ISOFIT Atmospheric Correction — Mongolia

1. Why Atmospheric Correction Matters

An imaging spectrometer measures at-sensor radiance \(L(\lambda)\) — a tangled superposition of light scattered by atmospheric molecules and aerosols, light reflected from the surface that transits the atmosphere twice, and the spherical-albedo coupling between the two. Recovering surface reflectance \(\rho(\lambda)\) requires inverting that radiative transfer chain pixel-by-pixel.

The algorithms here apply to a family of NASA imaging spectrometers — AVIRIS-Classic, AVIRIS-NG, AVIRIS-3, and EMIT — that share a common forward-model architecture in ISOFIT. The 2 scenes presented here come from EMIT.

2. The ISOFIT Algorithm

2.1 The Forward Model

ISOFIT writes the at-sensor radiance as the composition of a surface model \(\rho(\mathbf{x}_s; \lambda)\) and an atmosphere model \(\mathcal{A}(\mathbf{x}_a; \lambda)\):

where \(\mathbf{R}\) applies the spectral response of the instrument and \(\mathbf{x}_s\), \(\mathbf{x}_a\) are the surface- and atmospheric-state vectors. The state \(\mathbf{x}_a\) is kept low-dimensional (column water vapor, AOT at 550 nm) because well-mixed gases can be held at climatology with negligible error in retrieved \(\rho\).

2.2 Accelerated Optimal Estimation

OE inverts the forward model under a Gaussian prior and Gaussian instrument noise. The cost is:

The Accelerated formulation collapses the >280-dimensional Levenberg–Marquardt iteration into a closed-form surface inversion wrapped in a small two-dimensional outer search over the atmospheric state, so retrievals are orders of magnitude faster while still reporting a full posterior covariance.

2.3 Radiative Transfer Engines and sRTMnet

The forward model needs \(\{L_a, T_\downarrow T_\uparrow, s\}\) at every wavelength for every plausible atmospheric state. ISOFIT supports MODTRAN 6 (operational JPL reference), LibRadTran (open-source), 6S (open-source, fast), and sRTMnet, a deep neural emulator trained on millions of 6S calls. We use sRTMnet for both EMIT and AVIRIS pipelines.

2.4 The Multicomponent Surface Prior

Without a prior, OE on a 285-channel reflectance spectrum is ill-posed. The multicomponent surface model partitions a global reflectance training set (vegetation, soils, water, mineral surfaces, snow) by k-means and assigns a Gaussian prior to each cluster; per pixel, ISOFIT picks the most likely component from a radiance-domain pre-classification, then uses that component's prior in the OE inversion.

3. The "Standard" Reflectance We Compare Against

We compare to the official EMIT L2A surface reflectance product as distributed by NASA's LP DAAC. Each scene's NetCDF header records its provenance:

title:        EMIT L2A Estimated Surface Reflectance 60 m V001
sensor:       EMIT (Earth Surface Mineral Dust Source Investigation)
platform:     ISS
institution:  NASA Jet Propulsion Laboratory / California Institute of Technology
software_build_version: 010621/010627
product_version: V001

The "standard" is the JPL operational ISOFIT pipeline (MODTRAN-based) running inside the EMIT Science Data System. Our local retrieval uses the open-source ISOFIT 3.7.x release with the sRTMnet neural emulator and a default multicomponent surface configuration:

description = L2A Analytical per-pixel surface retrieval
              (segmentation_size=40, engine=sRTMnet, isofit_version=3.7.x)
samples = 1242, lines = 1280, bands = 285
interleave = bil, no data value = -9999

Both retrievals operate on the same EMIT L1B radiance cube. Differences come from the radiative-transfer engine (full MODTRAN vs. sRTMnet emulator), the surface library configuration, and the segmentation size used to amortize OE across spatially coherent blocks.

4. Scene Comparisons

Each scene below presents four primary diagnostics — RGB, mean+PC-pure spectra, 18-PC composite grid, and eigenvalue spectrum — followed by a collapsible accordion of fifteen mineral spectral indices.

Mongolia 1 — 11 Feb 2025

Figure 1. True-color render (R=660, G=560, B=470 nm; 2–98% stretch). Open circles mark the six PC-pure pixel locations whose spectra appear in Figure 2; pixels are at identical (row, col) on both panels.

Figure 2. Mean (black) and six PC-pure pixel spectra. Light-gray fill = 1–99% envelope across all valid pixels. Shaded vertical bands at 1250–1500 nm and 1750–2000 nm mark the masked water regions (lines break to NaN). Y-axis is bounded to the mean and selected spectra.

Figure 3. PCA composites — six rows of (R,G,B) = (PCₖ, PCₖ₊₁, PCₖ₊₂) for k = 1,4,7,10,13,16. Left = standard L2A; right = local ISOFIT.

Figure 4. Eigenvalue spectrum in log scale.

Mineral spectral indices for Mongolia 1 — 11 Feb 2025 (15 maps)

FEAI — Ferric iron alteration

FEAI = R(2.165)/R(0.82) + R(0.56)/R(0.66) [µm]

FEI_simple — Ferrous iron

FEI_simple = R(2.165)/R(1.65) [µm]

CLAY_TM — Generic clay (TM5/TM7 analog)

CLAY_TM = R(1.65)/R(2.205) [µm]

CLAI — Argillic alteration (alunite/kaolinite)

CLAI = (R(1.65)+R(2.205))/R(2.165) [µm]

ALI — Alunite (Ninomiya)

ALI = R(2.260)²/(R(2.165)·R(2.330)) [µm]

KAI1 — Kaolinite slope

KAI1 = R(2.260)/R(2.165) [µm]

KLI — Kaolinite doublet

KLI = (R(1.65)/R(2.165))·(R(2.330)/R(2.205)) [µm]

KAI3 — Kaolinite (alt 3-band)

KAI3 = (R(1.65)+R(2.260))/R(2.205) [µm]

OHI — OH-bearing minerals

OHI = (R(2.260)/R(2.205))·(R(1.65)/R(2.205)) [µm]

OHI3 — OH near 2.17 µm

OHI3 = (R(1.65)·R(2.260))/R(2.165)² [µm]

CLI — Calcite

CLI = (R(2.205)/R(2.330))·(R(2.395)/R(2.330)) [µm]

DOLI — Dolomite

DOLI = (R(2.205)+R(2.330))/R(2.260) [µm]

MGAI — Mg-OH/chlorite/epidote

MGAI = (R(2.395)+R(2.205))/R(2.330) [µm]

MONI — Montmorillonite

MONI = (R(1.65)+R(2.205))/R(2.260) [µm]

PRAI — Propylitic alteration

PRAI = (R(2.260)+R(2.395))/R(2.330) [µm]

Mongolia 2 — 03 Aug 2025

Figure 5. True-color render (R=660, G=560, B=470 nm; 2–98% stretch). Open circles mark the six PC-pure pixel locations whose spectra appear in Figure 6; pixels are at identical (row, col) on both panels.

Figure 6. Mean (black) and six PC-pure pixel spectra. Light-gray fill = 1–99% envelope across all valid pixels. Shaded vertical bands at 1250–1500 nm and 1750–2000 nm mark the masked water regions (lines break to NaN). Y-axis is bounded to the mean and selected spectra.

Figure 7. PCA composites — six rows of (R,G,B) = (PCₖ, PCₖ₊₁, PCₖ₊₂) for k = 1,4,7,10,13,16. Left = standard L2A; right = local ISOFIT.

Figure 8. Eigenvalue spectrum in log scale.

Mineral spectral indices for Mongolia 2 — 03 Aug 2025 (15 maps)

FEAI — Ferric iron alteration

FEAI = R(2.165)/R(0.82) + R(0.56)/R(0.66) [µm]

FEI_simple — Ferrous iron

FEI_simple = R(2.165)/R(1.65) [µm]

CLAY_TM — Generic clay (TM5/TM7 analog)

CLAY_TM = R(1.65)/R(2.205) [µm]

CLAI — Argillic alteration (alunite/kaolinite)

CLAI = (R(1.65)+R(2.205))/R(2.165) [µm]

ALI — Alunite (Ninomiya)

ALI = R(2.260)²/(R(2.165)·R(2.330)) [µm]

KAI1 — Kaolinite slope

KAI1 = R(2.260)/R(2.165) [µm]

KLI — Kaolinite doublet

KLI = (R(1.65)/R(2.165))·(R(2.330)/R(2.205)) [µm]

KAI3 — Kaolinite (alt 3-band)

KAI3 = (R(1.65)+R(2.260))/R(2.205) [µm]

OHI — OH-bearing minerals

OHI = (R(2.260)/R(2.205))·(R(1.65)/R(2.205)) [µm]

OHI3 — OH near 2.17 µm

OHI3 = (R(1.65)·R(2.260))/R(2.165)² [µm]

CLI — Calcite

CLI = (R(2.205)/R(2.330))·(R(2.395)/R(2.330)) [µm]

DOLI — Dolomite

DOLI = (R(2.205)+R(2.330))/R(2.260) [µm]

MGAI — Mg-OH/chlorite/epidote

MGAI = (R(2.395)+R(2.205))/R(2.330) [µm]

MONI — Montmorillonite

MONI = (R(1.65)+R(2.205))/R(2.260) [µm]

PRAI — Propylitic alteration

PRAI = (R(2.260)+R(2.395))/R(2.330) [µm]

5. Discussion

Across all scenes the true-color renders are visually indistinguishable: both retrievals flatten the atmospheric path radiance and recover surface color contrast. The PC-pure spectra agree closely on broad continuum shape but show systematic differences at the edges of the masked water regions — exactly the wavelengths where MODTRAN and the sRTMnet emulator differ most. The eigenvalue spectra are nearly parallel in their leading components but diverge in the tail, where atmospheric residuals live.

That divergence is informative. A perfect atmospheric correction would push residual covariance toward isotropic noise — a flat tail in log-eigenvalue space. Curvature in the tail indicates structured residuals that PCA can latch onto. We use that curvature, together with the higher-order PC composites, as a quick visual diagnostic of atmospheric-correction quality without ever needing ground truth.

6. Reproducibility

All figures here are generated by a single self-contained Python script (digital_whitepaper/build_whitepaper.py) that loads the standard L2A from the LP DAAC NetCDF, the local ISOFIT cube via the spectral ENVI reader, applies the water-band mask, fits PCA on a 80,000-pixel subsample, picks PC-pure pixels, and renders all comparison figures. The local ISOFIT runs are produced by:

# EMIT scene → ISOFIT 3.7.x + sRTMnet
from isofit.utils.apply_oe import apply_oe
apply_oe(
    input_radiance     = "<flight>_rdn",
    input_loc          = "<flight>_loc",
    input_obs          = "<flight>_obs",
    sensor             = "emit",
    surface_path       = "data/surface/emit_surface.mat",
    emulator_base      = ".../sRTMnet_v100.h5",
    segmentation_size  = 40,
    presolve           = True,
    analytical_line    = True,
)