24AI Assessing the Performance of Kolmogorov-Arnold Network in Satellite far-IR Surface Emissivity Retrieval

Kolmogorov-Arnold Network (KAN) has been recently introduced into the realm of machine learning and proposed to be an alternative to the traditional multi-layer perceptron (MLP) model with much better interpretability. Here, using far-IR surface emissivity retrieval as an example, we evaluate the performance of KAN with respect to the MLP model and a commonly used Bayesian inference in satellite remote sensing, the so-called optimal estimation method.

Surface emissivity is a critical property that influences the surface energy budget and, consequently, the surface climate. It varies with surface type and detailed physical properties of each surface type. Infrared surface emissivity has been routinely estimated from spaceborne observations for decades, but all for several narrow bands in the mid-IR window region.

The far-IR (15–100 µm) surface emissivity was not observed from space until the launch of two CubeSats of NASA’s PREFIRE mission in 2024. In polar regions, where water vapor is low, surface emission over 400-600 cm⁻¹ (the far-IR dirty window) can reach the top of the atmosphere. As a result, the surface emissivity in this spectral region can be inferred from satellite observations. Recent studies highlighting the significance of far-IR emissivity on polar climate simulations have driven NASA’s PREFIRE and ESA’s FORUM missions. Both missions aim to provide surface spectral emissivity as a core L2 product.

An efficient and accurate retrieval method is needed to estimate mid-IR and far-IR surface spectral emissivity for the PREFIRE mission. While an optimal-estimation-based (OE-based) algorithm can meet the PREFIRE L2 surface emissivity accuracy requirement, it is computationally expensive. Prior work has tried using a multi-layer perceptron (MLP) to estimate the surface spectral emissivities at 14 PREFIRE channels (6 in mid-IR and 8 in far-IR). The MLP results showed comparable or even better performance than the OE-based algorithm with a factor of 10⁵ in computational time savings. However, the MLP results could be lack of interpretability due to their black-box nature.

We implemented a KAN-based retrieval algorithm for PREFIRE surface emissivity retrievals. Testing with synthetic PREFIRE radiances, our results show that KAN outperforms or is on par with the other two methods: it is still much faster than the OE-based method by orders of magnitude with comparable performance, its retrievals outperform the MLP results in accuracy, and it is more interpretable than MLP. The mean absolute error (MAE) for surface emissivity retrievals are 0.0087 for MLP, 0.0085 for KAN, and 0.0069 for OE, respectively. Observations indicate that neural networks (NN) perform significantly better in the far-IR spectrum, with MLP showing a far-IR MAE of 0.0025, KAN at 0.0021, and OE at 0.0073. In the mid-IR spectrum, MLP and KAN have higher errors of 0.0169 and 0.0170, respectively, compared to OE’s 0.0065. Furthermore, both NN methods are robust against inaccurate clear-sky detection.