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Efficient Neural-Network-Based High-Resolution Radiative Transfer for CO___ Retrieval, and Application to Interferometric Sensing

Jordan Lontsi Tedongmo, Yann Ferrec, Laurence Croizé, Pablo Musé, Gabriele Facciolo, Andrés Almansa

arXiv:2608.14645v1cs.LGphysics.ao-ph

TL;DR

High-resolution radiative-transfer retrievals for greenhouse gases are computationally demanding, limiting efficient NanoCarb processing. This paper develops an MLP radiative-transfer surrogate integrated with the NanoCarb forward model, achieving low retrieval discrepancies while reducing computation from nearly a month to a few GPU hours.

  • Problem

    Existing greenhouse-gas satellite missions have insufficient spatial resolution, coverage, or revisit frequency for precise anthropogenic-emission detection and quantification.

  • Method

    The study trains a feedforward MLP with joint radiance and Jacobian losses, then integrates it into NanoCarb retrievals for CO2 and surface albedo.

  • Results

    Realistic airborne scenarios showed NN-based CO2 retrievals matching full-physics patterns with additional bias and standard deviation below 0.5 ppm, reducing processing from nearly a month to a few GPU hours.

  • Takeaways & Limitations

    The NanoCarb-integrated neural-network surrogate provides a fast forward model that preserves radiance accuracy and supports CO2 retrieval under the tested conditions.

Abstract

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Studying climate change requires reducing uncertainties in CO2 and CH4 emission estimates to better distinguish anthropogenic from natural sources, which motivates spaceborne measurements with improved revisit frequency and spatial coverage. In this context, the Horizon Europe SCARBOn project assesses a low-cost satellite constellation featuring the NanoCarb imaging interferometer as its core sensor for monitoring CO2 and CH4 emissions in the atmosphere. However, estimating CO2 and CH4 concentrations with high revisit and spatial coverage poses significant challenges: full-physics retrieval algorithms commonly used rely on repeated high-resolution radiative transfer (RT) simulations, which are computationally expensive when using line-by-line RT models. As an alternative, we propose in this study a feedforward multilayer perceptron (MLP) surrogate designed to accurately and efficiently predict top-of-atmosphere radiances in the CO2 weak band, using a combined mean absolute error (MAE) loss on radiances and RT Jacobians to preserve both spectral accuracy and sensitivity to geophysical parameters. Coupling the MLP-based RT surrogate with the NanoCarb instrumental response yields an efficient and precise forward model for NanoCarb measurements, which shows promising results for CO2 concentration retrieval.

I. INTRODUCTION

The introduction motivates improved monitoring of CO2 and CH4 emissions because existing satellite missions lack sufficient spatial resolution, coverage, or revisit frequency. It presents a fast neural-network surrogate for high-resolution CO2 radiative transfer, integrated into the NanoCarb forward model and evaluated for retrievals.

  • Motivation: Existing GHG satellite missions lack sufficient spatial resolution, coverage, or revisit frequency to quantify anthropogenic emissions with the required precision.This limitation motivates improved spatio-temporal monitoring of CO2 and CH4 emissions.
  • SCARBOn project: The Horizon Europe SCARBOn project assesses a low-cost satellite constellation using NanoCarb to monitor atmospheric CO2 and CH4 emissions.NanoCarb is described as the constellation’s miniature GHG sensor and core sensor.
  • Retrieval challenge: NanoCarb full-physics retrieval requires high-resolution radiative-transfer calculations across the sensor-response domain, creating a computational burden.The passage frames this burden as a motivation for replacing physics-based calculations with neural-network surrogates.
  • Contribution: The paper proposes a fast and accurate neural-network surrogate for high-resolution radiative transfer in the CO2 weak absorption band.The study targets a radiative-transfer surrogate rather than directly solving the inverse problem.
  • Contribution: Integrated into the NanoCarb forward model, the surrogate is evaluated for CO2 total-column and surface-albedo retrievals, including realistic airborne simulations.The evaluation covers both retrieval types and airborne simulation scenarios.

II. FORWARD AND INVERSE MODELS FOR CO2 ESTIMATION FROM NANOCARB MEASUREMENTS · A. NanoCarb instrumental model

NanoCarb is modeled as a static Fourier-transform imaging spectrometer whose Fabry–Perot interferometers and microlens array provide co-registered, interferometrically modulated views for snapshot measurements. Its forward model integrates Fabry–Perot-modulated high-resolution radiance, while gas-tuned interferograms and added detector noise support realistic CO2 observations.

  • A. NanoCarb instrumental model: NanoCarb combines low-finesse Fabry–Perot interferometers with a microlens array to produce multiple co-registered, differently modulated scene views in snapshot acquisition mode.The sensor is designed to measure CO2 and CH4 with wide-swath, high-spectral-resolution observations.
  • A. NanoCarb instrumental model: The instrumental model predicts focal-plane intensity as a function of incoming radiance using normalized Fabry–Perot transmission.For monochromatic radiation, the transmission is approximated by T_FP ≈ 1/(1 + M sin^2(φ/2)).
  • A. NanoCarb instrumental model: The transmission phase is φ = 2πσδ, where σ is wavenumber and δ is optical path difference, while M is a reflectivity-dependent finesse term.The phase shift and finesse determine the interferometric modulation.
  • A. NanoCarb instrumental model: Single-plate intensity is obtained by integrating Fabry–Perot-modulated radiance over the spectral band ∆σ.The integrated signal uses instrument transmission, optical–radiometric efficiency, incoming spectral radiance, and physical constants.
  • A. NanoCarb instrumental model: Simulating NanoCarb measurements requires high-resolution spectral radiances generated with a line-by-line radiative transfer model.The incoming radiance corresponds to the observed atmospheric column denoted by c_j.
  • A. NanoCarb instrumental model: Measurements across Fabry–Perot plates form a partial interferogram I whose dimension equals the number of FP thicknesses, with each component associated with a distinct OPD.The interferometric states therefore encode measurements at different optical path differences.
  • A. NanoCarb instrumental model: Thicknesses are tuned to target-gas absorption features, producing interferograms highly sensitive to CO2, CH4, or O2 concentration while reducing sensitivity to surface and atmospheric parameters.The response depends on FP thickness, incidence angle, temperature, and refractive index.
  • A. NanoCarb instrumental model: Realistic NanoCarb observations add Poisson photon noise and Gaussian read-out noise to ideal noiseless interferograms.This noise modeling reproduces signal degradation encountered in real measurements.

B. Simulation Setup for Realistic NanoCarb Measurements

The study evaluates the proposed approach using realistic NanoCarb airborne simulations derived from measured surface albedo and CO2 concentration maps. Simulations represent two resampled scenarios under specified atmospheric, altitude, spatial-resolution, and multi-angle observing conditions.

  • Measurement inputs: Simulated measurements combined airborne hyperspectral surface-albedo data with AVIRIS-NG CO2 total-column maps containing industrial emission plumes.Surface albedo came from AISA FENIX reflectance data, while CO2 maps came from the AVIRIS-NG Benchmark Dataset for Carbon Dioxide Plumes.
  • Scenario construction: Two distinct scenarios were constructed from these datasets and resampled to NanoCarb’s expected spatial resolution.The scenarios were designed from the real-data inputs before simulation.
  • Simulation configuration: Simulations assumed an airborne NanoCarb configuration at 3 km altitude with 15 m spatial resolution in an aerosol-free AFGL midlatitude-summer atmosphere.The high acquisition rate allowed each ground pixel to be observed from multiple viewing angles during scene overpass.

C. Retrieval algorithm

The retrieval algorithm uses Bayesian optimal estimation to jointly retrieve atmospheric CO2 total column and surface albedo from NanoCarb measurements. It evaluates a forward model with Gaussian measurement noise and prior constraints, then solves the resulting nonlinear least-squares problem with Levenberg–Marquardt.

  • Retrieval targets and assumptions: NanoCarb retrieves atmospheric CO2 total column primarily, while jointly estimating surface albedo because interferograms are highly albedo-sensitive.Surface pressure, sun–observation geometry, and water vapor and temperature profiles are assumed known.
  • Bayesian formulation: The framework follows a Bayesian formulation using classical Optimal Estimation to estimate a unique atmospheric state from independent views for each ground pixel.The estimator maximizes the posterior probability formed from the measurement likelihood and prior distribution.
  • Forward model and priors: The likelihood uses the NanoCarb forward model for each acquisition, with measurement noise assumed Gaussian and acquisition-dependent standard deviation σ(i).The forward model is evaluated at the corresponding observation angle.
  • Optimization: A Gaussian prior centered on ¯c with covariance matrix S makes the MAP estimator equivalent to a nonlinear least-squares minimization.The resulting optimization problem is solved using the Levenberg–Marquardt algorithm.

III. NEURAL NETWORK FORWARD MODEL · A. Training Data

The neural-network radiative-transfer model was trained and tested on synthetic scenarios spanning atmospheric, surface, and geometric variables relevant to CO2 weak-band radiance formation. Independent TIGR profiles and NanoCarb simulations supported end-to-end evaluation and broad geospatial representativity.

  • A. Training Data: Synthetic training data sampled the main atmospheric and surface parameters governing CO2 weak-band radiance formation at 3 km altitude under aerosol-free conditions.The inputs included CO2 total column, surface properties, solar–sensor geometry, and vertical temperature and water-vapor profiles.
  • A. Training Data: Training inputs included CO2 total column, albedo, altitude, pressure, solar–sensor geometry, and vertical profiles of temperature and water vapor.These variables were sampled according to the distributions summarized in Table I.
  • A. Training Data: The independent test set contained approximately 10,000 scenarios generated with 200 TIGR temperature and water-vapor profiles excluded from training.Remaining parameters were sampled as in Table I, with albedo uniformly spanning 0.05–0.7.
  • A. Training Data: The test scenarios used atmospheric profiles withheld from training to assess the neural-network forward model independently.This separation was implemented through the 200 excluded TIGR temperature and water-vapor profiles.
  • A. Training Data: High-resolution radiances and corresponding NanoCarb interferograms were simulated for end-to-end evaluation of the forward model.The simulations connected the radiative-transfer predictions with the instrument-level measurement representation.
  • A. Training Data: Broad parameter sampling combined with representative TIGR atmospheric profiles to cover realistic atmospheric and surface conditions with good geospatial representativity.This dataset-design rationale links parameter breadth and profile representativeness to the intended geographic coverage.

B. Neural Network architecture and Training

The radiative-transfer surrogate is a normalized feedforward MLP that predicts 7,499-channel radiance spectra from 20 input features. Training jointly minimizes radiance and Jacobian losses, with Jacobian weighting designed to preserve physically consistent sensitivities while regularizing the model.

  • Architecture: The surrogate concatenates 20 normalized inputs into one feature vector and predicts a full high-resolution radiance spectrum with 7,499 output channels.Each spectral channel corresponds to one output neuron.
  • Training objective: Training optimizes network weights and biases using a joint loss on normalized radiances and radiative-transfer Jacobians.The normalized target spectrum is derived from the radiative-transfer-computed radiance spectrum.
  • Training objective: The Jacobian loss enforces physically consistent sensitivities to input parameters and regularizes training.Reference Jacobians use finite differences, whereas predicted Jacobians use forward-mode automatic differentiation.
  • Training objective: Jacobian-loss weights balance input-parameter contributions according to mean radiance and mean Jacobian magnitudes.The weighting is defined proportionally to ymean divided by the absolute mean Jacobian magnitude for each input parameter.
  • Architecture: The selected MLP uses three hidden layers with 100, 500, and 3,500 neurons and ELU activations.This configuration provided the best trade-off between accuracy and computational efficiency.

IV. RESULTS

The NN-based NanoCarb forward model reproduces radiances and partial interferograms accurately, while introducing negligible retrieval errors and substantially reducing computation time. In realistic airborne scenarios, NN-based retrievals closely match full-physics results, with runtime falling from nearly one month to a few hours on GPU.

  • Forward-model accuracy: MARE remains below 0.04% across all channels and reaches at most 0.1% for the lowest-albedo cases.The evaluation used ≈10,000 independently simulated test cases.
  • Retrieval accuracy: 0.33% mean and 0.17% median relative errors occur for XCO2, compared with 0.02% and 0.009% for surface albedo.These errors were measured over ≈10,000 noise-free simulated NanoCarb measurements.
  • Computational efficiency: 150× lower CPU and more than 500× lower GPU forward-model computation time are achieved with negligible retrieval errors.The CPU benchmark used an Intel Xeon E5-2650 v4 @ 2.20,GHz, while the GPU benchmark used an NVIDIA Quadro RTX 6000.
  • Airborne-scenario validation: Retrieved albedo maps closely match references, with only marginal differences between full-physics and NN-based forward models in realistic airborne scenarios.The complete retrieval framework was validated on the airborne scenarios described in Sec. II-B.
  • Airborne-scenario validation: Runtime decreases from nearly one month with the full-physics model to only a few hours on GPU.This reduction accompanies the validation of the complete retrieval framework on realistic airborne scenarios.

V. CONCLUSIONS AND FUTURE WORK

The study demonstrates that neural-network surrogates can substantially accelerate radiative-transfer processing while maintaining low approximation and retrieval errors. In the NanoCarb test case, retrieval mean errors were 0.33% for CO2 and 0.02% for surface albedo.

  • Neural-network surrogates provide a flexible framework for substantially accelerating radiative-transfer processing in greenhouse-gas absorption bands.The computational gains are achieved while keeping approximation errors low.
  • <0.04% average radiance errors were obtained despite the large computational gains.The reported radiance approximation errors remained below 0.04% on average.
  • 0.33% retrieval mean error was achieved for CO2 and 0.02% for surface albedo in the NanoCarb test case.These results quantify retrieval performance for the reported test case.
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