Machine-learning-based approach for solar radiation model uncertainty identification, attribution and bias correction

Lipponen, Antti; Lezaca, Jorge; Saint-Drenan, Yves-Marie; Schroedter-Homscheidt, Marion; Arola, Antti

doi:10.5194/egusphere-2026-2743

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https://doi.org/10.5194/egusphere-2026-2743

Preprints

03 Jun 2026

| 03 Jun 2026

Status: this preprint is open for discussion and under review for Atmospheric Measurement Techniques (AMT).

Machine-learning-based approach for solar radiation model uncertainty identification, attribution and bias correction

Antti Lipponen, Jorge Lezaca, Yves-Marie Saint-Drenan, Marion Schroedter-Homscheidt, and Antti Arola

Abstract. Accurate surface solar irradiance (SSI) is essential for climate monitoring and solar energy applications, yet operational radiation data products such as the Copernicus Atmospheric Monitoring Service (CAMS) solar radiation service (CRS) still exhibit systematic and situation dependent errors. These are arising from uncertainties in clouds, aerosols and surface properties as well as from area-time mismatch between ground observations and pixel or model gridbox averaged properties. In this study, we develop a data-driven XGBoost-based uncertainty model that predicts the instantaneous CRS irradiance uncertainty for global horizontal (GHI), diffuse horizontal (DHI) and beam normal irradiance (BNI) using only the operational CRS inputs. We apply SHapley Additive exPlanations (SHAP) to quantify the contribution of individual physical predictors and to diagnose the dominant relations of observed deviations to CRS input parameters. Across all components, cloud optical depth is identified as the primary driver of CRS irradiance uncertainty. Aerosol optical depths of different aerosol components and surface reflectance (albedo and BRDF parameters) have additional component-dependent influences, particularly for DHI and BNI. The SHAP analysis also reveals a solar zenith angle dependence with contributions increasing at high solar zenith angles (SZA). A single-case analysis under overcast conditions demonstrates how SHAP can attribute individual large errors to specific cloud, aerosol and surface processes. Finally, we apply the trained situation-dependent model as a post-processing bias correction to the CRS irradiances. The bias correction reduces the median bias from 5.0 to −0.6 Wm^-2 for GHI and from 11.1 to 1.0 Wm^-2 for DHI. The bias correction improves the root-mean-squared errors and correlation coefficients for all components GHI, DHI, and BNI. The results demonstrate that physically interpretable machine-learning methods can both identify the dominant irradiance deviations based on operationally available CRS input parameters and provide an effective path for a post-processed bias correction.

Received: 13 May 2026 – Discussion started: 03 Jun 2026

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Antti Lipponen, Jorge Lezaca, Yves-Marie Saint-Drenan, Marion Schroedter-Homscheidt, and Antti Arola

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RC1: 'Comment on egusphere-2026-2743', Anonymous Referee #1, 03 Jun 2026 reply

This paper presents an error-correction framework for the CAMS solar radiation service (CRS) using an XGBoost-based regression model, with SHAP used for feature attribution. While the attempt to improve operational irradiance products is relevant, the work faces significant limitations in terms of scientific novelty, rigorous benchmarking, and the conceptual definition of “uncertainty.” The presentation of the methodology in Section 2.3 is unnecessarily opaque, and the scope of the study lacks a broader, more robust framework suitable for a general audience or global applications. Below are the detailed comments:

1. The methodology relies on standard tools (XGBoost + SHAP) applied to existing data, which limits the novelty of the contribution.

2. The findings regarding the drivers of error (e.g., cloud and aerosol influences) are largely intuitive and established in the literature. The paper would benefit from a more critical discussion on why a data-driven approach is necessary here if the drivers are already known, and what specific new insights these models provide beyond confirming known physics.

3. The authors should clarify why they chose to model the error specifically, rather than attempting to predict the irradiance or clear-sky index directly, and whether a direct prediction model was considered or tested as a baseline.

4. There is a major concern regarding the use of the term "uncertainty." In the atmospheric sciences and remote sensing, uncertainty implies a probabilistic, quantified measure (e.g., variance, confidence intervals). This work presents a point-regression model, which does not provide a probabilistic view. The authors should either adopt more precise terminology (e.g., "systematic deviation" or "bias") or incorporate formal uncertainty quantification techniques (e.g., quantile regression, ensemble methods, or evaluating metrics like CRPS, PIT, or reliability diagrams).

5. The study lacks a comparison with alternative methods. To justify the use of XGBoost, it is essential to benchmark against other statistical or simpler ML models (e.g., linear regression, random forests) to demonstrate the specific value added by this approach.

6. The current approach of training a single model for the entire disk is likely inappropriate, as errors in solar radiation retrievals are highly dependent on climate, seasonal regimes, and sky conditions. The authors should consider a foundation model in their future work.

7. Section 2.3 is unnecessarily complex. The algebraic derivation provided in Eq. (2) adds little value and obscures a straightforward procedure. The section could be significantly condensed by simply stating that a regression model was developed on the retrieval error.

8. The paper is saturated with repetitive plots that do not offer proportional informational gains. A more concise synthesis of the findings, perhaps moving some supplemental diagnostic plots to an appendix, would strengthen the narrative and focus the reader's attention on the key results.

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Citation: https://doi.org/10.5194/egusphere-2026-2743-RC1

Antti Lipponen, Jorge Lezaca, Yves-Marie Saint-Drenan, Marion Schroedter-Homscheidt, and Antti Arola

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Latest update: 03 Jun 2026

Short summary

We studied what causes errors in Copernicus Atmosphere Monitoring Service solar radiation data using explainable machine learning methods and ground-based observations. The analysis showed that cloud properties are the main source of errors, while aerosols and surface reflectance have smaller effects. The results improve understanding of the strengths and weaknesses of current models and can support future model development, forecasting and solar energy applications.