Everything everywhere all at once: A single-cell LSTM network unifying multi-frequency, missing data, and discharge assimilation for robust operational flood forecasting

Acuna Espinoza, Eduardo Jose; Álvarez Chaves, Manuel; Kratzert, Frederik; Klotz, Daniel; Gauch, Martin; Lang, Robert; Elfgang, Dominik; Dolich, Alexander; Loritz, Ralf; Ehret, Uwe

doi:10.5194/egusphere-2026-4885

Preprints

https://doi.org/10.5194/egusphere-2026-4885

Preprints

03 Sep 2026

| 03 Sep 2026

Everything everywhere all at once: A single-cell LSTM network unifying multi-frequency, missing data, and discharge assimilation for robust operational flood forecasting

Eduardo Jose Acuna Espinoza, Manuel Álvarez Chaves, Frederik Kratzert, Daniel Klotz, Martin Gauch, Robert Lang, Dominik Elfgang, Alexander Dolich, Ralf Loritz, and Uwe Ehret

Abstract. Long short-term memory (LSTM) networks have demonstrated state-of-the-art capabilities in operational flood forecasting, with recent missing-data handling strategies further improving pipeline robustness. Building on these advancements, we introduce the multi-frequency masked-forecasting LSTM (MF²LSTM), a model architecture that combines missing-data workflows with multi-frequency approaches to generate hourly streamflow forecasts. Additionally, our framework features a flexible data assimilation strategy to include real-time discharge information. This approach enhances forecast performance when real-time observations are available, and allows the model to keep operating when the discharge signal is absent, either by gauge failure or for prediction in ungauged basins. We benchmarked the MF²LSTM against the Large Area Runoff Simulation (LARSIM) model, the current operational flood-forecasting model used by several European countries, forcing both models with ICON-D2 meteorological products. Our results indicate that the MF²LSTM yields higher predictive accuracy than LARSIM. Overall, this framework presents a robust operational pipeline that demonstrates the viability of deep learning for hourly forecasting. Furthermore, by relying on a standard single-cell LSTM architecture, the approach highlights that structurally simple deep learning architectures can achieve high operation performance.

Received: 13 Aug 2026 – Discussion started: 03 Sep 2026

Competing interests: At least one of the (co-)authors is a member of the editorial board of Hydrology and Earth System Sciences.

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Eduardo Jose Acuna Espinoza, Manuel Álvarez Chaves, Frederik Kratzert, Daniel Klotz, Martin Gauch, Robert Lang, Dominik Elfgang, Alexander Dolich, Ralf Loritz, and Uwe Ehret

Status: final response (author comments only)

RC1: 'Comment on egusphere-2026-4885', Anonymous Referee #1, 26 Oct 2026

General Comments
This paper discusses and evaluates the integration of several recent operational-‘ecosystem’ developments linked to LSTM based hydrologic simulation and forecasting networks, benchmarking it against an existing operational process-model based system (LARSIM). The two major new developments built into the new architecture are the MME approach for handling missing input data, and a DA approach for leveraging real-time streamflow obs. in the forecast.

It’s a useful paper, well written and (mostly) clear, and is technically solid. And the title is wonderfully creative. The comments below include mostly reactions that the authors may consider, particularly as to whether to provide any additional perspective linking some of the methodological aspects to counterparts (such as DA, gap-filling, or post-processing) in traditional conceptual/PB-model forecasting systems. It is somewhat sparse in terms of providing perspective (ie in the intro or discussion, or methods) comparing/contrasting its methods with other research or practice, notwithstanding the experimental benchmarking versus LARSIM, which is commendable. In a few places, additional details are requested for clarity, and in one case, a validation of masking probability if it is feasible.
My strongest request for revision is for expanded analysis in the results section to give more perspective on the relative performance of (a) the DA aspect itself versus no-DA, and (b) the overall new MF²LSTM architecture with a spatial analysis, ideally illustrating any terrain or network related variations in performance. I do not expect any of the comments to require more than minor revisions (i.e., no re-running of experiments is suggested).

Specific Comments
Abstract: memorable acronyms are often shorter & easier to type/pronounce than the one used (MF²LSTM) – perhaps consider something like: “MF²L” or similar (w/o superscript & 4-5 letters). Authors’ choice of course.

line 17 (ln17): “these frameworks”. A semantic question -- are these ‘frameworks’ or just systems? Against a landscape of decades of operational forecasting systems based on conceptual & PB models that also include elements like DA, forcings & associated routines to fill RT data gaps, operational cycling, the authors might consider whether swapping in a DL model (instead of traditional model) transforms the resulting system into a different ‘framework’ (which is more indicative of a theoretical approach or concept, and implies some generality, ie, that the system is in fact a template, different from other existing templates). The term ‘framework’ has become a bit overloaded in recent literature. In contrast, I’d say the use of framework on ln 26 is more appropriate because MF modeling architectures are different/new concept, a distinct approach. Anyway, I defer to the authors’ preferences here.

ln 23: I suggest some elaboration, as this point is specific to the AI community, not more generally: “large-sample datasets at hourly resolution -- which have played a foundational role in the training and development of LSTM based modeling approaches -- are rare”. For many if not most op. flood forecasting systems, subdaily resolution datasets are more common, not rare, and daily modeling systems are more rare in this context (US, UK, Germany, NL, EFAS, and so on) – forcings range from hourly to 6 hourly, generally. These non-AI systems don’t train on large-sample datasets (yet) versus on large-domain contiguous forcing fields.
ln 29: alternative phrasing for “is injected into” would be something like ‘is used to update/constrain model states’

ln 30: It would be appropriate to recognize that DA has been studied for use in trad. op. hydrol. forecasting systems for decades (and it’s used in some though not as extensively as one would hope). Workshops such as https://hepex.org.au/joint-workshop-on-cahmda-vi-and-hepex-dafoh-iii/ illustrate the community work on the topic, for instance. St. Fleur is one reference pt for AI based systems but reference could also be made with non-AI based systems and study, which might allow drawing a nice contrast between what may be different when you try to apply DA with an AI based system. The impact on training is notable. In trad. systems, the models are generally trained w/o DA and then DA is added to the op. system, which means this issue may not be as relevant. There has always been a desire to jointly train params & states in trad. op. systems but it has often been computationally difficult, thus such system components (the model, the DA system, the calibration system) are less integrated (this seems to be somewhat limiting in LSTM system application as well). Additional discussion here could provide some perspective on how DA has featured in op. hydro. f’csting systems.
ln 55: Can the authors add several sentences to describe the characteristics of this state’s hydrology, including hydroclimate and degree of development/impairment? What fraction of these sites are headwaters vs regulated?

ln 67: several textbooks by Daniel Wilks are also more common/seminal references for the concept of forecast skill & skill scores. I get that the WMO guidelines are a recent summary.

ln 87: PNSE is an interesting metric. Persistence forecasts are a common/standard benchmark (ref. fcst) for streamflow and other types of forecasting. The more standard to incorporating a PF is to calculate a skill score using a metric like NSE (or whatever other score you prefer) of the test forecast versus NSE of a persistence forecast, ie NSE-SS = 1 – (NSE_fcst/NSE_{pers_fcst}). PNSE appears to be more direct. Does this have a reference in another paper? If so, please include it. If not, and this paper is the original source, it may become the key motivation of future citations for this paper. Note, a positive of the NSE is that there is a known breakpoint between scores with information beyond just knowing the climatological mean (at NSE=0), which conveys a general sense of the usability of the forecast. Here the equivalent is that PNSE=0 signifies not knowing anything more than the last value of the flow. But such forecasts could nonetheless be ‘skillful’ (eg, with errors of less than 10% up to some future lead time, dep. on persistence) at PNSE=0. Is there any value to the PNSE scores beyond just the benchmarking usage? Could be worth a bit more discussion/perspective. Note, there’s a recent paper by Wouter Knoben on inherent reference benchmarks in skill scores, as well as a comment by Martyn Clark (on a paper with a title like ‘Friends don’t let friends use NSE’) that provides some good discussion on the intrinsic benchmarks used in scores like NSE. Not suggesting here to cite them, but they could provide food for thought for a little elaboration about the PNSE, which seems new to me.
ln 100-104: It would be preferable if this were a more technical DA description using language familiar from the DA-hydrology-forecasting literature (ie recognizable). E.g., “… the assimilation module applies a signal shift to correct the forecast starting point, which progressively transitions to the initial trajectory” is unclear. Can the authors summarize more detail, e.g., the assimilation algorithm (which?, automated or not?) updates the model [which states, which forcings] -- in several simple straightforward sentences, at least summarizing briefly what may be in the Luce reference. E.g., does it use a method like EnKF to update hydrology states, or are only river-channel states updated (as sometimes is the case). Are only discharge obs used for updating or are other watershed obs (such as for snow) used?
ln 120: It would be helpful if this section included a sentence or two about the forcings used in calibration and operational spinup, and whether the met forecasts are corrected or post-processed to match their climatologies. This could be a relevant factor affecting the relative inferior performance of LARSIM vs the MF²L approach, in that the latter inherently corrects for met. fcst vs met forcing bias while the former doesn’t, if that’s indeed the case.

ln 150: Just a comment for perspective: an interesting contrast in trad. (ie conceptual, PB model-based) systems is that met. inputs and DA inputs (eg flow, snow, SM) are handled a bit differently to address missing values, which are normal in any real time system (ie in some large-domain systems, if you look at met. obs available in the day before initialization (t0-1d), they are degraded by about a third from those available 5 days previously (t0-5d). So the common approach is to QC and gap fill them, then construct the met. analyses used as input to the forecasting system. And this happens in RT with a lookback so that the records for spinup are ultimately updated using full record info. Due to this, an MME strategy is not needed for met. data to train such systems. For obs used in assimilation, such QC+gap fill can also be used (esp. if DA is on a regular cycle), but in some systems, assimilation only happens when obs become available (not when they’re missing), given that many types of Earth obs are expected to be discrete vs regular/continuous timeseries. In this case, also, the DA system does not train with MME-like approaches. This is not to suggest MME is not a viable strategy.

ln 161: I would just wonder if the AR loop parameters can be modeled as ‘static’ (including potential use of covariates related to flow regime & future met. input), such that this training could be separated from the overall system training, and applied cheaply once the parameters are set. Note, I see later on that this topic is handled somewhat via the teacher forcing + noise approach described in the appendix.
ln 180: Could the masking rates be validated against the actual occurrence of missing data in the streamflow network, especially for pstep? i.e., analyzing the missing obs frequency at t0, t-1, t-2 etc. It’s unclear to me if pstep can be a distributed (gage-specific) vector … gage dropouts are usually not random, as is suggested later (ln 263), with some gages being less reliable than others. I would guess that even pstep of 0.05 may be higher than the reality of this particular system. If is possible to add this, it would be an interesting data point.
ln 202: Just a comment: this behavior does match what’s expected. You could add a 3^rd plot (perhaps in an appendix, as I think it would be too messy to integrate into Fig 3, unless you made the box-whisker symbols very narrow) showing the NSE of a persistence forecast, just to show explicitly how it degrades with lead time. Note, 21 hours is a pretty short lead time so persistence outside of events can be skillful, depending on the river characteristics.
Fig 3 (top): The skill value annotations could be enlarged for readability, and if the y-axis extended to 1.1, probably plotted above the whiskers versus overplotting them. (same for Fig 4).
Results overall: Ideally, I would like to see more depth of analysis, as 2 visualizations are relatively narrow for a full research paper. One analysis to include would be a plot like Figs 3,4 but also showing the MF* method with and without DA. There is a summary table & example in Appendix 1, but it doesn’t show the impact of the DA clearly (e.g., Fig A2 compares with and without DA … but for 2 different metrics, as it’s showing more the comparison between pNaN levels.

Another analysis of interest would be a spatial depiction (map w/ gage points) of the performance and difference in performance between LARSIM & MF* at a particular lead time (or a few), and for the MF method w/o DA (+ difference). Clearly there is some variance across the network – it would be nice to see how it relates terrain & network topology.
Figure A1: legend for line colors is missing. Also, the 3^rd hydrograph in the figure is not described in the text (eg at ln ~306), and it’s unclear what it represents. Is the ‘seq. forecast benchmark’ for a particular lead time? Or another form of the model run in simulation mode?
ln 332: I think the AR-based (& teacher-forcing with noise) concept is reminiscent of the EnsPost AR-1 based postprocessing method used in the NWS HEFS system. I don’t think there is a great reference for it, but a HESS discussion paper (at least) exists. Depending what states/weights are updated in the LSTM-based system and how the assimilation increments to the states are propagated throughout the network, the DA scheme used here as applied to the future streamflow obs. may be partly akin to post-processing. EnsPost is itself a statistically formal (objective) variation on an even older common method of blending latest obs with forecasts (often done in an ad hoc manner, though expert guided). It would be useful if the authors could relate (i.e., discuss any similarities in objective or concept) their AR rollout (or teacher-forcing shortcut) to other existing methods from traditional model hydro. forecasting. That said, clearly the concept of DA applied here is a little different – ie 'assimilating' (in a way that's slightly unclear in the LSTM) an extended/projected streamflow obs., versus just using it to correct (post-process) a streamflow forecast (which is then assimilated into the routing system & propagates downstream, but not the trad. hydrology model itself).
Paper: Seo, D.-J., Herr, H. D., and Schaake, J. C.: A statistical post-processor for accounting of hydrologic uncertainty in short-range ensemble streamflow prediction, Hydrol. Earth Syst. Sci. Discuss., 3, 1987–2035, https://doi.org/10.5194/hessd-3-1987-2006, 2006.

Citation: https://doi.org/10.5194/egusphere-2026-4885-RC1
RC2:
'Comment on egusphere-2026-4885', Anonymous Referee #2, 30 Oct 2026
The article evaluates a multi-frequency masked forecasting LSTM (MF²LSTM) for short-term flood forecasting at the hourly time step on 138 in Baden-Württemberg, Germany. The approach is compared with the Larsim model for lead times up to 21 hours.
Though this is an interesting article, I think that several aspects could be improved to better demonstrate the usefulness of the proposed approach. Further clarifications could be given on the experimental design.
I suggest major revision before the article can be reconsidered for publication.
Detailed comments
Abstract: It could be said that the models were tested on 138 gauging stations in Germany.

Section 2.1: A bit more could be said on the test catchment set. What are the main rivers (their names could be shown on the map)? What are the main climate characteristics? Is there any influence of snow? (if yes, how is it accounted for in the tested models?). Etc. Distribution of a few climate or physical characteristics could be given (not only catchment area). I find this information would be useful to further analyse the results and the possible influence of catchment characteristics. There could also be some information given on the main flood events over the test period.

Section 2.2: The use of both NSE and PNSE is a redundant. They are based on the same error and therefore they deliver the same information in the comparison between models. I suggest only keeping PNSE, which is better suited for an evaluation in forecasting mode. If the authors wish to keep NSE as a reference more commonly known than PNSE, it could be replaced by the KGE criterion, whose three components would give information on which aspects of the hydrograph (bias, variability, timing) the MF²LSTM takes most of its advantage over LARSIM. Besides, appropriate references for these criteria should be cited: Nash and Sutcliffe (1970, https://doi.org/10.1016/0022-1694(70)90255-6) for NSE, PNSE should actually be better called Persistence index (PI) with reference to Kitanidis and Bras (1982, https://doi.org/10.1029/WR016i006p01034).

Section 2.2: The metrics used are classical but I think they only partially reflect criteria that are often used by flood forecasting centres. Three types of criteria could be added to complement the diagnosis. First it would be interesting to evaluate the capacity of models to anticipate streamflow thresholds. The threshold corresponding to Q95 already used by the authors could be selected. Criteria like probability of detection (POD), false alarm rate (FAR) or critical success index (CSI) could be computed and their evolution with lead time analysed. Maybe a single criterion could be added among those three, for example CSI which is the most integrative. Second it may be useful also to have information on the total volume that is forecasted by the models over the next h hours. This information can be useful for dam managers for example. A criterion like bias over the forecasting horizon (based on total volume from 1 to h hours) would be useful. Third, other event-based criteria may be more interesting to compute than (P)NSE at the event scale. Typically these may include the median (for all the events of a catchment) ratio between observed and simulated peak or the median time difference between observed and simulated peak, for a given lead time.

2 and 3: Please detail notations used. The lead should appear in the equations to clarify how criteria were computed.

Section 2.3.1: It is unclear for me how the LARSIM model was used over the test period. In operational conditions, a model traditionally uses meteorological observations to update its states from time step t-1 to time step t. At time step t, some assimilation is done, and then the model is run in forecasting mode with meteorological forecasts. Is it what was done here? This could be clarified to better know what was done exactly. Besides, the reference by Luce et al. (2006) is in German and not easily accessible for non-German-speaking readers. Could the authors say a bit more about how the assimilation process is done in LARSIM?

Section 2.3.2: Please say here whether ICON-D2 forecasts are probabilistic or deterministic (mentioned later in the text but could be useful here). About the overlap between calibration and validation, why not extending instead the calibration up to June 2021 and limit evaluation to get a more rigorous evaluation. If it does not change anything in the main conclusions, maybe just say it.

Section 2.4.2: line 166: Is not Decembre 2020 the end of the period?

Line 168: It was unclear for me which characteristics the authors refer to here?

Section 3: I found that there is space to improve the Results section and give more information to fully understand the results shown. First, as mentioned above, I think that the PNSE and NSE convey the same information about the respective performance of the two modelling approaches. This redundancy is not necessary. Second though the performance distribution of results over the 138 catchments are good to give a broad overview on model performance, one wonders whether performance is better for LARSIM than MF²LSTM on a part of the catchments or if the MF²LSTM advantage is systematic. Are there catchments where the MF²LSTM fails while LARSIM succeds? Third it would be interesting to have an analysis of performance depending on climate of physical catchment characteristics. Do they have any influence on results? Fourth I understood that the LSTM-based model is applied independently on each station, but it was unclear for me whether it can benefit from flow observations from neighbouring stations. If yes, to which extent does it benefit from flow observations from upstream stations? Similarly does the LARSIM model uses information from upstream stations? If yes does the integration of model forecasts made at upstream stations, which necessarily include errors, is a source of lower performance at downstream stations compared to integrating observations only (in an idealized forecast configuration)? The upstream-downstream consistency of forecasts could also be further analysed anyway.

Section3: I also missed a discussion on the impact of meteorological forecast quality on results. The tests could also be made using meteorological reanalysis instead of forecast, to see to which extent the weather forecast influences results.

Line 206-207: It is unclear whether the choice to include a forecast in the evaluation is based only on the observation at t+h exceeding the threshold. Please clarify this point.

Lines 192-195: I found that there is no demonstration of this point in the results shown in the article.

Line 195: “at lead time 21 hours”

Line 203: I wonder whether the narrower IQR is really a sufficient criterion for comparison. For example, graphs on PNSE in figures 3 and 4 show that LARSIM tends to get higher performance on some catchments. Could this be further analysed?

Figure 3: I was surprised that in Fig. 3, for NSE, the upper percentiles of the distributions seem to be exactly the same for the two models. Is it just by chance or something to check?

Figures 3, 4 and A2: Please clarify in the captions which percentiles of the criteria distributions are shown in boxplots. Indicate unit for lead time in x-axis.

Lines 218-220: Though the article shows that the proposed LSTM-based model is able to cope with gaps in data, I found that it does not show whether it provides a better behaviour than the LARSIM model in these conditions. The testing protocol could evaluate this by placing the models in the same conditions of gaps and evaluate their relative impact on their forecast quality.

Appendix A: I found the content of this appendix, which is central to demonstrate the ability of the proposed model to cope with gaps, would be better placed in the main text.

Line 283: Maybe I missed something, but I did not fully understand the case of ungauged sites mentioned here, which seems very different from the case tested here (?).

Table A1: I did not understand the content of this table. Are criteria actually computed on the same time steps? If not, I find the comparison difficult to establish. I neither did not fully understand why the two different criteria are computed and results obtained on the last row. Could the authors further explain these choices and results? At least for me they were not fully clear.

Figure A1: I missed the information on the catchment that is considered, the year, the severity of this event, for which lead time these forecast are provided, etc.
Citation: https://doi.org/10.5194/egusphere-2026-4885-RC2

Eduardo Jose Acuna Espinoza, Manuel Álvarez Chaves, Frederik Kratzert, Daniel Klotz, Martin Gauch, Robert Lang, Dominik Elfgang, Alexander Dolich, Ralf Loritz, and Uwe Ehret

Data sets

Supplementary data and results Eduardo Acuna https://doi.org/10.5281/zenodo.21907865

Model code and software

Code Eduardo Acuna https://doi.org/10.5281/zenodo.21907865

Eduardo Jose Acuna Espinoza, Manuel Álvarez Chaves, Frederik Kratzert, Daniel Klotz, Martin Gauch, Robert Lang, Dominik Elfgang, Alexander Dolich, Ralf Loritz, and Uwe Ehret

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Short summary

We present the Multi-Frequency Masked-Forecasting LSTM (MF²LSTM), a pipeline unifying multi-frequency modeling, missing-data handling, and real-time data assimilation for hourly streamflow forecasting. Forced with ICON-D2 weather data, MF²LSTM yields higher performance than LARSIM, the operational model used in Baden-Württemberg, Germany. Using a single-cell baseline, this work proves that simple deep learning models can deliver high-level operational performance without extra complexity.


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