NeuralFAO56 v1.0: A Scalable Physics-Informed Deep Learning Framework for Real-Time Evapotranspiration Estimation Across CONUS

Neupane, Adarsha; Samadi, Vidya

doi:10.5194/egusphere-2026-2300

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https://doi.org/10.5194/egusphere-2026-2300

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03 Jul 2026

| 03 Jul 2026

Status: this preprint is open for discussion and under review for Geoscientific Model Development (GMD).

NeuralFAO56 v1.0: A Scalable Physics-Informed Deep Learning Framework for Real-Time Evapotranspiration Estimation Across CONUS

Adarsha Neupane and Vidya Samadi

Abstract. Accurate estimation and forecasting of reference evapotranspiration (ETo) are essential for irrigation demand estimation. The FAO-56 Penman–Monteith formulation remains the physical standard for ETo computation, while recent advances in deep learning (DL) have demonstrated strong predictive skill for ETo forecasting. However, real-time ETo forecasting remains constrained by manual meteorological station identification, heterogeneous data acquisition, and labor-intensive preprocessing workflows. Existing software tools primarily support physics-based ETo estimation without real-time data integration or forecasting capability, whereas DL-based approaches often require manual data preparation, limiting automation and real-time applicability. This study introduces NeuralFAO56 Python package, a hybrid physics–data DL computational framework that embeds neural network–driven forecasting architectures for on-demand ETo estimation and forecasting across the continental United States (CONUS). NeuralFAO56 couples physics-based FAO-56 with DL sequence modeling within a unified pipeline that enables automated data acquisition, standardized preprocessing, and scalable deployment. The framework operates in dual modes: (i) physics-based FAO-56 ETo estimation using observed and forecasted meteorological inputs, and (ii) data-driven ETo forecasting using Long Short-Term Memory (LSTM) and Transformer architectures for multi-horizon (up to 7-day lead time) real-time forecast. The framework is evaluated across 867 stations at continental US spanning different climate regions. Results demonstrate strong short-term predictive skill, with performance degradation at longer lead times driven by reduced temporal predictability. Higher forecasting skill is observed in climatologically stable regions, while comparatively lower performance occurs in humid, convectively active regions. Overall, NeuralFAO56 provides a scalable, real-time framework that integrates physically based ETo modeling grounded in energy and mass conservation with DL forecasting and automated meteorological data pipelines to support short- to medium-range irrigation planning and management.

Received: 22 Apr 2026 – Discussion started: 03 Jul 2026

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Adarsha Neupane and Vidya Samadi

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RC1:
'Comment on egusphere-2026-2300', Anonymous Referee #1, 24 Aug 2026 reply
The manuscript presents an operationally useful, well-designed Python framework of NeuralFAO56 v1.0 that integrates FAO-56 Penman–Monteith reference-ET calculation with LSTM- and Transformer-based ET forecasting, using NWS real-time and forecast meteorology and NCEI historical archives, across a continental network of NWS–NCEI matched stations. The scope is suitable for a GMD Model description. The supporting evidence for the current publication, however, is not sufficient. The manuscript should be rethought after the authors make a response to the following substantive concerns. I would suggest the following comments, and hope that it will be helpful for the authors. I would suggest another resubmission:
Line 1: “Real-Time Evapotranspiration Estimation”, is an overstatement of what is demonstrated. The training evaluation is done based on NCEI data in a backward look, with the actual deployment being conducted for just one week. Take into account "Near-Real-Time Reference Evapotranspiration Forecasting". In addition, Physics-Informed is a good term in the DL literature. In the current manuscript the physics only appears as an offline FAO-56 label generator, not as a loss-function constraint; it would be better to call it “Physics-Guided” or “Hybrid Physics/Data-Driven”.

Line 10-32: Methods and the figure captions report 845 stations although there are 867 reported by the Abstract. Please check everywhere and explain the QA/QC step that decreases the number.

Line 10-32: The sentence “… support broader adoption of physics-informed machine learning in hydrologic prediction” is not supported by the evidence in the manuscript and should be toned down. The term “irrigation planning” also goes too far because ETo is a boundary condition, and scheduling needs crop coefficients (Kc) and/or ETa.

Line 52: Please remove “(4/30/2026 12:05:00 PMAllen et al., 1998” and replace with a clean citation.

Line 134: Figure 1 caption: replace “utilis” with “utils”. Please verify all module names against the released code.

Line 137: replace “componenet” with “component”.

Please start the introduction by explicitly stating (1) the maximum number of stations that previous DL-ETo studies have used, (2) that there are no existing packages that combine NWS real-time data for ETo with historical data from NCEI, and (3) that no previous continental-scale evaluation has been performed for all nine NOAA climate regions. NeuralFAO56 should be compared respect to Valipour et al. (2023), Ahmadi et al. (2023), Medina et al. (2018), Thorp (2022), and Vremec et al. (2024) that would help sharpen the contribution provided in table 1.

There is no independent evidence of the validity of ETo.The forecasts from LSTM/Transformer and NWS are compared to the FAO-56 ETo based on observed meteorology.The reference suffers itself from a systematic, regionally variable error, as is its solar radiation (Rs) which is derived from Hargreaves–Samani with a globally fixed kRS = 0.16, and no independent measurement of ETo has been used to validate either the reference or the DL forecasts.The manuscript should be benchmarked with the AmeriFlux/FLUXNET/SURFRAD/USCRN eddy-covariance ETo/ETref, and an independent ET product from remote sensing in a subset of stations co-located with the manuscript to support the claim of “real-time ETo forecasting”.

The DL forecasts are only compared to the physics-based FAO-56 pipeline.There are no naive baselines reported.Each defensible GMD-level evaluation should contain, at each lead time and for each NOAA region.These baselines should be beaten by a statistically significant margin for any DL claim before using the additional complexity of LSTM/Transformer.

Only deterministic skill of point forecast (NSE, KGE, MAE) is reported in the manuscript.Prediction intervals are needed for a GMD Model description, for an operational forecasting system.Two lightweight approaches are Monte-Carlo dropout during inference and multiple models using random seeds (deep ensembles of 5 models). The interval coverage should be provided in terms of Prediction interval coverage probability and Mean interval width at nominal 90% coverage.

In module FAO-56, Section 2, please specify if NeuralFAO56 imports the package pyfao56 (Thorp, 2022), imports and wraps the package, or re-implements FAO-56 equations. When depending on pyfao56 specify the exact version. In one paragraph, discuss the relation with PyEt (Vremec et al., 2024).

Repeat each experiment, reported in Section 2, at least 10 times across ≥ 10 random seeds, with the exact hyperparameter search space reported; report the hyperparameter sweep if the reported configuration is a default, or if the reported configuration was the result of tuning. Report averages ± SD in all tables and all figures.

For gaps greater than about 2 days, it is not defensible to use Section 2, preprocessing: forward-fill and backward-fill on daily meteorological time series. Use linear interpolation for small gaps (≤ 3 days) and a Kalman smoother or regression imputation for larger gaps or remove larger gaps. Justify the 5% threshold for missingness; Zhang & Post (2018) recommend that gap-filled series are still useful for hydrometeorological data at 10-20% missingness.

Section 2, train and test protocol: the 60/40 split by year is acceptable in principle, but the manuscript should confirm: 1- that only the train years are used for the fit of the Min–Max scaling parameters, 2- that there is no 7-day window of years extending across the split point, and 3- that the model selection uses a validation subset of years, not the test years.

Please provide an extra figure of station level NSE against lag-1 autocorrelation of daily ETo in Section 2.4.2 in Fig. 6. This will provide a measure of the informal saying that skill is primarily constrained by data characteristics.

The reported architectures are at the bottom of the possible design space.This observed equivalence may be due to either true data-limited saturation or under-parameterization.A short scaling study needs to be conducted consisting of 32, 64, 128 and 256 widths and 1, 2, 4 depths, evaluated on at least one representative station for each NOAA region, and reported best-of-search NSE, with 5-fold or block cross-validation.The only way the equivalence claim can be supported or if it is not, the paper becomes stronger as a result.

The same value of kRSis used for all stations and all nine NOAA climate regions ,0.16.This is contrary to FAO-56 recommendation which suggests that interior and coastal sites should be separated (≈0.16 vs. ≈0.19). It is also in conflict with the calibration literature.The authors should either follow the regional lookup or utilize observed Rs at co-located SURFRAD/USCRN sites, if available, or include a sensitivity study for kRS ± 25% and show that the conclusions in the "results" section are valid.

Three studies are cited and not engaged with which are closely related. 1- The current Python implementation of FAO-56, pyfao56 (Thorp, 2022, SoftwareX 19, 101208), is the 'legacy' Python implementation of FAO-56 and should be mentioned as an explicit dependency or comparison. 2- For a GMD reader, the primary reference is the current GMD paper by Vremec et al. (2024) which uses a Python PET package. 3- The improvement that NeuralFAO56 can offer over the work of Valipour et al. (2023) should be measured, preferably in a Table 1, for example, by calculating the RMSE for the 1-day forecasts for all the 30 CONUS sites with hybrid ML/DL at the 10-day horizon in order to quantify this contribution.

Look-back sensitivity is not mentioned in the text in section 2.4.2, but there is no table or figure provided in this regard. Include a sensitivity table (rows = look-back; columns = NSE/KGE/MAE by NOAA region), or be clear that only 7 days were tested and provide justification.

In addition to the training cost, report also inference-time cost per station per day, as specified in Section 2.4.6 in Table 3.

As of yet, the current “Code and Data Availability” section does not satisfy Copernicus GMD policy requirements.All requirements must be completed prior to publication.

The near-real-time evaluation of the forecast allows a window of 7 days.This is not enough to cover the overall “operational readiness” terminology in the Abstract and Conclusion.The evaluation must be made at least once every four seasons and provide MAE distributions per window for all 845 stations.These expanded results may be presented in the Abstract and Conclusion.

In the conclusion section, the sentence “reinforces its reliability, scalability, and operational readiness of environmental prediction systems” is not backed up without independent validation, uncertainty quantification and multi-window real-time evaluation. Revise it and provide a supported claim.

While making Code and Data available, split them into two DOIs, attach a tagged release from GitHub, provide a license, specify the environment and provide a user manual.

I recommend removing section 2.4. Results and Discussion should be separated into two different sections.This would enhance readability of the manuscript and help to differentiate the findings of the study from their interpretation.

Use consistent units throughout (mm day-1 not “mm day-1”).

In the reference list, Vremec: the correct one is https://doi:10.5194/gmd-17-7083-2024.

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Citation: https://doi.org/10.5194/egusphere-2026-2300-RC1
RC2: 'Comment on egusphere-2026-2300', Anonymous Referee #2, 02 Sep 2026 reply

This manuscript presents NeuralFAO56 v1.0, an automated Python framework that combines FAO-56 Penman–Monteith reference evapotranspiration calculations with LSTM- and Transformer-based forecasting and integrates NWS/NCEI meteorological data acquisition within a single workflow. I see practical value in the automated data pipeline, the CONUS-wide implementation across 845 stations, and the attempt to compare physics-based and data-driven forecasting approaches within the same operational framework.
However, after reading the manuscript, I remain uncertain about the central scientific and operational contribution of the proposed framework. In particular, the manuscript needs to more clearly establish what is meant by “physics-informed,” why the DL pathway is needed when meteorological forecasts can already be propagated directly through FAO-56, and exactly what information is used by the DL models. These issues are central to the interpretation and reproducibility of the study.
Major comments
1. The use of “physics-informed” in the title and throughout the manuscript needs stronger justification.
The title presents NeuralFAO56 as a “Physics-Informed Deep Learning Framework,” and the manuscript frequently refers to coupling physics-based FAO-56 with DL. However, based on the current methodology, I understand the framework primarily as two forecasting pathways integrated within a common software environment: FAO-56 uses observed or forecast meteorological forcing, whereas the LSTM and Transformer models perform data-driven forecasting from historical records.
I could not identify a mechanism through which the FAO-56 physics directly informs the learning process—for example, through a physics-based loss term, physical constraints, conservation requirements, physics-derived internal states, or another explicit interaction with the neural-network architecture.
The authors should therefore explain precisely what makes the DL component “physics-informed.” If the integration occurs mainly at the workflow/software level rather than within the learning process, terminology such as “hybrid physics-based and data-driven framework” may more accurately describe the contribution. This is not simply a terminology issue because the current wording implies a stronger methodological integration between physics and machine learning than is evident from the manuscript.
2. The central added value of the DL pathway over direct FAO-56 forecasting is not yet convincingly demonstrated. Figure 10 should play a much more central role in establishing this value.
The practical motivation for the DL component is currently unclear to me. If short-term meteorological forecasts are already available from NWS, future ETo can be obtained directly by propagating those forecasts through FAO-56. The key question is therefore not simply whether an LSTM or Transformer can reproduce or predict a historical FAO-56-derived ETo time series, but whether the DL pathway provides meaningful additional predictive skill. If short-term weather forecasts are already available, users can directly calculate future ETo with FAO-56. Why is an additional DL forecasting pathway needed?
Figure 10 appears to be the most important experiment for answering this question because it directly compares forecast-driven FAO-56, LSTM, and Transformer predictions against a common reference derived from observed meteorology. However, this prospective comparison is limited to a single seven-day period, 8–14 November 2025.
Given that this is the only direct prospective comparison between the two forecasting strategies, the manuscript should explain why this particular period was used and whether it was selected a priori based on data availability or another criterion. More importantly, a single November window does not establish whether the relative performance shown in Figure 10 is representative of other meteorological conditions. For much of CONUS, November is also outside the primary growing and irrigation season, whereas the manuscript makes broader claims regarding irrigation planning and operational readiness.
I therefore hope the authors could strengthen this part of the study substantially. Multiple independent forecast windows covering contrasting conditions—particularly growing-season/high-ETo periods—would allow the manuscript to answer the much more useful question of when, where, and at what lead time the DL pathway provides added value over forecast-weather-driven FAO-56. Without such evidence, it remains difficult to understand why a user should select the DL pathway rather than directly use available meteorological forecasts with FAO-56.
3. The DL predictor set and the information available to the models at forecast time are not sufficiently documented. This is important both for reproducibility and for interpreting the regional results.
The manuscript lists meteorological variables retrieved from NWS/NCEI and explains that input variables exceeding the 5% missing-data threshold are removed before training. However, I could not find a clear specification of the exact predictor vector ultimately supplied to the LSTM and Transformer models. Please explicitly report the exact meteorological variables used as DL predictors, clarify whether any forecast meteorological information is supplied to the DL models during the forecast horizon, and indicate whether the same predictor set is used across all stations.
Specific comments
1. Solar-radiation approximation and fixed kRS.

The FAO-56 reference ETo depends on incoming solar radiation, but Rs is estimated using the Hargreaves–Samani formulation with kRS fixed at 0.16 for all stations. Because the study spans nine NOAA climate regions and interprets spatial differences in ETo forecasting performance, the uncertainty associated with applying a spatially uniform kRS deserves further consideration. I do not assume that this choice necessarily explains the reported regional performance patterns; however, the manuscript currently provides little information on how sensitive the derived ETo values are to this assumption. A limited sensitivity analysis using representative stations or climate regions would therefore be useful to determine whether reasonable variation in kRS materially affects the magnitude of ETo or the main regional conclusions. If the impact is small, demonstrating this would also strengthen confidence in the robustness of the current framework.
2. Line 52.

The citation contains an apparent editing artifact: “(4/30/2026 12:05:00 PMAllen et al., 1998; ASCE, 2005).” Please correct this citation.
3. Line 137.

“Data acquisition componenet” should be corrected to “Data acquisition component.”
4. Lines 711–716 / Conclusion.

The statement “Across 845 stations selected to represent four distinct NOAA climate regions” appears incorrect. The full analysis includes 845 stations across nine NOAA climate regions, whereas four representative stations from four regions are used for the detailed station-level analysis. Please revise this sentence accordingly.

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Citation: https://doi.org/10.5194/egusphere-2026-2300-RC2

Adarsha Neupane and Vidya Samadi

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We developed a new tool that combines physical science and artificial intelligence to estimate and predict how much water plants need. It automatically gathers weather data and produces reliable short-term forecasts across many locations. Results show strong accuracy in most regions. This approach can help farmers and water managers make better irrigation decisions and use water more efficiently.


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