arxiv: 2605.07981 · v1 · submitted 2026-05-08 · ⚛️ physics.optics · physics.ao-ph

Recognition: no theorem link

Learning from Translation: Seasonal Errors and Feature Importance of the ERA5 Turbulence Predictions

Arial Tolentino, Luat T. Vuong, Markus Petters

Authors on Pith no claims yet

Pith reviewed 2026-05-11 03:01 UTC · model grok-4.3

classification ⚛️ physics.optics physics.ao-ph

keywords optical turbulenceERA5 reanalysismachine learning predictionfeature importancesolar radiationseasonal performanceCn2 strengthatmospheric energy transfer

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The pith

Machine learning models show solar radiation as the main driver of optical turbulence predictions from ERA5 data across sites and seasons.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The authors train machine learning models on one year of local turbulence measurements paired with ERA5 reanalysis inputs to predict near-surface optical turbulence strength. They then test how well the models extrapolate to other years at the same California and New York sites. The models produce consistent results despite different terrain and weather, yet they perform better in summer with higher correlation and lower errors. Feature importance analysis across all cases points to solar radiation as the leading predictor. The work concludes that radiative energy transfer plays a central role in turbulence and that ERA5 lacks some seasonal environmental factors needed for full accuracy.

Core claim

Training machine learning models on one year of co-located Cn2 observations and ERA5 data allows temporal extrapolation to other years at the same sites, yielding multi-year turbulence time series with stable performance across Southern California and New York. All models exhibit stronger correlation, quicker convergence, and reduced errors during summer months. Regardless of location, solar radiation ranks as the top feature of importance, indicating its central role in driving atmospheric turbulence via radiative energy transfer. Seasonal differences in both errors and which ERA5 features matter most point to influences from unmonitored factors such as atmospheric composition.

What carries the argument

Machine learning models that map ERA5 reanalysis variables to Cn2 turbulence strength, assessed through feature importance rankings and seasonal error patterns.

Load-bearing premise

That the feature importance rankings produced by the machine learning models capture physical causes of turbulence rather than statistical patterns tied to the particular training data or model choice.

What would settle it

Measure actual turbulence under conditions of matched solar radiation but differing atmospheric composition such as aerosol loading, then check whether adding composition variables to the ERA5 inputs reduces the seasonal prediction errors.

Figures

Figures reproduced from arXiv: 2605.07981 by Arial Tolentino, Luat T. Vuong, Markus Petters.

**Figure 1.** Figure 1: 3D elevation maps of the two study regions with the anemometer data measurement station locations shown in red. In Southern California (SCA), most of the sites are between the ocean and mountains (left), while in New York State (NYS), the station topography varies and include lakes, valleys, and ocean peninsula (right). the atmospheric boundary layer, and vary over several orders of magnitude, typically be… view at source ↗

**Figure 2.** Figure 2: Overview of the turbulence modeling workflow. A MOST-derived C 2 n from ground observations is used to train and evaluate a yearly ERA5 based regression model. The annual model is subsequently decomposed into seasonal models to capture regime dependent behavior and extract seasonal features of importance. This study follows the measure–correlate–predict framework summarized in [PITH_FULL_IMAGE:figures/ful… view at source ↗

**Figure 3.** Figure 3: Monthly distributions of log10(C 2 n ) for SCA (a) and NYS (b). Box plots summarize the median, inter-quartile range, and overall variability for each month. both regions. However, variability of this seasonal cycle differ substantially between regions. There is pronounced seasonal contrast in NYS C 2 n . Winter months are characterized by lower median values and relatively narrower IQRs compared to other … view at source ↗

**Figure 4.** Figure 4: Heatmaps of annual station-specific model performance. Pearson correlation and RMSE for (a-b) SCA and (c-d) NYS. which are trained on a single year and evaluated on all remaining years at the same station. Rows indicate training stations and columns indicate the calendar year used for model training. The annual models trained on SCA compared to those trained with NYS data exhibit higher correlations and l… view at source ↗

**Figure 5.** Figure 5: Seasonal model performance for SCA (left) and NYS (right). Pearson correlation (top panels) and RMSE (bottom panels) for annually trained models (solid lines) and seasonally trained models (shaded ±1σ and ±2σ bands). Points denote station MCP performance. To evaluate regime dependence, annual model performance is compared against seasonally trained models [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗

**Figure 6.** Figure 6: (a) Annual feature importance comparison between SCA and NYS. Seasonal evolution of grouped feature importance for (b) SCA and (c) NYS, respectively. fractional contribution of a feature to the total model importance. These unit-normalized SHAP values are plot on a logarithmic scale to emphasize differences across orders of magnitude. In [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗

read the original abstract

Turbulence is a phenomena that is {\it locally} and statistically characterized by measurements, but it is caused by {\it nonlocal} energy cascades associated with the environment. The presence of turbulence coincides with fluctuations in the refractive index, which impact optical sensing, imaging, and signaling applications. Here, we study the machine learning models that predict near-surface optical turbulence strength $C_n^2$, derived from anemometer-based surface flux measurements through Monin-Obukhov similarity theory, using ERA5 reanalysis data as model inputs. We evaluate the model's ability to perform temporal extrapolation by training on one year of co-located $C_n^2$ observations and ERA5 data, and applying the model to ERA5 data from other years at the same site to reconstruct a multi-year time series. We compare the predictions across Southern California and New York. In spite of varying weather and terrain, the ML models show consistent performance and seasonal behavior across training years. All models show greater correlation, faster convergence, and lower prediction errors in the summer. However, some ERA5 features drive predictions in New York but not California and vice versa, and such feature dependence depends on the season. Seasonal error and feature trends suggest that turbulence is affected by atmospheric composition or other seasonal environmental considerations that are not currently monitored by ERA5. We find, regardless of terrain, the primary feature of importance to turbulence prediction is solar radiation, which underlines the central role of radiative energy transfer in driving atmospheric turbulence. We point toward physics-informed ML translation and feature selection as tools for improving the generalizability of data-driven models.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper shows ML models trained on one year of ERA5 and Cn2 data can extrapolate to other years at the same sites with consistent seasonal error patterns, but the claim that solar radiation is the primary driver of turbulence regardless of terrain rests on an unsupported leap from feature importance to physical causation.

read the letter

The core result is that models trained on co-located observations and ERA5 inputs at two sites maintain usable performance when applied to later years, with lower errors and faster convergence in summer for both Southern California and New York. The work also tracks how feature rankings shift by location and season, noting that some ERA5 variables matter at one site but not the other. This gives a concrete check on how well reanalysis data can stand in for missing long-term turbulence records at fixed locations. The seasonal trends are presented as evidence that unmonitored factors like atmospheric composition affect the predictions, which is a reasonable practical observation for users of ERA5 in optical applications. The comparison across terrains adds a small empirical layer that prior single-site studies did not emphasize. The main weakness is the interpretation of the feature importance results. The paper states that solar radiation ranks highest regardless of terrain and therefore plays the central physical role in driving turbulence through radiative energy transfer. Feature importance metrics only show which inputs the model uses most for prediction inside the training distribution; they do not separate causation from correlation. Solar radiation is tied to temperature, boundary-layer height, and surface fluxes, all of which also influence stability, so the ranking alone cannot establish a universal mechanism. No ablation or controlled test is described that would hold those confounders fixed. The abstract supplies no numerical error values or validation details, which makes it hard to judge how large the seasonal gains actually are. Readers working on site-specific optical turbulence forecasting or on ML translation from reanalysis data will get the most from the seasonal and location comparisons. The empirical workflow is clear enough that the paper merits a serious referee, provided the discussion of feature importances is revised to stay within what the metrics actually support. I would send it for review with that targeted request.

Referee Report

3 major / 2 minor

Summary. The manuscript trains machine learning models to predict near-surface optical turbulence strength Cn² (derived from anemometer surface flux measurements via Monin-Obukhov similarity theory) using ERA5 reanalysis variables as inputs. Models are trained on one year of co-located data at sites in Southern California and New York, then applied to ERA5 data from other years at the same locations for temporal extrapolation and multi-year reconstruction. The authors report consistent model performance across training years despite differing weather and terrain, with improved correlation, faster convergence, and lower errors during summer months; site- and season-specific differences in feature importance; and solar radiation as the dominant predictor regardless of terrain, which they interpret as evidence for the central physical role of radiative energy transfer in driving turbulence. They suggest physics-informed ML translation and feature selection to enhance generalizability.

Significance. If the reported seasonal trends and feature rankings are robust, the work could help identify key drivers for data-driven turbulence modeling and improve extrapolation across years and sites for optical applications. The temporal-extrapolation setup and cross-terrain comparison are useful for assessing model generalizability. However, the central interpretation that feature importance directly indicates physical causation (rather than statistical association) would need stronger support to have broad impact on the field.

major comments (3)

[Abstract, results] Abstract and results sections: The claims of 'consistent performance,' 'greater correlation, faster convergence, and lower prediction errors in the summer,' and site-specific feature differences are stated without any quantitative metrics (e.g., R², RMSE, MAE, or convergence rates) or details on the validation procedure, error distributions, or statistical significance tests for the temporal extrapolation. This absence makes it impossible to evaluate the magnitude or robustness of the reported seasonal and cross-site behaviors.
[Abstract, feature importance analysis] Abstract and feature-importance discussion: The claim that solar radiation is 'the primary feature of importance to turbulence prediction' 'regardless of terrain' and 'underlines the central role of radiative energy transfer in driving atmospheric turbulence' is not supported by the presented evidence. Feature-importance rankings from ML models trained on ERA5 inputs reflect statistical associations within the training distribution; solar radiation is known to be correlated with other ERA5 variables (temperature, humidity, boundary-layer height, surface fluxes) that also influence stability and Cn². No ablation studies, partial-dependence plots holding confounders fixed, or causal-inference methods are described to distinguish correlation from causation.
[Methods, results] Methods and results: The workflow trains on co-located Cn² observations and ERA5 data then applies the model to independent ERA5 periods at the same sites. While this avoids direct circularity, the manuscript does not report whether the derived Cn² targets (via Monin-Obukhov) are computed consistently across years or whether any site-specific calibration parameters are held fixed, which could affect the apparent seasonal error trends.

minor comments (2)

[Abstract] Abstract: 'Turbulence is a phenomena' should read 'Turbulence is a phenomenon.'
[Results] The manuscript would benefit from a table or figure summarizing quantitative performance metrics (R², RMSE, etc.) for each site, season, and training year to support the textual claims.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive comments, which have helped us identify areas where the manuscript can be clarified and strengthened. We address each major comment below with specific plans for revision.

read point-by-point responses

Referee: [Abstract, results] Abstract and results sections: The claims of 'consistent performance,' 'greater correlation, faster convergence, and lower prediction errors in the summer,' and site-specific feature differences are stated without any quantitative metrics (e.g., R², RMSE, MAE, or convergence rates) or details on the validation procedure, error distributions, or statistical significance tests for the temporal extrapolation. This absence makes it impossible to evaluate the magnitude or robustness of the reported seasonal and cross-site behaviors.

Authors: We agree that the abstract presents these findings qualitatively and that explicit quantitative support is needed for proper evaluation. The results section contains the relevant metrics (seasonal R², RMSE, MAE, training convergence curves) and describes the temporal extrapolation protocol with cross-validation. To resolve this, we will revise the abstract to incorporate key quantitative values and add a dedicated paragraph in the results section detailing the validation procedure, error distributions, and statistical significance testing for seasonal differences. revision: yes
Referee: [Abstract, feature importance analysis] Abstract and feature-importance discussion: The claim that solar radiation is 'the primary feature of importance to turbulence prediction' 'regardless of terrain' and 'underlines the central role of radiative energy transfer in driving atmospheric turbulence' is not supported by the presented evidence. Feature-importance rankings from ML models trained on ERA5 inputs reflect statistical associations within the training distribution; solar radiation is known to be correlated with other ERA5 variables (temperature, humidity, boundary-layer height, surface fluxes) that also influence stability and Cn². No ablation studies, partial-dependence plots holding confounders fixed, or causal-inference methods are described to distinguish correlation from causation.

Authors: We accept that feature-importance rankings capture statistical associations and that solar radiation is correlated with other ERA5 variables. The original phrasing was intended to note the feature's consistent top ranking and its physical plausibility under Monin-Obukhov theory. In revision we will (i) soften the abstract and discussion language to emphasize correlation, (ii) add partial-dependence plots to illustrate marginal effects, and (iii) include an explicit limitations paragraph on confounders and the desirability of future causal analyses. revision: partial
Referee: [Methods, results] Methods and results: The workflow trains on co-located Cn² observations and ERA5 data then applies the model to independent ERA5 periods at the same sites. While this avoids direct circularity, the manuscript does not report whether the derived Cn² targets (via Monin-Obukhov) are computed consistently across years or whether any site-specific calibration parameters are held fixed, which could affect the apparent seasonal error trends.

Authors: The Cn² targets are obtained from the standard Monin-Obukhov similarity relations using fixed universal constants and literature roughness lengths applied uniformly to all years and sites; no year-specific or site-specific recalibration is performed. We will add an explicit statement in the Methods section confirming this uniform computation procedure to demonstrate that the reported seasonal trends are not artifacts of inconsistent target derivation. revision: yes

Circularity Check

0 steps flagged

No circularity in the ML training, extrapolation, or feature-importance workflow.

full rationale

The paper trains supervised models on one year of co-located ERA5 inputs and Cn² targets (the latter obtained via Monin-Obukhov similarity from surface-flux observations), then evaluates on ERA5 data from independent years at the same sites. Feature importances are computed directly from the fitted models' behavior on these held-out periods; the reported ranking of solar radiation is therefore an empirical output of the trained predictor, not a quantity defined in terms of itself or recovered by construction from the training labels. No self-citation is invoked to justify the core workflow or the uniqueness of the chosen features, and the seasonal-error analysis likewise rests on direct comparison of model outputs against the same independent ERA5 time series. The interpretive sentence linking feature rank to 'the central role of radiative energy transfer' is an after-the-fact gloss rather than a load-bearing step in any derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the validity of Monin-Obukhov similarity theory for deriving the target Cn² variable and on the assumption that ERA5 variables capture the dominant drivers of near-surface turbulence.

axioms (1)

domain assumption Monin-Obukhov similarity theory accurately derives Cn² from anemometer-based surface flux measurements
This is invoked to create the ground-truth target variable from observations for training the ML models.

pith-pipeline@v0.9.0 · 5597 in / 1169 out tokens · 61047 ms · 2026-05-11T03:01:24.759745+00:00 · methodology

discussion (0)

Reference graph

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