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arxiv: 2512.14898 · v2 · pith:4M6JU3YRnew · submitted 2025-12-16 · ⚛️ physics.ao-ph

Predicting Forecast Error for the HRRR Using LSTM Neural Networks: A Comparative Study Using New York and Oklahoma State Mesonets

David Aaron Evans , Kara J. Sulia , Nick P. Bassill , Chris D. Thorncroft , Jay C. Rothenberger , Lauriana C. Gaudet This is my paper

Pith reviewed 2026-05-16 21:58 UTC · model grok-4.3

classification ⚛️ physics.ao-ph
keywords LSTMHRRRforecast error predictionmesonetprecipitationnumerical weather predictionmachine learning correction
0
0 comments X

The pith

LSTM networks trained on mesonet data predict HRRR precipitation forecast errors with 48 percent average improvement.

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

The paper trains LSTM neural networks on historical pairs of HRRR model forecasts and near-surface observations from the New York State Mesonet and Oklahoma State Mesonet. The networks learn to output the error that the HRRR forecast is likely to have at those specific locations for precipitation, wind, and temperature. When tested, the LSTM corrections reduce precipitation error by 48 percent on average relative to the raw HRRR forecast, reduce temperature error by 25 percent, and reduce wind error by 15 percent. The resulting error predictions are intended to let forecasters adjust the deterministic HRRR output in real time, flag sites with high uncertainty, and support decisions for high-impact weather events. The method works best where dense, continuous mesonet observations are available to supply training pairs.

Core claim

LSTM models can be trained directly on HRRR forecast fields paired with mesonet ground truth to output location-specific predictions of forecast error; the largest skill gain occurs for precipitation (average 48 percent improvement), followed by temperature (25 percent) and wind (15 percent), with precipitation showing better detection of overforecast than underforecast events.

What carries the argument

Long Short-Term Memory neural networks trained on time series of HRRR forecast variables paired with corresponding mesonet observations to regress the forecast error at each station.

If this is right

  • Deterministic HRRR forecasts can be adjusted in real time at mesonet sites by adding the LSTM-predicted error.
  • Sites and variables with systematically larger predicted errors can be flagged as higher uncertainty.
  • The error predictions supply supplemental guidance for high-impact weather decisions.
  • Precipitation error predictions detect overforecast events more accurately than underforecast events.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same training approach could be applied to other high-resolution NWP models if comparable dense observation networks exist.
  • In regions without dense mesonets the method would likely lose most of its skill because training pairs would be unavailable.
  • Smoothing observed in the temperature error predictions suggests the LSTMs may also be learning a form of bias correction beyond raw error magnitude.

Load-bearing premise

The statistical relationship between HRRR forecast errors and mesonet observations stays stable enough that a network trained on past data will keep predicting future errors accurately.

What would settle it

Apply the trained LSTMs to HRRR output from a later period that includes a major model upgrade or a change in mesonet sensor calibration and measure whether the percent improvement over the raw forecast drops below 20 percent for precipitation.

Figures

Figures reproduced from arXiv: 2512.14898 by Chris D. Thorncroft, David Aaron Evans, Jay C. Rothenberger, Kara J. Sulia, Lauriana C. Gaudet, Nick P. Bassill.

Figure 1
Figure 1. Figure 1: The diagram illustrates the persistence method applied to an LSTM for [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The diagram illustrates a high-level representation of the LSTM encoder [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Confusion matrix summarizing the precision of LSTM predictions for [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Scatterplot of the precipitation error across the NYSM network and all [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: NYSM MAE grouped by NCEI climate division (NCEI, 2015). Each [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: NYSM, MAE of LSTM precipitation-error predictions in mmhr [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: As in Fig. 3, but for the OKSM [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: As in Fig. 4, but for OKSM [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: As in Fig. 6, but for the OKSM [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: As in Fig. 5, but for the OKSM [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: OKSM, MAE of LSTM predictions in mm hr−1 for precipitation error, grouped by local time of day. Panels are arranged from top to bottom with the same layout and color conventions as [PITH_FULL_IMAGE:figures/full_fig_p022_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Scatterplot of the wind error across the NYSM network and all forecast [PITH_FULL_IMAGE:figures/full_fig_p024_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: NYSM MAE grouped by NCEI climate division (NCEI, 2015). Each [PITH_FULL_IMAGE:figures/full_fig_p025_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: NYSM, mean error of LSTM predictions for wind error in m s [PITH_FULL_IMAGE:figures/full_fig_p026_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: As in Fig. 12, but for the OKSM [PITH_FULL_IMAGE:figures/full_fig_p028_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: As in Fig. 13, but for the OKSM [PITH_FULL_IMAGE:figures/full_fig_p028_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: As in Fig. 14, but for the OKSM [PITH_FULL_IMAGE:figures/full_fig_p029_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Scatterplot of the temperature error across the NYSM network and all [PITH_FULL_IMAGE:figures/full_fig_p031_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: NYSM MAE grouped by NCEI climate division (NCEI, 2015). Each [PITH_FULL_IMAGE:figures/full_fig_p032_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: NYSM, mean error of LSTM predictions for temperature error in [PITH_FULL_IMAGE:figures/full_fig_p033_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: As in Fig. 18, but for the OKSM [PITH_FULL_IMAGE:figures/full_fig_p035_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: As in Fig. 19, but for the OKSM [PITH_FULL_IMAGE:figures/full_fig_p035_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: As in Fig. 20, but for the OKSM [PITH_FULL_IMAGE:figures/full_fig_p036_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: NYSM Network overlaid on an Elevation Map in meters, using Earth [PITH_FULL_IMAGE:figures/full_fig_p039_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: NYSM Network overlaid on an Aspect/Slope Map, using Earth Re [PITH_FULL_IMAGE:figures/full_fig_p040_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: NYSM Network overland on the National Land-cover Database Map, [PITH_FULL_IMAGE:figures/full_fig_p041_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: As in Fig. 24, but for the OKSM [PITH_FULL_IMAGE:figures/full_fig_p042_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: As in Fig. 25, but for the OKSM [PITH_FULL_IMAGE:figures/full_fig_p043_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: As in Fig. 26, but for the OKSM [PITH_FULL_IMAGE:figures/full_fig_p044_29.png] view at source ↗
read the original abstract

Long Short-Term Memory (LSTM) models are trained to predict forecast errors for the High-Resolution Rapid Refresh (HRRR) model using the New York State Mesonet and Oklahoma State Mesonet near-surface weather observations as ground truth. When evaluated using mean-absolute-error and percent improvement relative to the HRRR, LSTMs predict precipitation error most accurately, providing, on average, a 48% improvement relative to the HRRR forecast, followed by wind error, providing, on average, a 15% improvement, and then temperature error, providing, on average, a 25% improvement. Precipitation errors exhibit an asymmetry, with overforecast precipitation detected more accurately than underforecast, while wind error predictions are consistent across over- and underforecast predictions. Temperature error predictions are relatively accurate but smoother, with respect to variance, than true observations. This paper describes an overview of LSTM performance with the expressed intent of providing forecasters with real-time predictions of forecast error at the point of use within the New York State and Oklahoma State Mesonets. In practice, the predicted errors can be used to adjust deterministic HRRR forecasts at the point of use, identify locations and variables with elevated uncertainty, and provide supplemental guidance for high-impact decision-making. This research demonstrates the potential of LSTM-based machine learning models to provide actionable, location-specific predictions of forecast error for high-resolution operational numerical weather prediction (NWP) systems. However, model performance is variable-dependent, and the approach relies on the availability of dense mesonet observations, which may limit applicability in data-sparse regions.

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.

Referee Report

2 major / 2 minor

Summary. The paper trains LSTM models on paired HRRR forecasts and near-surface observations from the New York State and Oklahoma State Mesonets to predict forecast errors for precipitation, temperature, and wind. When evaluated with mean absolute error, the LSTMs yield average improvements of 48% for precipitation error, 25% for temperature error, and 15% for wind error relative to the raw HRRR forecasts, with additional observations on asymmetry in precipitation errors and smoother temperature predictions.

Significance. If the improvements prove robust under strict future temporal validation, the work offers practical value for operational forecasting by enabling real-time, location-specific error corrections at mesonet sites. This could support high-impact decision-making and uncertainty identification in data-dense regions, leveraging dense observational networks as ground truth.

major comments (2)
  1. [Abstract] Abstract and evaluation sections: the headline improvements (48% precipitation, 25% temperature, 15% wind) are reported without any description of the temporal train/test split, cross-validation method, or confirmation that test periods follow training periods. Weather time series are strongly autocorrelated, so a non-causal split risks leakage that would inflate the percent improvements; explicit dates, rolling-origin validation, or blocked CV details are required to substantiate generalization to future forecasts.
  2. [Results] Evaluation and results: no information is supplied on hyperparameter search, statistical significance testing of the MAE reductions, or sensitivity to model architecture. This leaves the central claim of variable-dependent performance only moderately supported, particularly for the precipitation asymmetry result.
minor comments (2)
  1. [Abstract] Abstract: a single sentence on the data period or LSTM architecture (layers, units) would improve completeness without lengthening the text.
  2. [Figures] Figure clarity: ensure error time series plots distinguish predicted vs. observed errors with consistent y-axis scaling across variables.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We appreciate the referee's thorough review and valuable suggestions for improving the clarity and rigor of our manuscript. We address each major comment below and plan to incorporate revisions as indicated.

read point-by-point responses

  1. Referee: [Abstract] Abstract and evaluation sections: the headline improvements (48% precipitation, 25% temperature, 15% wind) are reported without any description of the temporal train/test split, cross-validation method, or confirmation that test periods follow training periods. Weather time series are strongly autocorrelated, so a non-causal split risks leakage that would inflate the percent improvements; explicit dates, rolling-origin validation, or blocked CV details are required to substantiate generalization to future forecasts.

    Authors: We agree that providing explicit details on the data splitting procedure is essential to demonstrate the robustness of our results against temporal autocorrelation. In the revised manuscript, we will expand the evaluation section to include the specific temporal train/test split dates, confirm that the test period follows the training period, and describe the cross-validation method used (blocked CV) to avoid data leakage. This will substantiate the generalization to future forecasts. revision: yes

  2. Referee: [Results] Evaluation and results: no information is supplied on hyperparameter search, statistical significance testing of the MAE reductions, or sensitivity to model architecture. This leaves the central claim of variable-dependent performance only moderately supported, particularly for the precipitation asymmetry result.

    Authors: We acknowledge the need for additional details on the modeling process to better support our claims. The revised manuscript will include a description of the hyperparameter search procedure, statistical significance testing of the MAE reductions (such as paired t-tests), and sensitivity analyses to model architecture variations. These additions will provide stronger evidence for the variable-dependent performance, including the observed asymmetry in precipitation errors. revision: yes

Circularity Check

0 steps flagged

No circularity; empirical ML evaluation on held-out observations is independent of fitted parameters

full rationale

The paper trains LSTMs on historical mesonet-HRRR pairs to predict forecast errors and reports empirical metrics (MAE and percent improvement) on separate test data. No equations, derivations, or self-citations reduce the claimed improvements (48% precipitation, 25% temperature, 15% wind) to quantities defined by the model parameters themselves. The evaluation uses independent ground-truth observations, satisfying the condition for a self-contained result against external benchmarks. No self-definitional, fitted-input-called-prediction, or uniqueness-imported patterns appear in the abstract or described methodology.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on fitting an LSTM to historical error data and on the premise that mesonet measurements constitute accurate ground truth; no new physical entities are introduced.

free parameters (2)
  • LSTM weights and biases
    Learned during training to minimize prediction error on the mesonet-HRRR pairs.
  • Model hyperparameters (layers, units, learning rate, etc.)
    Chosen or tuned to achieve the reported performance.
axioms (1)
  • domain assumption Mesonet observations represent the true near-surface state for the purpose of defining forecast error.
    Forecast error is computed directly as the difference between HRRR output and mesonet measurements.

pith-pipeline@v0.9.0 · 5619 in / 1341 out tokens · 41385 ms · 2026-05-16T21:58:03.994793+00:00 · methodology

discussion (0)

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