ=0.92, ϕ=30° | 0.0571 | 0.0571 | 2.313e-06 | 0.00% |
| μ=0.92, ϕ=60° | 0.0564 | 0.0564 | 2.323e-06 | 0.00% |
| μ=0.92, ϕ=90° | 0.0581 | 0.0581 | 2.386e-06 | 0.00% |
| μ=0.92, ϕ=120° | 0.0630 | 0.0630 | 2.493e-06 | 0.00% |
| μ=0.92, ϕ=150° | 0.0684 | 0.0684 | 2.600e-06 | 0.00% |
| μ=0.92, ϕ=180° | 0.0709 | 0.0709 | 2.643e-06 | 0.00% |
| μ=0.96, ϕ=0° | 0.0539 | 0.0539 | 2.092e-06 | 0.00% |
| μ=0.96, ϕ=30° | 0.0537 | 0.0537 | 2.098e-06 | 0.00% |
| μ=0.96, ϕ=60° | 0.0539 | 0.0539 | 2.116e-06 | 0.00% |
| μ=0.96, ϕ=90° | 0.0555 | 0.0555 | 2.161e-06 | 0.00% |
| μ=0.96, ϕ=120° | 0.0586 | 0.0586 | 2.237e-06 | 0.00% |
| μ=0.96, ϕ=150° | 0.0619 | 0.0619 | 2.306e-06 | 0.00% |
| μ=0.96, ϕ=180° | 0.0632 | 0.0632 | 2.332e-06 | 0.00% |
| μ=0.98, ϕ=0° | 0.0524 | 0.0524 | 1.995e-06 | 0.00% |
| μ=0.98, ϕ=30° | 0.0525 | 0.0525 | 1.993e-06 | 0.00% |
| μ=0.98, ϕ=60° | 0.0529 | 0.0529 | 2.016e-06 | 0.00% |
| μ=0.98, ϕ=90° | 0.0542 | 0.0542 | 2.055e-06 | 0.00% |
| μ=0.98, ϕ=120° | 0.0563 | 0.0563 | 2.100e-06 | 0.00% |
| μ=0.98, ϕ=150° | 0.0583 | 0.0583 | 2.147e-06 | 0.00% |
| μ=0.98, ϕ=180° | 0.0591 | 0.0591 | 2.163e-06 | 0.00% |
| μ=1.0, ϕ=0° | 0.0530 | 0.0530 | 1.953e-06 | 0.00% |
| μ=1.0, ϕ=30° | 0.0530 | 0.0530 | 1.953e-06 | 0.00% |
| μ=1.0, ϕ=60° | 0.0530 | 0.0530 | 1.953e-06 | 0.00% |
| μ=1.0, ϕ=90° | 0.0530 | 0.0530 | 1.953e-06 | 0.00% |
| μ=1.0, ϕ=120° | 0.0530 | 0.0530 | 1.953e-06 | 0.00% |
| μ=1.0, ϕ=150° | 0.0530 | 0.0530 | 1.953e-06 | 0.00% |
| μ=1.0, ϕ=180° | 0.0530 | 0.0530 | 1.953e-06 | 0.00% |
Stokes Q n=100 median rel = 0.01% max rel = 0.14% median |Δ| = 3.092e-06 max |Δ| = 3.310e-05 (excluded 12 cells with |truth| < 1.000e-02)
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| μ=0.02, ϕ=0° | -0.0175 | -0.0175 | 2.446e-05 | 0.14% |
| μ=0.02, ϕ=30° | -0.0648 | -0.0649 | 2.660e-05 | 0.04% |
| μ=0.02, ϕ=60° | -0.1596 | -0.1597 | 3.090e-05 | 0.02% |
| μ=0.02, ϕ=90° | -0.2075 | -0.2076 | 3.310e-05 | 0.02% |
| μ=0.02, ϕ=120° | -0.1613 | -0.1613 | 3.104e-05 | 0.02% |
| μ=0.02, ϕ=150° | -0.0676 | -0.0677 | 2.685e-05 | 0.04% |
| μ=0.02, ϕ=180° | -0.0208 | -0.0208 | 2.475e-05 | 0.12% |
| μ=0.06, ϕ=0° | -0.0177 | -0.0177 | 5.887e-06 | 0.03% |
| μ=0.06, ϕ=30° | -0.0594 | -0.0594 | 6.460e-06 | 0.01% |
| μ=0.06, ϕ=60° | -0.1433 | -0.1433 | 7.601e-06 | 0.01% |
| μ=0.06, ϕ=90° | -0.1866 | -0.1866 | 8.204e-06 | 0.00% |
| μ=0.06, ϕ=120° | -0.1476 | -0.1476 | 7.707e-06 | 0.01% |
| μ=0.06, ϕ=150° | -0.0669 | -0.0669 | 6.628e-06 | 0.01% |
| μ=0.06, ϕ=180° | -0.0263 | -0.0263 | 6.090e-06 | 0.02% |
| μ=0.1, ϕ=0° | -0.0152 | -0.0152 | 5.312e-06 | 0.03% |
| μ=0.1, ϕ=30° | -0.0527 | -0.0527 | 5.804e-06 | 0.01% |
| μ=0.1, ϕ=60° | -0.1284 | -0.1284 | 6.805e-06 | 0.01% |
| μ=0.1, ϕ=90° | -0.1682 | -0.1682 | 7.344e-06 | 0.00% |
| μ=0.1, ϕ=120° | -0.1347 | -0.1347 | 6.949e-06 | 0.01% |
| μ=0.1, ϕ=150° | -0.0638 | -0.0638 | 6.053e-06 | 0.01% |
| μ=0.1, ϕ=180° | -0.0280 | -0.0280 | 5.601e-06 | 0.02% |
| μ=0.16, ϕ=0° | -0.0099 | -0.0099 | 4.738e-06 | — |
| μ=0.16, ϕ=30° | -0.0427 | -0.0427 | 5.176e-06 | 0.01% |
| μ=0.16, ϕ=60° | -0.1091 | -0.1091 | 6.082e-06 | 0.01% |
| μ=0.16, ϕ=90° | -0.1451 | -0.1451 | 6.604e-06 | 0.00% |
| μ=0.16, ϕ=120° | -0.1178 | -0.1178 | 6.284e-06 | 0.01% |
| μ=0.16, ϕ=150° | -0.0577 | -0.0577 | 5.527e-06 | 0.01% |
| μ=0.16, ϕ=180° | -0.0272 | -0.0272 | 5.143e-06 | 0.02% |
| μ=0.2, ϕ=0° | -0.0061 | -0.0061 | 4.327e-06 | — |
| μ=0.2, ϕ=30° | -0.0365 | -0.0365 | 4.745e-06 | 0.01% |
| μ=0.2, ϕ=60° | -0.0983 | -0.0983 | 5.592e-06 | 0.01% |
| μ=0.2, ϕ=90° | -0.1322 | -0.1322 | 6.104e-06 | 0.00% |
| μ=0.2, ϕ=120° | -0.1080 | -0.1080 | 5.831e-06 | 0.01% |
| μ=0.2, ϕ=150° | -0.0534 | -0.0534 | 5.142e-06 | 0.01% |
| μ=0.2, ϕ=180° | -0.0256 | -0.0256 | 4.786e-06 | 0.02% |
| μ=0.28, ϕ=0° | 0.0013 | 0.0013 | 3.523e-06 | — |
| μ=0.28, ϕ=30° | -0.0255 | -0.0255 | 3.902e-06 | 0.02% |
| μ=0.28, ϕ=60° | -0.0804 | -0.0804 | 4.687e-06 | 0.01% |
| μ=0.28, ϕ=90° | -0.1113 | -0.1113 | 5.167e-06 | 0.00% |
| μ=0.28, ϕ=120° | -0.0916 | -0.0916 | 4.965e-06 | 0.01% |
| μ=0.28, ϕ=150° | -0.0451 | -0.0451 | 4.383e-06 | 0.01% |
| μ=0.28, ϕ=180° | -0.0212 | -0.0212 | 4.068e-06 | 0.02% |
| μ=0.32, ϕ=0° | 0.0048 | 0.0048 | 3.155e-06 | — |
| μ=0.32, ϕ=30° | -0.0208 | -0.0208 | 3.520e-06 | 0.02% |
| μ=0.32, ϕ=60° | -0.0730 | -0.0730 | 4.277e-06 | 0.01% |
| μ=0.32, ϕ=90° | -0.1028 | -0.1028 | 4.747e-06 | 0.00% |
| μ=0.32, ϕ=120° | -0.0848 | -0.0848 | 4.563e-06 | 0.01% |
| μ=0.32, ϕ=150° | -0.0411 | -0.0411 | 4.025e-06 | 0.01% |
| μ=0.32, ϕ=180° | -0.0188 | -0.0188 | 3.737e-06 | 0.02% |
| μ=0.4, ϕ=0° | 0.0112 | 0.0112 | 2.495e-06 | 0.02% |
| μ=0.4, ϕ=30° | -0.0123 | -0.0124 | 2.839e-06 | 0.02% |
| μ=0.4, ϕ=60° | -0.0607 | -0.0607 | 3.543e-06 | 0.01% |
| μ=0.4, ϕ=90° | -0.0887 | -0.0887 | 4.006e-06 | 0.00% |
| μ=0.4, ϕ=120° | -0.0730 | -0.0730 | 3.852e-06 | 0.01% |
| μ=0.4, ϕ=150° | -0.0338 | -0.0338 | 3.363e-06 | 0.01% |
| μ=0.4, ϕ=180° | -0.0136 | -0.0136 | 3.111e-06 | 0.02% |
| μ=0.52, ϕ=0° | 0.0197 | 0.0197 | 1.649e-06 | 0.01% |
| μ=0.52, ϕ=30° | -0.0020 | -0.0020 | 1.965e-06 | — |
| μ=0.52, ϕ=60° | -0.0465 | -0.0465 | 2.632e-06 | 0.01% |
| μ=0.52, ϕ=90° | -0.0727 | -0.0727 | 3.073e-06 | 0.00% |
| μ=0.52, ϕ=120° | -0.0590 | -0.0590 | 2.950e-06 | 0.00% |
| μ=0.52, ϕ=150° | -0.0236 | -0.0236 | 2.512e-06 | 0.01% |
| μ=0.52, ϕ=180° | -0.0053 | -0.0053 | 2.275e-06 | — |
| μ=0.64, ϕ=0° | 0.0270 | 0.0270 | 9.351e-07 | 0.00% |
| μ=0.64, ϕ=30° | 0.0064 | 0.0064 | 1.239e-06 | — |
| μ=0.64, ϕ=60° | -0.0359 | -0.0359 | 1.878e-06 | 0.01% |
| μ=0.64, ϕ=90° | -0.0608 | -0.0608 | 2.292e-06 | 0.00% |
| μ=0.64, ϕ=120° | -0.0477 | -0.0477 | 2.180e-06 | 0.00% |
| μ=0.64, ϕ=150° | -0.0141 | -0.0141 | 1.763e-06 | 0.01% |
| μ=0.64, ϕ=180° | 0.0033 | 0.0033 | 1.539e-06 | — |
| μ=0.72, ϕ=0° | 0.0313 | 0.0313 | 5.260e-07 | 0.00% |
| μ=0.72, ϕ=30° | 0.0112 | 0.0112 | 8.195e-07 | 0.01% |
| μ=0.72, ϕ=60° | -0.0302 | -0.0302 | 1.449e-06 | 0.00% |
| μ=0.72, ϕ=90° | -0.0543 | -0.0543 | 1.849e-06 | 0.00% |
| μ=0.72, ϕ=120° | -0.0412 | -0.0412 | 1.724e-06 | 0.00% |
| μ=0.72, ϕ=150° | -0.0079 | -0.0079 | 1.305e-06 | — |
| μ=0.72, ϕ=180° | 0.0093 | 0.0093 | 1.085e-06 | — |
| μ=0.84, ϕ=0° | 0.0367 | 0.0367 | 2.530e-08 | 0.00% |
| μ=0.84, ϕ=30° | 0.0170 | 0.0170 | 2.685e-07 | 0.00% |
| μ=0.84, ϕ=60° | -0.0233 | -0.0233 | 8.718e-07 | 0.00% |
| μ=0.84, ϕ=90° | -0.0462 | -0.0462 | 1.244e-06 | 0.00% |
| μ=0.84, ϕ=120° | -0.0322 | -0.0322 | 1.092e-06 | 0.00% |
| μ=0.84, ϕ=150° | 0.0016 | 0.0016 | 6.559e-07 | — |
| μ=0.84, ϕ=180° | 0.0189 | 0.0189 | 4.251e-07 | 0.00% |
| μ=0.92, ϕ=0° | 0.0392 | 0.0392 | 3.365e-07 | 0.00% |
| μ=0.92, ϕ=30° | 0.0198 | 0.0198 | 5.817e-08 | 0.00% |
| μ=0.92, ϕ=60° | -0.0198 | -0.0198 | 5.296e-07 | 0.00% |
| μ=0.92, ϕ=90° | -0.0416 | -0.0416 | 8.714e-07 | 0.00% |
| μ=0.92, ϕ=120° | -0.0263 | -0.0263 | 6.991e-07 | 0.00% |
| μ=0.92, ϕ=150° | 0.0085 | 0.0085 | 2.384e-07 | — |
| μ=0.92, ϕ=180° | 0.0262 | 0.0262 | 7.490e-09 | 0.00% |
| μ=0.96, ϕ=0° | 0.0398 | 0.0398 | 4.750e-07 | 0.00% |
| μ=0.96, ϕ=30° | 0.0205 | 0.0205 | 1.949e-07 | 0.00% |
| μ=0.96, ϕ=60° | -0.0185 | -0.0185 | 3.807e-07 | 0.00% |
| μ=0.96, ϕ=90° | -0.0395 | -0.0395 | 6.995e-07 | 0.00% |
| μ=0.96, ϕ=120° | -0.0232 | -0.0232 | 5.012e-07 | 0.00% |
| μ=0.96, ϕ=150° | 0.0124 | 0.0124 | 1.286e-08 | 0.00% |
| μ=0.96, ϕ=180° | 0.0305 | 0.0305 | 2.340e-07 | 0.00% |
| μ=0.98, ϕ=0° | 0.0397 | 0.0397 | 5.307e-07 | 0.00% |
| μ=0.98, ϕ=30° | 0.0205 | 0.0205 | 2.474e-07 | 0.00% |
| μ=0.98, ϕ=60° | -0.0181 | -0.0181 | 3.042e-07 | 0.00% |
| μ=0.98, ϕ=90° | -0.0385 | -0.0385 | 6.172e-07 | 0.00% |
| μ=0.98, ϕ=120° | -0.0215 | -0.0215 | 3.883e-07 | 0.00% |
| μ=0.98, ϕ=150° | 0.0147 | 0.0147 | 1.039e-07 | 0.00% |
| μ=0.98, ϕ=180° | 0.0330 | 0.0330 | 3.525e-07 | 0.00% |
| μ=1.0, ϕ=0° | 0.0376 | 0.0376 | 5.296e-07 | 0.00% |
| μ=1.0, ϕ=30° | 0.0188 | 0.0188 | 2.698e-07 | 0.00% |
| μ=1.0, ϕ=60° | -0.0188 | -0.0188 | 2.698e-07 | 0.00% |
| μ=1.0, ϕ=90° | -0.0376 | -0.0376 | 5.296e-07 | 0.00% |
| μ=1.0, ϕ=120° | -0.0188 | -0.0188 | 2.698e-07 | 0.00% |
| μ=1.0, ϕ=150° | 0.0188 | 0.0188 | 2.698e-07 | 0.00% |
| μ=1.0, ϕ=180° | 0.0376 | 0.0376 | 5.296e-07 | 0.00% |
Stokes U n=69 median rel = 0.00% max rel = 0.01% median |Δ| = 6.936e-07 max |Δ| = 7.021e-06 (excluded 43 cells with |truth| < 1.000e-02)
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| μ=0.02, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.02, ϕ=30° | 0.0439 | 0.0439 | 3.657e-06 | 0.01% |
| μ=0.02, ϕ=60° | 0.0736 | 0.0737 | 6.231e-06 | 0.01% |
| μ=0.02, ϕ=90° | 0.0813 | 0.0813 | 7.021e-06 | 0.01% |
| μ=0.02, ϕ=120° | 0.0671 | 0.0671 | 5.939e-06 | 0.01% |
| μ=0.02, ϕ=150° | 0.0374 | 0.0374 | 3.364e-06 | 0.01% |
| μ=0.02, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.06, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.06, ϕ=30° | 0.0443 | 0.0443 | 9.677e-07 | 0.00% |
| μ=0.06, ϕ=60° | 0.0705 | 0.0705 | 1.588e-06 | 0.00% |
| μ=0.06, ϕ=90° | 0.0715 | 0.0715 | 1.699e-06 | 0.00% |
| μ=0.06, ϕ=120° | 0.0534 | 0.0534 | 1.362e-06 | 0.00% |
| μ=0.06, ϕ=150° | 0.0272 | 0.0272 | 7.311e-07 | 0.00% |
| μ=0.06, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.1, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.1, ϕ=30° | 0.0444 | 0.0444 | 8.875e-07 | 0.00% |
| μ=0.1, ϕ=60° | 0.0676 | 0.0676 | 1.423e-06 | 0.00% |
| μ=0.1, ϕ=90° | 0.0636 | 0.0636 | 1.452e-06 | 0.00% |
| μ=0.1, ϕ=120° | 0.0425 | 0.0425 | 1.100e-06 | 0.00% |
| μ=0.1, ϕ=150° | 0.0192 | 0.0192 | 5.649e-07 | 0.00% |
| μ=0.1, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.16, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.16, ϕ=30° | 0.0441 | 0.0441 | 8.568e-07 | 0.00% |
| μ=0.16, ϕ=60° | 0.0638 | 0.0638 | 1.327e-06 | 0.00% |
| μ=0.16, ϕ=90° | 0.0540 | 0.0540 | 1.266e-06 | 0.00% |
| μ=0.16, ϕ=120° | 0.0296 | 0.0296 | 8.693e-07 | 0.00% |
| μ=0.16, ϕ=150° | 0.0099 | 0.0099 | 4.090e-07 | — |
| μ=0.16, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.2, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.2, ϕ=30° | 0.0437 | 0.0437 | 8.333e-07 | 0.00% |
| μ=0.2, ϕ=60° | 0.0616 | 0.0616 | 1.264e-06 | 0.00% |
| μ=0.2, ϕ=90° | 0.0487 | 0.0487 | 1.166e-06 | 0.00% |
| μ=0.2, ϕ=120° | 0.0228 | 0.0228 | 7.434e-07 | 0.00% |
| μ=0.2, ϕ=150° | 0.0050 | 0.0050 | 3.223e-07 | — |
| μ=0.2, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.28, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.28, ϕ=30° | 0.0429 | 0.0429 | 8.015e-07 | 0.00% |
| μ=0.28, ϕ=60° | 0.0576 | 0.0576 | 1.153e-06 | 0.00% |
| μ=0.28, ϕ=90° | 0.0402 | 0.0402 | 9.827e-07 | 0.00% |
| μ=0.28, ϕ=120° | 0.0121 | 0.0121 | 5.428e-07 | 0.00% |
| μ=0.28, ϕ=150° | -0.0027 | -0.0027 | 1.811e-07 | — |
| μ=0.28, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.32, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.32, ϕ=30° | 0.0425 | 0.0425 | 7.763e-07 | 0.00% |
| μ=0.32, ϕ=60° | 0.0559 | 0.0559 | 1.109e-06 | 0.00% |
| μ=0.32, ϕ=90° | 0.0368 | 0.0368 | 9.017e-07 | 0.00% |
| μ=0.32, ϕ=120° | 0.0078 | 0.0078 | 4.577e-07 | — |
| μ=0.32, ϕ=150° | -0.0057 | -0.0057 | 1.255e-07 | — |
| μ=0.32, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.4, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.4, ϕ=30° | 0.0416 | 0.0416 | 7.379e-07 | 0.00% |
| μ=0.4, ϕ=60° | 0.0529 | 0.0529 | 1.018e-06 | 0.00% |
| μ=0.4, ϕ=90° | 0.0309 | 0.0309 | 7.710e-07 | 0.00% |
| μ=0.4, ϕ=120° | 0.0006 | 0.0006 | 3.034e-07 | — |
| μ=0.4, ϕ=150° | -0.0107 | -0.0107 | 2.309e-08 | 0.00% |
| μ=0.4, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.52, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.52, ϕ=30° | 0.0404 | 0.0404 | 6.936e-07 | 0.00% |
| μ=0.52, ϕ=60° | 0.0492 | 0.0492 | 9.167e-07 | 0.00% |
| μ=0.52, ϕ=90° | 0.0241 | 0.0241 | 6.026e-07 | 0.00% |
| μ=0.52, ϕ=120° | -0.0075 | -0.0075 | 1.322e-07 | — |
| μ=0.52, ϕ=150° | -0.0163 | -0.0163 | 9.095e-08 | 0.00% |
| μ=0.52, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.64, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.64, ϕ=30° | 0.0391 | 0.0391 | 6.511e-07 | 0.00% |
| μ=0.64, ϕ=60° | 0.0459 | 0.0459 | 8.213e-07 | 0.00% |
| μ=0.64, ϕ=90° | 0.0186 | 0.0186 | 4.710e-07 | 0.00% |
| μ=0.64, ϕ=120° | -0.0138 | -0.0138 | 9.849e-09 | 0.00% |
| μ=0.64, ϕ=150° | -0.0206 | -0.0206 | 1.801e-07 | 0.00% |
| μ=0.64, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.72, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.72, ϕ=30° | 0.0383 | 0.0383 | 6.191e-07 | 0.00% |
| μ=0.72, ϕ=60° | 0.0439 | 0.0439 | 7.621e-07 | 0.00% |
| μ=0.72, ϕ=90° | 0.0153 | 0.0153 | 3.918e-07 | 0.00% |
| μ=0.72, ϕ=120° | -0.0174 | -0.0174 | 9.441e-08 | 0.00% |
| μ=0.72, ϕ=150° | -0.0230 | -0.0230 | 2.374e-07 | 0.00% |
| μ=0.72, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.84, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.84, ϕ=30° | 0.0369 | 0.0369 | 5.783e-07 | 0.00% |
| μ=0.84, ϕ=60° | 0.0407 | 0.0407 | 6.819e-07 | 0.00% |
| μ=0.84, ϕ=90° | 0.0106 | 0.0106 | 2.660e-07 | 0.00% |
| μ=0.84, ϕ=120° | -0.0224 | -0.0224 | 2.088e-07 | 0.00% |
| μ=0.84, ϕ=150° | -0.0263 | -0.0263 | 3.124e-07 | 0.00% |
| μ=0.84, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.92, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.92, ϕ=30° | 0.0356 | 0.0356 | 5.414e-07 | 0.00% |
| μ=0.92, ϕ=60° | 0.0382 | 0.0382 | 6.114e-07 | 0.00% |
| μ=0.92, ϕ=90° | 0.0071 | 0.0071 | 1.825e-07 | — |
| μ=0.92, ϕ=120° | -0.0259 | -0.0259 | 2.990e-07 | 0.00% |
| μ=0.92, ϕ=150° | -0.0285 | -0.0285 | 3.589e-07 | 0.00% |
| μ=0.92, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.96, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.96, ϕ=30° | 0.0348 | 0.0348 | 5.217e-07 | 0.00% |
| μ=0.96, ϕ=60° | 0.0365 | 0.0365 | 5.645e-07 | 0.00% |
| μ=0.96, ϕ=90° | 0.0049 | 0.0049 | 1.288e-07 | — |
| μ=0.96, ϕ=120° | -0.0281 | -0.0281 | 3.501e-07 | 0.00% |
| μ=0.96, ϕ=150° | -0.0299 | -0.0299 | 3.929e-07 | 0.00% |
| μ=0.96, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.98, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.98, ϕ=30° | 0.0341 | 0.0341 | 5.012e-07 | 0.00% |
| μ=0.98, ϕ=60° | 0.0354 | 0.0354 | 5.342e-07 | 0.00% |
| μ=0.98, ϕ=90° | 0.0034 | 0.0034 | 9.170e-08 | — |
| μ=0.98, ϕ=120° | -0.0295 | -0.0295 | 3.766e-07 | 0.00% |
| μ=0.98, ϕ=150° | -0.0307 | -0.0307 | 4.095e-07 | 0.00% |
| μ=0.98, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=1.0, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=1.0, ϕ=30° | 0.0325 | 0.0325 | 4.556e-07 | 0.00% |
| μ=1.0, ϕ=60° | 0.0325 | 0.0325 | 4.556e-07 | 0.00% |
| μ=1.0, ϕ=90° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=1.0, ϕ=120° | -0.0325 | -0.0325 | 4.556e-07 | 0.00% |
| μ=1.0, ϕ=150° | -0.0325 | -0.0325 | 4.556e-07 | 0.00% |
| μ=1.0, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
Float32
Stokes I n=112 median rel = 0.01% max rel = 0.06% median |Δ| = 1.893e-05 max |Δ| = 6.683e-05
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| μ=0.02, ϕ=0° | 0.4412 | 0.4413 | 6.617e-05 | 0.01% |
| μ=0.02, ϕ=30° | 0.3944 | 0.3944 | 5.984e-05 | 0.02% |
| μ=0.02, ϕ=60° | 0.3009 | 0.3009 | 4.720e-05 | 0.02% |
| μ=0.02, ϕ=90° | 0.2546 | 0.2547 | 4.100e-05 | 0.02% |
| μ=0.02, ϕ=120° | 0.3025 | 0.3025 | 4.754e-05 | 0.02% |
| μ=0.02, ϕ=150° | 0.3972 | 0.3973 | 6.041e-05 | 0.02% |
| μ=0.02, ϕ=180° | 0.4445 | 0.4445 | 6.683e-05 | 0.02% |
| μ=0.06, ϕ=0° | 0.3925 | 0.3925 | 1.111e-05 | 0.00% |
| μ=0.06, ϕ=30° | 0.3522 | 0.3522 | 7.896e-06 | 0.00% |
| μ=0.06, ϕ=60° | 0.2721 | 0.2721 | 1.507e-06 | 0.00% |
| μ=0.06, ϕ=90° | 0.2334 | 0.2334 | 1.544e-06 | 0.00% |
| μ=0.06, ϕ=120° | 0.2764 | 0.2764 | 1.972e-06 | 0.00% |
| μ=0.06, ϕ=150° | 0.3597 | 0.3597 | 8.758e-06 | 0.00% |
| μ=0.06, ϕ=180° | 0.4011 | 0.4011 | 1.209e-05 | 0.00% |
| μ=0.1, ϕ=0° | 0.3508 | 0.3508 | 3.849e-05 | 0.01% |
| μ=0.1, ϕ=30° | 0.3157 | 0.3158 | 3.260e-05 | 0.01% |
| μ=0.1, ϕ=60° | 0.2462 | 0.2462 | 2.092e-05 | 0.01% |
| μ=0.1, ϕ=90° | 0.2135 | 0.2135 | 1.550e-05 | 0.01% |
| μ=0.1, ϕ=120° | 0.2526 | 0.2526 | 2.223e-05 | 0.01% |
| μ=0.1, ϕ=150° | 0.3267 | 0.3268 | 3.487e-05 | 0.01% |
| μ=0.1, ϕ=180° | 0.3635 | 0.3635 | 4.111e-05 | 0.01% |
| μ=0.16, ϕ=0° | 0.2986 | 0.2986 | 1.742e-05 | 0.01% |
| μ=0.16, ϕ=30° | 0.2697 | 0.2697 | 1.356e-05 | 0.01% |
| μ=0.16, ϕ=60° | 0.2128 | 0.2128 | 6.017e-06 | 0.00% |
| μ=0.16, ϕ=90° | 0.1870 | 0.1870 | 2.727e-06 | 0.00% |
| μ=0.16, ϕ=120° | 0.2214 | 0.2214 | 7.566e-06 | 0.00% |
| μ=0.16, ϕ=150° | 0.2847 | 0.2847 | 1.625e-05 | 0.01% |
| μ=0.16, ϕ=180° | 0.3159 | 0.3159 | 2.052e-05 | 0.01% |
| μ=0.2, ϕ=0° | 0.2694 | 0.2694 | 2.371e-05 | 0.01% |
| μ=0.2, ϕ=30° | 0.2438 | 0.2438 | 1.943e-05 | 0.01% |
| μ=0.2, ϕ=60° | 0.1937 | 0.1937 | 1.104e-05 | 0.01% |
| μ=0.2, ϕ=90° | 0.1717 | 0.1717 | 7.527e-06 | 0.00% |
| μ=0.2, ϕ=120° | 0.2034 | 0.2034 | 1.313e-05 | 0.01% |
| μ=0.2, ϕ=150° | 0.2607 | 0.2607 | 2.306e-05 | 0.01% |
| μ=0.2, ϕ=180° | 0.2889 | 0.2889 | 2.790e-05 | 0.01% |
| μ=0.28, ϕ=0° | 0.2215 | 0.2215 | 1.912e-05 | 0.01% |
| μ=0.28, ϕ=30° | 0.2014 | 0.2014 | 1.947e-05 | 0.01% |
| μ=0.28, ϕ=60° | 0.1622 | 0.1622 | 2.009e-05 | 0.01% |
| μ=0.28, ϕ=90° | 0.1462 | 0.1462 | 2.017e-05 | 0.01% |
| μ=0.28, ϕ=120° | 0.1735 | 0.1734 | 1.936e-05 | 0.01% |
| μ=0.28, ϕ=150° | 0.2209 | 0.2209 | 1.822e-05 | 0.01% |
| μ=0.28, ϕ=180° | 0.2441 | 0.2441 | 1.767e-05 | 0.01% |
| μ=0.32, ϕ=0° | 0.2018 | 0.2019 | 8.618e-06 | 0.00% |
| μ=0.32, ϕ=30° | 0.1839 | 0.1839 | 6.080e-06 | 0.00% |
| μ=0.32, ϕ=60° | 0.1492 | 0.1492 | 1.239e-06 | 0.00% |
| μ=0.32, ϕ=90° | 0.1356 | 0.1356 | 4.455e-07 | 0.00% |
| μ=0.32, ϕ=120° | 0.1610 | 0.1610 | 3.521e-06 | 0.00% |
| μ=0.32, ϕ=150° | 0.2043 | 0.2043 | 1.002e-05 | 0.00% |
| μ=0.32, ϕ=180° | 0.2254 | 0.2254 | 1.315e-05 | 0.01% |
| μ=0.4, ϕ=0° | 0.1689 | 0.1689 | 9.797e-06 | 0.01% |
| μ=0.4, ϕ=30° | 0.1547 | 0.1547 | 7.495e-06 | 0.00% |
| μ=0.4, ϕ=60° | 0.1275 | 0.1275 | 3.164e-06 | 0.00% |
| μ=0.4, ϕ=90° | 0.1179 | 0.1179 | 1.858e-06 | 0.00% |
| μ=0.4, ϕ=120° | 0.1399 | 0.1399 | 5.845e-06 | 0.00% |
| μ=0.4, ϕ=150° | 0.1761 | 0.1761 | 1.213e-05 | 0.01% |
| μ=0.4, ϕ=180° | 0.1936 | 0.1936 | 1.514e-05 | 0.01% |
| μ=0.52, ϕ=0° | 0.1310 | 0.1310 | 1.993e-05 | 0.02% |
| μ=0.52, ϕ=30° | 0.1212 | 0.1212 | 1.969e-05 | 0.02% |
| μ=0.52, ϕ=60° | 0.1028 | 0.1028 | 1.914e-05 | 0.02% |
| μ=0.52, ϕ=90° | 0.0976 | 0.0976 | 1.875e-05 | 0.02% |
| μ=0.52, ϕ=120° | 0.1153 | 0.1153 | 1.879e-05 | 0.02% |
| μ=0.52, ϕ=150° | 0.1429 | 0.1429 | 1.906e-05 | 0.01% |
| μ=0.52, ϕ=180° | 0.1560 | 0.1560 | 1.923e-05 | 0.01% |
| μ=0.64, ϕ=0° | 0.1023 | 0.1023 | 2.145e-06 | 0.00% |
| μ=0.64, ϕ=30° | 0.0960 | 0.0960 | 1.264e-06 | 0.00% |
| μ=0.64, ϕ=60° | 0.0844 | 0.0844 | 2.581e-07 | 0.00% |
| μ=0.64, ϕ=90° | 0.0824 | 0.0824 | 2.539e-07 | 0.00% |
| μ=0.64, ϕ=120° | 0.0963 | 0.0963 | 2.138e-06 | 0.00% |
| μ=0.64, ϕ=150° | 0.1165 | 0.1165 | 5.406e-06 | 0.00% |
| μ=0.64, ϕ=180° | 0.1261 | 0.1261 | 6.938e-06 | 0.01% |
| μ=0.72, ϕ=0° | 0.0868 | 0.0868 | 2.791e-05 | 0.03% |
| μ=0.72, ϕ=30° | 0.0824 | 0.0824 | 2.607e-05 | 0.03% |
| μ=0.72, ϕ=60° | 0.0746 | 0.0746 | 2.292e-05 | 0.03% |
| μ=0.72, ϕ=90° | 0.0742 | 0.0742 | 2.307e-05 | 0.03% |
| μ=0.72, ϕ=120° | 0.0856 | 0.0856 | 2.832e-05 | 0.03% |
| μ=0.72, ϕ=150° | 0.1014 | 0.1015 | 3.542e-05 | 0.03% |
| μ=0.72, ϕ=180° | 0.1088 | 0.1089 | 3.871e-05 | 0.04% |
| μ=0.84, ϕ=0° | 0.0679 | 0.0678 | 3.142e-05 | 0.05% |
| μ=0.84, ϕ=30° | 0.0659 | 0.0658 | 3.080e-05 | 0.05% |
| μ=0.84, ϕ=60° | 0.0627 | 0.0627 | 2.975e-05 | 0.05% |
| μ=0.84, ϕ=90° | 0.0640 | 0.0639 | 2.993e-05 | 0.05% |
| μ=0.84, ϕ=120° | 0.0716 | 0.0716 | 3.194e-05 | 0.04% |
| μ=0.84, ϕ=150° | 0.0812 | 0.0812 | 3.456e-05 | 0.04% |
| μ=0.84, ϕ=180° | 0.0856 | 0.0856 | 3.577e-05 | 0.04% |
| μ=0.92, ϕ=0° | 0.0578 | 0.0578 | 8.321e-06 | 0.01% |
| μ=0.92, ϕ=30° | 0.0571 | 0.0571 | 8.285e-06 | 0.01% |
| μ=0.92, ϕ=60° | 0.0564 | 0.0564 | 8.180e-06 | 0.01% |
| μ=0.92, ϕ=90° | 0.0582 | 0.0581 | 8.011e-06 | 0.01% |
| μ=0.92, ϕ=120° | 0.0630 | 0.0630 | 7.819e-06 | 0.01% |
| μ=0.92, ϕ=150° | 0.0684 | 0.0684 | 7.657e-06 | 0.01% |
| μ=0.92, ϕ=180° | 0.0709 | 0.0709 | 7.594e-06 | 0.01% |
| μ=0.96, ϕ=0° | 0.0539 | 0.0539 | 2.187e-05 | 0.04% |
| μ=0.96, ϕ=30° | 0.0537 | 0.0537 | 2.181e-05 | 0.04% |
| μ=0.96, ϕ=60° | 0.0539 | 0.0539 | 2.179e-05 | 0.04% |
| μ=0.96, ϕ=90° | 0.0555 | 0.0555 | 2.206e-05 | 0.04% |
| μ=0.96, ϕ=120° | 0.0586 | 0.0586 | 2.269e-05 | 0.04% |
| μ=0.96, ϕ=150° | 0.0619 | 0.0619 | 2.338e-05 | 0.04% |
| μ=0.96, ϕ=180° | 0.0633 | 0.0632 | 2.369e-05 | 0.04% |
| μ=0.98, ϕ=0° | 0.0524 | 0.0524 | 2.877e-05 | 0.05% |
| μ=0.98, ϕ=30° | 0.0524 | 0.0525 | 2.884e-05 | 0.05% |
| μ=0.98, ϕ=60° | 0.0529 | 0.0529 | 2.921e-05 | 0.06% |
| μ=0.98, ϕ=90° | 0.0542 | 0.0542 | 3.014e-05 | 0.06% |
| μ=0.98, ϕ=120° | 0.0563 | 0.0563 | 3.156e-05 | 0.06% |
| μ=0.98, ϕ=150° | 0.0582 | 0.0583 | 3.290e-05 | 0.06% |
| μ=0.98, ϕ=180° | 0.0591 | 0.0591 | 3.346e-05 | 0.06% |
| μ=1.0, ϕ=0° | 0.0530 | 0.0530 | 2.230e-06 | 0.00% |
| μ=1.0, ϕ=30° | 0.0530 | 0.0530 | 2.230e-06 | 0.00% |
| μ=1.0, ϕ=60° | 0.0530 | 0.0530 | 2.230e-06 | 0.00% |
| μ=1.0, ϕ=90° | 0.0530 | 0.0530 | 2.230e-06 | 0.00% |
| μ=1.0, ϕ=120° | 0.0530 | 0.0530 | 2.230e-06 | 0.00% |
| μ=1.0, ϕ=150° | 0.0530 | 0.0530 | 2.230e-06 | 0.00% |
| μ=1.0, ϕ=180° | 0.0530 | 0.0530 | 2.230e-06 | 0.00% |
Stokes Q n=100 median rel = 0.02% max rel = 0.09% median |Δ| = 6.289e-06 max |Δ| = 3.804e-05 (excluded 12 cells with |truth| < 1.000e-02)
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| μ=0.02, ϕ=0° | -0.0175 | -0.0175 | 1.216e-05 | 0.07% |
| μ=0.02, ϕ=30° | -0.0648 | -0.0649 | 1.859e-05 | 0.03% |
| μ=0.02, ϕ=60° | -0.1596 | -0.1597 | 3.148e-05 | 0.02% |
| μ=0.02, ϕ=90° | -0.2075 | -0.2076 | 3.804e-05 | 0.02% |
| μ=0.02, ϕ=120° | -0.1612 | -0.1613 | 3.179e-05 | 0.02% |
| μ=0.02, ϕ=150° | -0.0676 | -0.0677 | 1.915e-05 | 0.03% |
| μ=0.02, ϕ=180° | -0.0208 | -0.0208 | 1.280e-05 | 0.06% |
| μ=0.06, ϕ=0° | -0.0177 | -0.0177 | 7.206e-06 | 0.04% |
| μ=0.06, ϕ=30° | -0.0594 | -0.0594 | 3.824e-06 | 0.01% |
| μ=0.06, ϕ=60° | -0.1433 | -0.1433 | 2.973e-06 | 0.00% |
| μ=0.06, ϕ=90° | -0.1866 | -0.1866 | 6.517e-06 | 0.00% |
| μ=0.06, ϕ=120° | -0.1476 | -0.1476 | 3.468e-06 | 0.00% |
| μ=0.06, ϕ=150° | -0.0669 | -0.0669 | 2.971e-06 | 0.00% |
| μ=0.06, ϕ=180° | -0.0263 | -0.0263 | 6.208e-06 | 0.02% |
| μ=0.1, ϕ=0° | -0.0153 | -0.0152 | 6.292e-06 | 0.04% |
| μ=0.1, ϕ=30° | -0.0527 | -0.0527 | 8.951e-08 | 0.00% |
| μ=0.1, ϕ=60° | -0.1284 | -0.1284 | 1.299e-05 | 0.01% |
| μ=0.1, ϕ=90° | -0.1682 | -0.1682 | 1.985e-05 | 0.01% |
| μ=0.1, ϕ=120° | -0.1347 | -0.1347 | 1.430e-05 | 0.01% |
| μ=0.1, ϕ=150° | -0.0638 | -0.0638 | 2.374e-06 | 0.00% |
| μ=0.1, ϕ=180° | -0.0280 | -0.0280 | 3.652e-06 | 0.01% |
| μ=0.16, ϕ=0° | -0.0099 | -0.0099 | 8.479e-06 | — |
| μ=0.16, ϕ=30° | -0.0427 | -0.0427 | 4.016e-06 | 0.01% |
| μ=0.16, ϕ=60° | -0.1091 | -0.1091 | 5.073e-06 | 0.00% |
| μ=0.16, ϕ=90° | -0.1451 | -0.1451 | 1.011e-05 | 0.01% |
| μ=0.16, ϕ=120° | -0.1178 | -0.1178 | 6.607e-06 | 0.01% |
| μ=0.16, ϕ=150° | -0.0577 | -0.0577 | 1.363e-06 | 0.00% |
| μ=0.16, ϕ=180° | -0.0272 | -0.0272 | 5.420e-06 | 0.02% |
| μ=0.2, ϕ=0° | -0.0061 | -0.0061 | 8.576e-06 | — |
| μ=0.2, ϕ=30° | -0.0365 | -0.0365 | 3.336e-06 | 0.01% |
| μ=0.2, ϕ=60° | -0.0982 | -0.0983 | 7.342e-06 | 0.01% |
| μ=0.2, ϕ=90° | -0.1322 | -0.1322 | 1.335e-05 | 0.01% |
| μ=0.2, ϕ=120° | -0.1080 | -0.1080 | 9.450e-06 | 0.01% |
| μ=0.2, ϕ=150° | -0.0534 | -0.0534 | 2.883e-07 | 0.00% |
| μ=0.2, ϕ=180° | -0.0256 | -0.0256 | 4.389e-06 | 0.02% |
| μ=0.28, ϕ=0° | 0.0013 | 0.0013 | 9.962e-06 | — |
| μ=0.28, ϕ=30° | -0.0256 | -0.0255 | 9.354e-06 | 0.04% |
| μ=0.28, ϕ=60° | -0.0804 | -0.0804 | 8.060e-06 | 0.01% |
| μ=0.28, ϕ=90° | -0.1113 | -0.1113 | 7.191e-06 | 0.01% |
| μ=0.28, ϕ=120° | -0.0916 | -0.0916 | 7.343e-06 | 0.01% |
| μ=0.28, ϕ=150° | -0.0451 | -0.0451 | 8.105e-06 | 0.02% |
| μ=0.28, ϕ=180° | -0.0212 | -0.0212 | 8.534e-06 | 0.04% |
| μ=0.32, ϕ=0° | 0.0048 | 0.0048 | 9.495e-06 | — |
| μ=0.32, ϕ=30° | -0.0208 | -0.0208 | 5.711e-06 | 0.03% |
| μ=0.32, ϕ=60° | -0.0730 | -0.0730 | 2.080e-06 | 0.00% |
| μ=0.32, ϕ=90° | -0.1028 | -0.1028 | 6.695e-06 | 0.01% |
| μ=0.32, ϕ=120° | -0.0848 | -0.0848 | 4.345e-06 | 0.01% |
| μ=0.32, ϕ=150° | -0.0411 | -0.0411 | 1.775e-06 | 0.00% |
| μ=0.32, ϕ=180° | -0.0188 | -0.0188 | 4.956e-06 | 0.03% |
| μ=0.4, ϕ=0° | 0.0112 | 0.0112 | 9.585e-06 | 0.09% |
| μ=0.4, ϕ=30° | -0.0124 | -0.0124 | 5.558e-06 | 0.04% |
| μ=0.4, ϕ=60° | -0.0607 | -0.0607 | 2.745e-06 | 0.00% |
| μ=0.4, ϕ=90° | -0.0887 | -0.0887 | 7.758e-06 | 0.01% |
| μ=0.4, ϕ=120° | -0.0730 | -0.0730 | 5.426e-06 | 0.01% |
| μ=0.4, ϕ=150° | -0.0338 | -0.0338 | 9.176e-07 | 0.00% |
| μ=0.4, ϕ=180° | -0.0136 | -0.0136 | 4.220e-06 | 0.03% |
| μ=0.52, ϕ=0° | 0.0197 | 0.0197 | 6.287e-06 | 0.03% |
| μ=0.52, ϕ=30° | -0.0020 | -0.0020 | 6.603e-06 | — |
| μ=0.52, ϕ=60° | -0.0465 | -0.0465 | 7.194e-06 | 0.02% |
| μ=0.52, ϕ=90° | -0.0727 | -0.0727 | 7.372e-06 | 0.01% |
| μ=0.52, ϕ=120° | -0.0590 | -0.0590 | 6.837e-06 | 0.01% |
| μ=0.52, ϕ=150° | -0.0236 | -0.0236 | 5.982e-06 | 0.03% |
| μ=0.52, ϕ=180° | -0.0053 | -0.0053 | 5.574e-06 | — |
| μ=0.64, ϕ=0° | 0.0270 | 0.0270 | 8.702e-06 | 0.03% |
| μ=0.64, ϕ=30° | 0.0064 | 0.0064 | 5.526e-06 | — |
| μ=0.64, ϕ=60° | -0.0359 | -0.0359 | 1.072e-06 | 0.00% |
| μ=0.64, ϕ=90° | -0.0608 | -0.0608 | 5.125e-06 | 0.01% |
| μ=0.64, ϕ=120° | -0.0477 | -0.0477 | 3.465e-06 | 0.01% |
| μ=0.64, ϕ=150° | -0.0141 | -0.0141 | 1.377e-06 | 0.01% |
| μ=0.64, ϕ=180° | 0.0033 | 0.0033 | 3.918e-06 | — |
| μ=0.72, ϕ=0° | 0.0313 | 0.0313 | 1.683e-05 | 0.05% |
| μ=0.72, ϕ=30° | 0.0112 | 0.0112 | 8.026e-06 | 0.07% |
| μ=0.72, ϕ=60° | -0.0302 | -0.0302 | 1.011e-05 | 0.03% |
| μ=0.72, ϕ=90° | -0.0543 | -0.0543 | 2.089e-05 | 0.04% |
| μ=0.72, ϕ=120° | -0.0412 | -0.0412 | 1.551e-05 | 0.04% |
| μ=0.72, ϕ=150° | -0.0079 | -0.0079 | 1.326e-06 | — |
| μ=0.72, ϕ=180° | 0.0093 | 0.0093 | 6.031e-06 | — |
| μ=0.84, ϕ=0° | 0.0367 | 0.0367 | 8.135e-06 | 0.02% |
| μ=0.84, ϕ=30° | 0.0170 | 0.0170 | 2.518e-06 | 0.01% |
| μ=0.84, ϕ=60° | -0.0233 | -0.0233 | 8.928e-06 | 0.04% |
| μ=0.84, ϕ=90° | -0.0463 | -0.0462 | 1.534e-05 | 0.03% |
| μ=0.84, ϕ=120° | -0.0322 | -0.0322 | 1.111e-05 | 0.03% |
| μ=0.84, ϕ=150° | 0.0016 | 0.0016 | 1.249e-06 | — |
| μ=0.84, ϕ=180° | 0.0189 | 0.0189 | 3.784e-06 | 0.02% |
| μ=0.92, ϕ=0° | 0.0392 | 0.0392 | 1.460e-06 | 0.00% |
| μ=0.92, ϕ=30° | 0.0198 | 0.0198 | 1.294e-06 | 0.01% |
| μ=0.92, ϕ=60° | -0.0198 | -0.0198 | 9.173e-07 | 0.00% |
| μ=0.92, ϕ=90° | -0.0416 | -0.0416 | 6.206e-07 | 0.00% |
| μ=0.92, ϕ=120° | -0.0263 | -0.0263 | 5.523e-07 | 0.00% |
| μ=0.92, ϕ=150° | 0.0085 | 0.0085 | 6.552e-07 | — |
| μ=0.92, ϕ=180° | 0.0262 | 0.0262 | 7.362e-07 | 0.00% |
| μ=0.96, ϕ=0° | 0.0398 | 0.0398 | 8.775e-06 | 0.02% |
| μ=0.96, ϕ=30° | 0.0205 | 0.0205 | 4.214e-06 | 0.02% |
| μ=0.96, ϕ=60° | -0.0185 | -0.0185 | 4.989e-06 | 0.03% |
| μ=0.96, ϕ=90° | -0.0396 | -0.0395 | 9.888e-06 | 0.03% |
| μ=0.96, ϕ=120° | -0.0232 | -0.0232 | 5.895e-06 | 0.03% |
| μ=0.96, ϕ=150° | 0.0124 | 0.0124 | 2.645e-06 | 0.02% |
| μ=0.96, ϕ=180° | 0.0305 | 0.0305 | 6.962e-06 | 0.02% |
| μ=0.98, ϕ=0° | 0.0397 | 0.0397 | 2.572e-05 | 0.06% |
| μ=0.98, ϕ=30° | 0.0205 | 0.0205 | 1.344e-05 | 0.07% |
| μ=0.98, ϕ=60° | -0.0181 | -0.0181 | 1.132e-05 | 0.06% |
| μ=0.98, ϕ=90° | -0.0385 | -0.0385 | 2.445e-05 | 0.06% |
| μ=0.98, ϕ=120° | -0.0215 | -0.0215 | 1.366e-05 | 0.06% |
| μ=0.98, ϕ=150° | 0.0147 | 0.0147 | 9.382e-06 | 0.06% |
| μ=0.98, ϕ=180° | 0.0330 | 0.0330 | 2.102e-05 | 0.06% |
| μ=1.0, ϕ=0° | 0.0376 | 0.0376 | 6.084e-06 | 0.02% |
| μ=1.0, ϕ=30° | 0.0188 | 0.0188 | 3.047e-06 | 0.02% |
| μ=1.0, ϕ=60° | -0.0188 | -0.0188 | 3.047e-06 | 0.02% |
| μ=1.0, ϕ=90° | -0.0376 | -0.0376 | 6.084e-06 | 0.02% |
| μ=1.0, ϕ=120° | -0.0188 | -0.0188 | 3.047e-06 | 0.02% |
| μ=1.0, ϕ=150° | 0.0188 | 0.0188 | 3.047e-06 | 0.02% |
| μ=1.0, ϕ=180° | 0.0376 | 0.0376 | 6.084e-06 | 0.02% |
Stokes U n=69 median rel = 0.02% max rel = 0.06% median |Δ| = 7.085e-06 max |Δ| = 2.278e-05 (excluded 43 cells with |truth| < 1.000e-02)
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| μ=0.02, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.02, ϕ=30° | 0.0439 | 0.0439 | 8.500e-06 | 0.02% |
| μ=0.02, ϕ=60° | 0.0736 | 0.0737 | 1.440e-05 | 0.02% |
| μ=0.02, ϕ=90° | 0.0813 | 0.0813 | 1.610e-05 | 0.02% |
| μ=0.02, ϕ=120° | 0.0671 | 0.0671 | 1.351e-05 | 0.02% |
| μ=0.02, ϕ=150° | 0.0374 | 0.0374 | 7.600e-06 | 0.02% |
| μ=0.02, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.06, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.06, ϕ=30° | 0.0443 | 0.0443 | 4.801e-06 | 0.01% |
| μ=0.06, ϕ=60° | 0.0705 | 0.0705 | 7.812e-06 | 0.01% |
| μ=0.06, ϕ=90° | 0.0715 | 0.0715 | 8.220e-06 | 0.01% |
| μ=0.06, ϕ=120° | 0.0534 | 0.0534 | 6.440e-06 | 0.01% |
| μ=0.06, ϕ=150° | 0.0272 | 0.0272 | 3.416e-06 | 0.01% |
| μ=0.06, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.1, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.1, ϕ=30° | 0.0443 | 0.0444 | 8.745e-06 | 0.02% |
| μ=0.1, ϕ=60° | 0.0676 | 0.0676 | 1.360e-05 | 0.02% |
| μ=0.1, ϕ=90° | 0.0636 | 0.0636 | 1.324e-05 | 0.02% |
| μ=0.1, ϕ=120° | 0.0425 | 0.0425 | 9.356e-06 | 0.02% |
| μ=0.1, ϕ=150° | 0.0192 | 0.0192 | 4.502e-06 | 0.02% |
| μ=0.1, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.16, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.16, ϕ=30° | 0.0441 | 0.0441 | 7.085e-06 | 0.02% |
| μ=0.16, ϕ=60° | 0.0638 | 0.0638 | 1.058e-05 | 0.02% |
| μ=0.16, ϕ=90° | 0.0540 | 0.0540 | 9.546e-06 | 0.02% |
| μ=0.16, ϕ=120° | 0.0296 | 0.0296 | 5.952e-06 | 0.02% |
| μ=0.16, ϕ=150° | 0.0099 | 0.0099 | 2.459e-06 | — |
| μ=0.16, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.2, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.2, ϕ=30° | 0.0437 | 0.0437 | 8.544e-06 | 0.02% |
| μ=0.2, ϕ=60° | 0.0616 | 0.0616 | 1.239e-05 | 0.02% |
| μ=0.2, ϕ=90° | 0.0487 | 0.0487 | 1.049e-05 | 0.02% |
| μ=0.2, ϕ=120° | 0.0228 | 0.0228 | 5.776e-06 | 0.03% |
| μ=0.2, ϕ=150° | 0.0050 | 0.0050 | 1.939e-06 | — |
| μ=0.2, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.28, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.28, ϕ=30° | 0.0429 | 0.0429 | 1.744e-06 | 0.00% |
| μ=0.28, ϕ=60° | 0.0576 | 0.0576 | 2.681e-06 | 0.00% |
| μ=0.28, ϕ=90° | 0.0402 | 0.0402 | 2.572e-06 | 0.01% |
| μ=0.28, ϕ=120° | 0.0121 | 0.0121 | 1.774e-06 | 0.01% |
| μ=0.28, ϕ=150° | -0.0027 | -0.0027 | 8.288e-07 | — |
| μ=0.28, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.32, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.32, ϕ=30° | 0.0425 | 0.0425 | 7.043e-06 | 0.02% |
| μ=0.32, ϕ=60° | 0.0559 | 0.0559 | 9.639e-06 | 0.02% |
| μ=0.32, ϕ=90° | 0.0368 | 0.0368 | 7.081e-06 | 0.02% |
| μ=0.32, ϕ=120° | 0.0077 | 0.0078 | 2.635e-06 | — |
| μ=0.32, ϕ=150° | -0.0057 | -0.0057 | 3.975e-08 | — |
| μ=0.32, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.4, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.4, ϕ=30° | 0.0416 | 0.0416 | 7.736e-06 | 0.02% |
| μ=0.4, ϕ=60° | 0.0529 | 0.0529 | 1.019e-05 | 0.02% |
| μ=0.4, ϕ=90° | 0.0309 | 0.0309 | 6.712e-06 | 0.02% |
| μ=0.4, ϕ=120° | 0.0006 | 0.0006 | 1.424e-06 | — |
| μ=0.4, ϕ=150° | -0.0107 | -0.0107 | 1.031e-06 | 0.01% |
| μ=0.4, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.52, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.52, ϕ=30° | 0.0404 | 0.0404 | 1.719e-07 | 0.00% |
| μ=0.52, ϕ=60° | 0.0492 | 0.0492 | 8.709e-08 | 0.00% |
| μ=0.52, ϕ=90° | 0.0241 | 0.0241 | 6.832e-07 | 0.00% |
| μ=0.52, ϕ=120° | -0.0075 | -0.0075 | 1.108e-06 | — |
| μ=0.52, ϕ=150° | -0.0163 | -0.0163 | 8.532e-07 | 0.01% |
| μ=0.52, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.64, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.64, ϕ=30° | 0.0391 | 0.0391 | 6.363e-06 | 0.02% |
| μ=0.64, ϕ=60° | 0.0459 | 0.0459 | 7.731e-06 | 0.02% |
| μ=0.64, ϕ=90° | 0.0186 | 0.0186 | 3.740e-06 | 0.02% |
| μ=0.64, ϕ=120° | -0.0138 | -0.0138 | 1.259e-06 | 0.01% |
| μ=0.64, ϕ=150° | -0.0206 | -0.0206 | 2.626e-06 | 0.01% |
| μ=0.64, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.72, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.72, ϕ=30° | 0.0383 | 0.0383 | 1.701e-05 | 0.04% |
| μ=0.72, ϕ=60° | 0.0439 | 0.0439 | 1.975e-05 | 0.04% |
| μ=0.72, ϕ=90° | 0.0153 | 0.0153 | 7.496e-06 | 0.05% |
| μ=0.72, ϕ=120° | -0.0174 | -0.0174 | 6.775e-06 | 0.04% |
| μ=0.72, ϕ=150° | -0.0230 | -0.0230 | 9.517e-06 | 0.04% |
| μ=0.72, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.84, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.84, ϕ=30° | 0.0369 | 0.0369 | 1.038e-05 | 0.03% |
| μ=0.84, ϕ=60° | 0.0407 | 0.0407 | 1.132e-05 | 0.03% |
| μ=0.84, ϕ=90° | 0.0106 | 0.0106 | 2.589e-06 | 0.02% |
| μ=0.84, ϕ=120° | -0.0224 | -0.0224 | 6.848e-06 | 0.03% |
| μ=0.84, ϕ=150° | -0.0263 | -0.0263 | 7.789e-06 | 0.03% |
| μ=0.84, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.92, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.92, ϕ=30° | 0.0356 | 0.0356 | 4.057e-07 | 0.00% |
| μ=0.92, ϕ=60° | 0.0382 | 0.0382 | 5.551e-07 | 0.00% |
| μ=0.92, ϕ=90° | 0.0071 | 0.0071 | 3.953e-07 | — |
| μ=0.92, ϕ=120° | -0.0259 | -0.0259 | 1.267e-07 | 0.00% |
| μ=0.92, ϕ=150° | -0.0285 | -0.0285 | 1.086e-08 | 0.00% |
| μ=0.92, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.96, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.96, ϕ=30° | 0.0348 | 0.0348 | 8.138e-06 | 0.02% |
| μ=0.96, ϕ=60° | 0.0366 | 0.0365 | 8.488e-06 | 0.02% |
| μ=0.96, ϕ=90° | 0.0049 | 0.0049 | 9.401e-07 | — |
| μ=0.96, ϕ=120° | -0.0281 | -0.0281 | 6.849e-06 | 0.02% |
| μ=0.96, ϕ=150° | -0.0299 | -0.0299 | 7.199e-06 | 0.02% |
| μ=0.96, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.98, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=0.98, ϕ=30° | 0.0341 | 0.0341 | 2.190e-05 | 0.06% |
| μ=0.98, ϕ=60° | 0.0354 | 0.0354 | 2.278e-05 | 0.06% |
| μ=0.98, ϕ=90° | 0.0034 | 0.0034 | 2.398e-06 | — |
| μ=0.98, ϕ=120° | -0.0294 | -0.0295 | 1.863e-05 | 0.06% |
| μ=0.98, ϕ=150° | -0.0307 | -0.0307 | 1.950e-05 | 0.06% |
| μ=0.98, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=1.0, ϕ=0° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=1.0, ϕ=30° | 0.0325 | 0.0325 | 5.267e-06 | 0.02% |
| μ=1.0, ϕ=60° | 0.0325 | 0.0325 | 5.267e-06 | 0.02% |
| μ=1.0, ϕ=90° | 0.0000 | 0.0000 | 0.000e+00 | — |
| μ=1.0, ϕ=120° | -0.0325 | -0.0325 | 5.267e-06 | 0.02% |
| μ=1.0, ϕ=150° | -0.0325 | -0.0325 | 5.267e-06 | 0.02% |
| μ=1.0, ϕ=180° | 0.0000 | 0.0000 | 0.000e+00 | — |
Case B — solar_tester scalar (Task 1)
🧪 VLIDORT regression table
23-layer atmosphere from VLIDORT's 2p8p3_solar_tester.f90, Stokes-I only, isotropic Henyey-Greenstein aerosol (g=0.8, ω̃=0.95, τ=0.5) with NMOMENTS=15 to match VLIDORT's NSTREAMS=8. SZA=35°, RAZ=0°, 3 viewing zenith angles. TOA upwelling and BOA downwelling Stokes-I.
Float64
Stokes I_TOA_up n=3 median rel = 0.05% max rel = 0.05% median |Δ| = 3.025e-05 max |Δ| = 3.155e-05
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| vza=10.0°, raz=0°, TOA-up | 0.0646 | 0.0646 | 2.995e-05 | 0.05% |
| vza=20.0°, raz=0°, TOA-up | 0.0640 | 0.0641 | 3.025e-05 | 0.05% |
| vza=40.0°, raz=0°, TOA-up | 0.0656 | 0.0656 | 3.155e-05 | 0.05% |
Stokes I_BOA_dn n=3 median rel = 0.06% max rel = 0.06% median |Δ| = 1.062e-04 max |Δ| = 2.359e-04
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| vza=10.0°, raz=0°, BOA-dn | 0.1049 | 0.1050 | 5.851e-05 | 0.06% |
| vza=20.0°, raz=0°, BOA-dn | 0.1825 | 0.1826 | 1.062e-04 | 0.06% |
| vza=40.0°, raz=0°, BOA-dn | 0.3861 | 0.3864 | 2.359e-04 | 0.06% |
Float32
Stokes I_TOA_up n=3 median rel = 0.04% max rel = 0.05% median |Δ| = 2.923e-05 max |Δ| = 2.945e-05
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| vza=10.0°, raz=0°, TOA-up | 0.0646 | 0.0646 | 2.945e-05 | 0.05% |
| vza=20.0°, raz=0°, TOA-up | 0.0640 | 0.0641 | 2.873e-05 | 0.04% |
| vza=40.0°, raz=0°, TOA-up | 0.0656 | 0.0656 | 2.923e-05 | 0.04% |
Stokes I_BOA_dn n=3 median rel = 0.05% max rel = 0.07% median |Δ| = 7.475e-05 max |Δ| = 1.871e-04
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| vza=10.0°, raz=0°, BOA-dn | 0.1049 | 0.1050 | 7.475e-05 | 0.07% |
| vza=20.0°, raz=0°, BOA-dn | 0.1825 | 0.1826 | 4.713e-05 | 0.03% |
| vza=40.0°, raz=0°, BOA-dn | 0.3862 | 0.3864 | 1.871e-04 | 0.05% |
Case C — solar_tester vector Stokes-IQU (Task 1)
🧪 VLIDORT regression table
Same 23-layer atmosphere as Case B but with vector RT (Stokes-IQU) and the PROBLEM-III aerosol Greek coefficients shipped with VLIDORT. Q/U truth signs flipped to vSmartMOM's Hovenier convention.
Float64
Stokes I_TOA_up n=3 median rel = 0.05% max rel = 0.05% median |Δ| = 3.235e-05 max |Δ| = 3.251e-05
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| vza=10.0°, raz=10°, TOA-up | 0.0696 | 0.0696 | 3.251e-05 | 0.05% |
| vza=20.0°, raz=10°, TOA-up | 0.0677 | 0.0677 | 3.219e-05 | 0.05% |
| vza=40.0°, raz=10°, TOA-up | 0.0664 | 0.0664 | 3.235e-05 | 0.05% |
Stokes I_BOA_dn n=3 median rel = 0.06% max rel = 0.06% median |Δ| = 8.916e-05 max |Δ| = 2.148e-04
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| vza=10.0°, raz=10°, BOA-dn | 0.0992 | 0.0992 | 5.472e-05 | 0.06% |
| vza=20.0°, raz=10°, BOA-dn | 0.1554 | 0.1555 | 8.916e-05 | 0.06% |
| vza=40.0°, raz=10°, BOA-dn | 0.3528 | 0.3530 | 2.148e-04 | 0.06% |
Stokes Q_TOA_up n=3 median rel = 0.03% max rel = 0.04% median |Δ| = 6.328e-06 max |Δ| = 9.096e-06
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| vza=10.0°, raz=10°, TOA-up | 0.0128 | 0.0128 | 4.478e-06 | 0.04% |
| vza=20.0°, raz=10°, TOA-up | 0.0182 | 0.0182 | 6.328e-06 | 0.03% |
| vza=40.0°, raz=10°, TOA-up | 0.0280 | 0.0280 | 9.096e-06 | 0.03% |
Stokes Q_BOA_dn n=3 median rel = 0.08% max rel = 0.11% median |Δ| = 1.025e-06 max |Δ| = 2.053e-06
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| vza=10.0°, raz=10°, BOA-dn | 0.0027 | 0.0027 | 1.025e-06 | 0.04% |
| vza=20.0°, raz=10°, BOA-dn | -0.0007 | -0.0007 | 8.353e-07 | 0.11% |
| vza=40.0°, raz=10°, BOA-dn | -0.0025 | -0.0025 | 2.053e-06 | 0.08% |
Stokes U_TOA_up n=3 median rel = 0.04% max rel = 0.04% median |Δ| = 1.625e-06 max |Δ| = 2.177e-06
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| vza=10.0°, raz=10°, TOA-up | 0.0037 | 0.0037 | 1.297e-06 | 0.04% |
| vza=20.0°, raz=10°, TOA-up | 0.0046 | 0.0046 | 1.625e-06 | 0.04% |
| vza=40.0°, raz=10°, TOA-up | 0.0062 | 0.0062 | 2.177e-06 | 0.04% |
Stokes U_BOA_dn n=3 median rel = 0.06% max rel = 0.12% median |Δ| = 1.043e-07 max |Δ| = 6.449e-07
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| vza=10.0°, raz=10°, BOA-dn | -0.0016 | -0.0016 | 6.449e-07 | 0.04% |
| vza=20.0°, raz=10°, BOA-dn | -0.0002 | -0.0002 | 1.043e-07 | 0.06% |
| vza=40.0°, raz=10°, BOA-dn | -0.0001 | -0.0001 | 6.588e-08 | 0.12% |
Float32
Stokes I_TOA_up n=3 median rel = 0.06% max rel = 0.07% median |Δ| = 4.422e-05 max |Δ| = 4.698e-05
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| vza=10.0°, raz=10°, TOA-up | 0.0696 | 0.0696 | 4.422e-05 | 0.06% |
| vza=20.0°, raz=10°, TOA-up | 0.0677 | 0.0677 | 4.337e-05 | 0.06% |
| vza=40.0°, raz=10°, TOA-up | 0.0664 | 0.0664 | 4.698e-05 | 0.07% |
Stokes I_BOA_dn n=3 median rel = 0.08% max rel = 0.09% median |Δ| = 8.752e-05 max |Δ| = 2.848e-04
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| vza=10.0°, raz=10°, BOA-dn | 0.0991 | 0.0992 | 8.752e-05 | 0.09% |
| vza=20.0°, raz=10°, BOA-dn | 0.1555 | 0.1555 | 5.903e-05 | 0.04% |
| vza=40.0°, raz=10°, BOA-dn | 0.3527 | 0.3530 | 2.848e-04 | 0.08% |
Stokes Q_TOA_up n=3 median rel = 0.03% max rel = 0.04% median |Δ| = 6.072e-06 max |Δ| = 9.280e-06
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| vza=10.0°, raz=10°, TOA-up | 0.0128 | 0.0128 | 4.530e-06 | 0.04% |
| vza=20.0°, raz=10°, TOA-up | 0.0182 | 0.0182 | 6.072e-06 | 0.03% |
| vza=40.0°, raz=10°, TOA-up | 0.0280 | 0.0280 | 9.280e-06 | 0.03% |
Stokes Q_BOA_dn n=3 median rel = 0.14% max rel = 0.18% median |Δ| = 1.304e-06 max |Δ| = 3.401e-06
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| vza=10.0°, raz=10°, BOA-dn | 0.0027 | 0.0027 | 8.281e-07 | 0.03% |
| vza=20.0°, raz=10°, BOA-dn | -0.0007 | -0.0007 | 1.304e-06 | 0.18% |
| vza=40.0°, raz=10°, BOA-dn | -0.0025 | -0.0025 | 3.401e-06 | 0.14% |
Stokes U_TOA_up n=3 median rel = 0.03% max rel = 0.04% median |Δ| = 1.542e-06 max |Δ| = 2.279e-06
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| vza=10.0°, raz=10°, TOA-up | 0.0037 | 0.0037 | 1.293e-06 | 0.03% |
| vza=20.0°, raz=10°, TOA-up | 0.0046 | 0.0046 | 1.542e-06 | 0.03% |
| vza=40.0°, raz=10°, TOA-up | 0.0062 | 0.0062 | 2.279e-06 | 0.04% |
Stokes U_BOA_dn n=3 median rel = 0.16% max rel = 0.19% median |Δ| = 3.247e-07 max |Δ| = 6.857e-07
| Geometry | Modeled | Truth | |Δ| | |Δ|/|truth| |
|---|---|---|---|---|
| vza=10.0°, raz=10°, BOA-dn | -0.0016 | -0.0016 | 6.857e-07 | 0.04% |
| vza=20.0°, raz=10°, BOA-dn | -0.0002 | -0.0002 | 3.247e-07 | 0.19% |
| vza=40.0°, raz=10°, BOA-dn | -0.0001 | -0.0001 | 8.909e-08 | 0.16% |
Reproducing
bash
julia --project=docs docs/build_benchmarks.jlReference data lives under test/vlidort_baseline/reference_data/ (Siewert + VLIDORT-shipped) and test/benchmarks/natraj_trues.jl (Natraj 2009 transcribed). Configurations are at test/vlidort_baseline/configs/ and test/benchmarks/natraj.yaml.