RiverMamba: A State Space Model for Global River Discharge and Flood Forecasting
Authors: Mohamad Hakam Shams Eddin
Yikui Zhang
Stefan Kollet
Juergen Gall
Venue: NeurIPS 2025 poster ()
Keywords: Mamba
Earth science
climate science
hydrology
flood forecasting
river discharge
Primary area: machine_learning_for_sciences
TL;DR: We present a novel deep learning model for global river discharge and flood forecasting

Abstract: Recent deep learning approaches for river discharge forecasting have improved the accuracy and efficiency in flood forecasting, enabling more reliable early warning systems for risk management. Nevertheless, existing deep learning approaches in hydrology remain largely confined to local-scale applications and do not leverage the inherent spatial connections of bodies of water. Thus, there is a strong need for new deep learning methodologies that are capable of modeling spatio-temporal relations to improve river discharge and flood forecasting for scientific and operational applications. To address this, we present RiverMamba, a novel deep learning model that is pretrained with long-term reanalysis data and that can forecast global river discharge and floods on a $0.05^\circ$ grid up to 7 days lead time, which is of high relevance in early warning. To achieve this, RiverMamba leverages efficient Mamba blocks that enable the model to capture spatio-temporal relations in very large river networks and enhance its forecast capability for longer lead times. The forecast blocks integrate ECMWF HRES meteorological forecasts, while accounting for their inaccuracies through spatio-temporal modeling. Our analysis demonstrates that RiverMamba provides reliable predictions of river discharge across various flood return periods, including extreme floods, and lead times, surpassing both AI- and physics-based models. The source code and datasets are publicly available at the project page https://hakamshams.github.io/RiverMamba.

RiverMamba: A State Space Model for Global River Discharge and Flood Forecasting
Mohamad Hakam Shams Eddin
Juergen Gall
Institute of Computer Science, University of Bonn Lamarr Institute for Machine Learning and Artificial Intelligence {shams, (alll)iiai.uii-bae
Yikui Zhang
Stefan Kollet
Institute Bio- and Geosciences Agrosphere (IBG-3), Research Centre Jülich Centre for Bigh-Peeffrmmace Scientific Computing in Terrestrial Systems, Geoverbund ABC/J, Jülich
fyik.zhang, s k.kollet)@fz-juulleeee
Abstract
Recent deep learning approaches for river discharge forecasting have improved the accuracy and efficiency in flood forecasting, enabling more reliable early warning systems for risk management. Nevertheless, existing deep learning approaches hydrology remain largely confined to local-scale applications and do not leverage the inherent spatial connections of bodies of water. Thus, there strong need for new deep learning methodologies that are capable of modeling spatio-temporal rela- tions to improve river discharge and flood forecasting for scientific and operational applications. To address this, we present RiverMamba, novel deep learning model that is pretrained with long-term reanalysis data and that can forecast global river discharge and floods on 0.05% grid up to 7 days lead time, which is of high rele- vance early warning. To achieve this, RiverMamba leverages efficient Mamba blocks that enable the model to capture spatio-temporal relations in very large river networks and enhance its forecast capability for longer lead times. The forecast blocks integrate ECMWF HRES meteorological forecasts, while accounting for their inaceuracies through spatio-tempol modeling. Our analysis demonstrates that RiverMamba provides reliable predictions of river discharge across various flood return periods, including extreme floods, and lead times, surpassing both AI- and physics-based models. The source code and datasets are publicly available the project page httpps //hakaassaam github. 1o Riverrammal
Introduction
Riverine floods are one of the most destructive natural disasters, with their risk anticipated rise in the future result of climate change and socioeconomic developments (H5). They arise from compound effects, including atmospheric conditions like heavy precipitation caused by circulation patterns and snowmelt succeeding high temperature, all shaped by the specific characteristics of the river drainage area [6]. The interaction of these elements influences flood timing, scale, and severity changing climate may
(6]. This complexity makes future flood risk assessment challenging, alter these drivers in unpredictable ways 77. Therefore, carly prediction of flood risk, especially for extreme floods, is key measure for effective flood risk mitigation g 9
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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GloFAS reanalysii
RiverMambs
day lead time (2024-05-30) 00--0)
2 days lead time (2024:05-31)
days lead time 12024-06 06-01)
days lead time (022400-02))
days lead time (2024-06- (03---06-33
Z-year flood
5-year flood
10-year flood
20-year flood
Figure 1: Example of a 5-day forecast of river discharge and flood events. In early June 2024, a significant flood affected Southern Germany. While the top row shows the floods obtained from the GloFAS reanalysis, the bottom row shows the river discharge forecast by our approach. The severity of floods is categorized by the statistical flood return period, i.e., occurring every 10 years.
To support national forecasting initiatives, current operational flood early warning systems can forecast river discharge in real-time and provide flood forecasts at different scales [IH[2]] The discharge forecasts derived from these systems be further processed using inundation models create anticipated flooded areas 13 14]. The Global Flood Awareness System (GloFAS) [15] 16), developed under the Copernicus Emergency Management Service (CEMS) and operated by the European Centre for Medium- Range Weather Forecasts (ECMWF), represents the cutting-edge physics-based model for real-time and worldwide hydrological forecasting. However, physics-based hydrological models are expensive to run and require extensive calibration to handle complex catchment characteristics.
Al-based early warning systems thus considered vital tools to enhance climate risk resilience [8] and to enable flood forecasting without requiring full physical process understanding [99 20). While deep-learning approaches for weather forecasting 221 have been investigated in recent years, very little work has been done for forecasting river discharge at large spatial regions since it is very challenging. It requires the combination of sparse gauged river observations with high-resolution land surface, re-analysis, and weather forecast data. Furthermore, floods occur rarely and the goal to forecast floods of different severity as shown in Fig. [[] Recently, an LSTM-based model has been proposed [24]. While it achieves promising results, it forecasts floods only locally at sparse river basins and does not consider routing. Modeling spatio-temporal relations, however, very important and required to generate consistent dense maps as in Fig. I since river discharge at points near connected bodies of water is highly correlated.
In this work, we propose the first deep learning approach for global river discharge and flood forecast- ing that is not only capable of forecasting at sparse gauged observation points, but also of forecasting accurate, high-resolution (0.05%) global river discharge maps. order to deal with the sparseness of gauged river points and the computational complexity of modeling spatio-temporal relations at the global scale, our proposed RiverMamba leverages Mamba blocks, which are bidirectional state space models (85.28). and spatio-temporal forecast blocks. Using a specialized procedure to convert sampled points into ID sequences, RiverMamba maintains a very large spatio-temporal receptive field, connecting the routing of the river channel networks and the teleconnection of meteorological data across space and time. RiverMamba has thus the possibility to consider a spatio-temporal context that covers very large river networks like the Amazon River. The forecast layers are further forced by high-resolution metcorological data (HRES) to generate medium-range river discharge forecasts up days lead time. To address uncertainty in the meteorological forcing, we built the forecast layers so that they can, for each catchment point, incorporate information about meteorological forcing from the neighboring points and throughout the temporal dimension. Thus, RiverMamba ensures a consistent forecast through space and time. Our contributions can be summarized follows:
We introduce a novel Mamba-based approach, called RiverManba, for global river discharge and flood forecasting. is the first deep learning approach that is capable of providing maps of global river discharge forecasting at 0.05*, and it introduces novel methodology to

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hydrology. It is able to integrate sparse gauged observations, river attributes, high-reso reshuresolttion reanalysis data, and weather forecast. The efficient structure allows to model spatio-temporal relations covering entire river networks.
We evaluate RiverMamba on both long-term real-world reanalysis and observational data where it outperforms state-of-the-art AI- and physics-based operational systems for global flood forecasting.
2 Related works
Flood forecasting, Floods can be categorized into three common types. The first type is the fluvial or riverine flood [29]. It occurs when the water level in stream rises and overflows onto the adjacent land. The second type is the coastal flood, also known as storm surges [30]. The third type is the pluvial flood, often referred to as flash flood [3 that can occur with extreme rainfalls. Machine learning (ML) has become an essential element for the development of hydrological simulation and flood models [34 351. Each type of flood has unique drivers and impacts. Consequently, ML methods require different strategies to forecast them. Related tasks to flood forecasting are urban flood modeling 39 flood inundation 42) and flood extension and susceptibility mapping 445 46
In this work, we are interested in forecasting riverine floods (fluvial) based on river discharge.
River discharge forecasting. River discharge can be used to detect fluvial flood signals when the magnitude of the flow exceeds certain thresholds. Current deep learning methods for forecasting river discharge are primarily based on locally lumped models 47 48]. hypothesizing that a single model can generalize across many catchments without considering the spatial-tempor
information
over grids [49]. The dominating backbone the LSTM model [50] which is used in most recent studies such as EA-LSTM 52), ED-LSTM [53 [54, Hydra-LSTM (55], MC-LSTM [56). MF- LSTM [57] and DRUM 588 These models learn features specific to individual rivers or entities and lack spatial and topological information. However, river networks have spatio-temporal causal relations [59]. Only few studies deviate from this conventional modeling and propose to model the network topology with Graph Neural Networks [60)62]. They are still limited to small scales and the graph models fail in most cases to capture topological information [60]. Others applied an LSTM model on coarse grid to estimate runoff and then coupled it with a river routing model to produce daily discharge at coarse resolution [63]. In (64] LSTT resolves local runoff spatially on regular grid in central Europe. Then, routing the runoff along the entire river networks is implemented as ID-convolutions and fully connected layers. The impact of defining routing explicitly with physics-informee neural networks has also showed an advantage in recent studies, especially, in improving streamflow in large continental river networks compared to models that do not consider routing 665 66). In hybrid modeling framework, physical equations including river routing parametrized using 3D-convolutions and fully connected layers for distributed hydrological modeling [67]. The most relevant work is the Encoder-Decoder LSTM [51] developed for the Google global operational forecasting system [24], which is a locally lumped model. In this work, distinct from previous works, propose approach that is capable of modeling large spatio-temporal context and forecasting medium-range river discharge at grid-scale.
State space model (SSMs) and the Mamba family. Linear SSMs 255 and structured SSMs like S4 226 and S5 [27] were primarily introduced for long-sequence modeling in NLP. Recently, Mamba introduced the selective scan mechanism, enabling efficient training and timear-time inference. Built upon Mamba, VMamba [68] and Vim [69] in the vision domain were introduced as appealing alternatives to the quadratic complexity of vision transformers [70] while improving scaling efficiency on long token sequences. A series of works have adapted Mamba to tasks like image generation image classification 73 74. video understanding 77| 76), motion generation [77), dense
28
71 72
action anticipation (78), and point cloud processing [79] 80) In this work, we propose a Mamba-based approach for global river discharge and flood forecasting.
3
RiverMamba
In this work, we present the first deep learning approach that not only forecasts flood events at sparse gauged river observations, but that is capable of forecasting accurate, high-resolution (i.e., at 0.05") maps of river discharge up to few days at global scale, as shown in Figs. D and 2 These maps are essential to forecast flood events of various severity like flood that re-occurs statistically within
3

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RiverMamba
Pieer Clomaaoe
(N NERASI Merec
XL12
Xt+
Hindcast-Layer
Forecast-Blon Block
BeFAS- Rearatycis
HRES
Embedding
Temporal Down sas-saampigggg
Se Serialization
Deserfalization
ERAS- Reanslysis
LOAN
Mamba
LOAN
Forecast Block
Forerast Block
Forecast Block
CPC
MLP
MLP
MLP
Intial condition
(Kcioras: Xisks X
Static maps Xatoric
AN
AN
AN
Figure 2: An overview of the proposed RiverMamba model for river discharge forecasting. The model forecasts at time t, high-resolution river discharge maps X X1+1:t4 1:t+- from initial conditions (X (xt-Tit-1
ERAS (x++124
w--Tt-1 1-t-1tt2 1:t-2), static river attributes (Xstatie), and metcorological forecasts (HHEES GloF CPC
1.5-year return period or 'flood of the century'. This is very challenging since it requires model that models spatial-temporal relations in efficient way and integrates different sources of data (Fig. 2..
As input, we use the initial condition of the forecasts from ERA5-Land reanalysis 81. denoted -i-Tt-1 by XERAS = 1xt-T EXERAS.... XERAS X--1 EERAS the initial condition GloFAS from the GloFAS reanaylsis data [82) and the initial condition X X1-T--10-2 from the operational global unified gauge- based analysis daily precipitation
We also include data from weather forecasts, where we use the high-resolution meteorological foreing forecasts X++1++L from the ECMWF Integrated HES
SKL 35
Forecast System (IFS), where L is the lead time for the forecast. We generate the river discharge forecast at 6, using 00:00 UTC as reference time, for ++1 until L+L. This means that we not address nowcasting but only forecasting as it is more relevant. We also do not include any nowcasts (XHRES) as input. The rationale behind this is to ensure broader applicability, since many weather forecast systems especially ML models provide forecasts at 0. However, adding nowcasts to the model is straightforward if they are available. To make the setup as realistic as possible, we do not include any data after 00:00 UTC and consider XGIoFAS and X XERAS at day 1 and Xere at day - 2. Additionally, we include river attributes X like catchment morphology from LISFLOOD 86 The input variables are described in details in the suppl. material. Given these inputs, RiverMamba forecasts changes of the daily mean river discharge AXt+ 1:14- relative the daily mean river discharge t i... xt-1 by xt#
dis24 The forecast daily mean river discharge thus given
dis24 = Xt-1
di.24 + AX++1 dis24
An overview of RiverMamba is shown in Fig. 2 For training, we sample P points that are on the land surface and near water bodies. The details are described in the suppl. material. For each point p. we obtain temporal sequence of embedding vectors ((-T:t- (p):
X Xmbeaa = LN (Tanh (Concat(Lineatt (XERAS()) Linss()))),nirrrrrii Linear (X o
As())) Linear X (x)))
where LN is the layer norm and Linear is the projection layer. The dimensions of the input are XERAS E BBXxxxxxV, XCtoFAS R BxxTxxXV, and XCPC E 3 where B is the batch size, V, is the number variables from ERA5, and V, is the number of variables from GloFAS. The embedding Xambed E Bx where = 192 is the dimensionality the embedding, is then the input to the encoder defined by the hindcast layers.

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Hindcast layer. The hindcast layers model pptii-ttempord relations and aggregate the observations over time. Except for the 1s layer which processes the full temporal resolution, the temporal resolution is down-sampled by factor of 2 with a linear layer at the beginning of each hindcast layer, such that the output of the last hindcast layer Xhindeast E R RBBx1xxxx has a temporal resolution of T T= 1. In our implementation, we chose T = 4 as for the GloFAS operational system and temporal down-sampling of 2. Consequently, we defined 3 layers to encode the input.
The hindcast layers further integrate the static river attributes Xstatic that contain additional infor- mation like catchment morphology, which is relevant for flood forecasting. While we analyze the impact of the different inputs, in particular the river attributes, in the suppl. material, another key aspect of the hindcast blocks the specialized serialization of the spatio-temporal points and the Mamba blocks [28 68 69]. The serialization defines the way the sampled points are connected, and the Mamba block efficiently updates the features of each point based on the spatio-temporal structure. This is a very important design choice since transformer blocks are computationally infeasible for global flood forecasting, whereas [24] does not consider spatial relations at all. the suppl. material, we also show that alternative using Flash-Attention [87 88 is inferior in terms of inference time and accuracy compared to our approach.
The output of the last hindcast layer is then processed along with the HRES meteorological forcing by forecast blocks, and MLP-bal b-sed regression heads predict for each lead time the difference of daily mean river discharge AX dis24 with respect to the daily mean river discharge at t-1. In the following, we describe the components of RiverMamba in details.
Hindcast block. As shown in Fig. the hindeast block has three main components: serialization and deserialization, location-aware adaptive normalization layers (LOAN) to integrate static river attributes, and the Mamba block.
Serialization. The serialization defines the spatio-temporal scanning path over all sampled points for the following Mamba block. For this, we propose space-filling curves that sequentially traverse through all points. The concept was introduced in [89] and the space-filling can be defined as a bijective function & 2 + N, where every point in the discrete space corresponds to unique index within the sequence. We call this mapping the serialized encoding. The serialized decoding is done as $-1 : N- Z3, where every index is mapped back into its corresponding position. We call this deserialization. We investigated three curves: the Generalized Hilbert (Gilbert) curve, which is generalized version of the Hilbert curve (90). as well as the Sweep and Zigzag curves in vertical and horizontal directions. Examples of space-filling curves in 2D are illustrated in Fig. 3 As shown in the suppl. material, combination of Sweep and Gilbert curves performs best. To this end, each hindcast block has its own eurve. As shown in Fig. 3] we sweep in the first block over the horizontal direction. The spatial curves are connected over time by continuing the last point of the curve at t with the first point of the curve at t+1. The second block then sweeps over the vertical direction and we continue with the Gilbert curve and its transposed. These four space-filling curves are iterated. By altering the curves sequentially through the hindcast blocks, the sampled points will be connected and scanned from diverse spatial perspectives, enabling River- Mamba to capture different contextual features.
Figure 3: Illustraioon of the spatial scans in River- Mamba. Larger images are in the supp. material.
Location-awee aware adaptive normalization layer. In order to condition the model on static river attributes Sstatic, the location- aware adaptive normalization layer (LOAN) [9]] modulates the features X within the hindcast block:
LOAN(X) = 1 -xx-"
+ (X.tteeiee(XXttttia
(2)
where a linear layer projects Xstatic E R.I.P.V. with V, being the number of static variables, to B.I.P.K The output is then duplicated along the temporal dimension so that the output has the dimension IR B.P.PK / E RB...PP and E B.P.P. are the mean and standard deviation of X along the channel dimension, respectively, and X E B.T. the input to the LOAN layer. Both J and are duplicated K times along the last dimension match X. The layer normalizes the features
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Prijecion
Deserialize tiiitiion
Serialization
Preneweedt
Cancan
LOAN
Backward
Backward Selective SSM
LOAN
MLP
cb
Conv10
Forward
Forward Se selective SSM
Embedding
ConvID
Mamba Block
HRES Xaxes
Static maps Xatatic
Figure 4: The structure of the hindcast block and forecast block. Both use a bidirectional Mamba block and the forecast block has the same structure the hindcast block, but it additionally incorporates meteorological forecasts (HRES) by concatenation. The forecast block also includes LOON layers although is not shown in Fig.
and adds a systematic bias based on the attributes. For instance, the features are normalized and biased based on location attributes that have impact on drainage and floods.
Mamba block. Fig. 4 shows a more detailed structure of the hindcast block with the elements of the Mamba block. After the input is serialized into a ID sequence based the block-specific space-filling curve and the features are normalized by the LOAN layer, the Mamba block processes the features of the sampled points along the sequence.
The Mamba block is based on state-space model that transforms a sequence of states sr() into another representation v(t) through an implicit hidden latent state htt) and first-order ordinary differential equation:
(t) Ah(t - Br(t), s(t) = Ch(t) + Dr(().
To integrate Eq. 33 into deep learning framework, S4 [26] parametrized the system with the matrices (A, B, D) and discretized it with a timescale parameter A:
h4 Ah + Br, (
Ch. + Dri,
(4)
B (AA) (c I)AB
where A and B are the discretized versions of the system. Recently, S6 228 proposed to make Eqs. and (5) time-variant. To this end, the parameters B(x), C(z),, and A (x) become dependent on the input state This representation of state-space model is called Mamba, which is an efficient alternative to transformers [92] particularly when processing many points as in our case.
Fig. illustrates the steps of the Mamba block. The normalized sequence X BBX is projected into R Bx (x and (Tx where Tx is the length of the sequence. Note that the order of the elements the sequence depends on the serialization, which differs between the hindcast blocks. We use a bi-directional approach that converts into x', using a forward and backward I-D causal convolution, where o E {f. denotes the forward or backward pass. For each direction, B,, C.. and A, are obtained by projection layers from x" and A,, and B, computed using Eq. (5). The selective SSM then uses Eq. 4 to obtain y forward and Ybackward for the forward and backward pass, respectively. The final output y is obtained by gating y forward and y Ybackward via SiLU(z) and adding them up. Finally, y normalized and projected back linearly The complete algorithm for the Mamba block is described in the suppl. material, After the Mamba block, the hindcast block includes another LOAN layer followed by an MLP. The final output X is then deserialized at the end since the next hindcast block uses different serialization.
(
Forecasting layer. While the hindcast layers encode the sequence of past input variables into K -dddmennionnl vector per sampled point, i.e., X Nandoast E BRBxxxxPxx the forecasting layers forecast the difference of daily mean river discharge Ax++1 dis24 for each lead time I, using Xhindeast and meteorological forecasts x(+1:t+L input, as shown in Fig. 2 The forecast blocks have the HRES
same structure as the hindcast blocks except that the forecast block incorporates the meteorological
forcing (HRES). This is done by projecting x(- X with a linear layer to 64 dimensions, serializing it, and concatenating it with the input X as illustrated in Fig. 4 The processing of HRES is done
sequentially, i.c., have L forecast blocks and the (-th forecast block processes X/+1/ HRES. We argue

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that this design is crucial to ensure that the temporal relationships between the meteorological forcing and the initial conditions are maintained.
The output of all forecast blocks is processed by I. regression heads implemented as multi-layer perceptrons (MLP) where the output for the lead time t + I is obtained as:
AX + dis21 Linear [ReLU Concat (Linear(X (aaaar/XX/reeaaaa forecust), Linear (X (orosas
(6)
where X
forecust are the features from the I-th forecast block and x X+1 are the concate- nated features from all forecast blocks except of the I-th block. The linear layers project the
forceast
input X X
forceust or X x++1:+L) to 32 dimensions and the last linear projection estimates finally dis24 E BXIXXx1
ffoecast
AXt+
Training, As already mentioned, we sample P points around the globe for training. As target value for training, we first use the river discharge data from the GloFAS reanalysis as ground truth and then fine-tune on sparse observations using data from the Global Runoff Data Centre (GRDC). For GRDC fine-tuning, we take P as the number of input points per sample and compute the loss only on points where GRDC observations are available without considering reanalysis data from GloFAS. We obtain
the target values by AX die2s =
*X (p) X Xis2s (p), where X are the values from GloFAS or GRDC. For the training loss, we propose a weighted version of the mean-squared error (MSE) loss:
1+1
B
P (p)++(p))
L "XXXXL
1
bit+l divza Ax diszd (p)1
(7)
b=1pm1
where the batch size. Since the severity of flood is highly important for flood forecasting and severe floods occur rarely, the weighting factor w*,++(p)) takes this into account. The severity of a flood ranked by the statistical flood return period in years, which we denote by r and ranges from 1.5 to 500. These ranges are also used in GloFAS. We note that high return period event simply reflects statistical rarity in streamflow magnitude, and should not be equated with a flood event without additional context, e.g., thresholds or inundation. The return period is used here as a proxy indicator of hydrological extremity, which we call flood. The severity of a flood is thus given by git (p) = max, {r: di)2 {
2 0.(m)) }. where 0, is the statistical threshold for a given flood return period r. We also include the case r=0 with 0,=00 for defining events that are not floods. Using this notation, the weighting is thus given by
pbhet (p)
if phatt(() >
whetl (p) =
(8)
otherwise.
We thus weight the loss based on the flood return period if flood occurred at location p and time I ++4 I, and we use if there has been no flood. We further weight the loss with ūhr++ = (I.-++1)) where we give a higher weight to a shorter lead time / and use a=0.25. This compensates for the sequential structure of the forecast blocks where each forecast block takes the features of the previous block as input. The final weight is thus given by w (p) ((+++1""++((p))) Since river discharge exhibits a very large dynamic with varying orders of magnitude. we transform the discharge values by sign( A. log(l
[1 + |a.)). We evaluate the impact of the weighting in Table 2 (a) and provide more details in the suppl. material. For inference, we can forecast floods for any set of points or densely as in Fig.
4 Experimental results
Dataset. We obtain data for river discharge from the ECMWF GloFAS reanalysis 82 It is generated by forcing the LISFLOOD hydrological model [93] using meteorological data from ERAS (94] GloFAS reanalysis combines physics-based simulation with observations to generate a consistent reconstruction of the past. The dataset is provided as a daily averaged discharge on a global coverage 3 aremin grid (0.05%). We use the GloFAS reanalysis as a target discharge for training and testing the model in Sec. 4.1 The ablation studies are done using GloFAS reanalysis over Europe, In addition, we fine-tune and test the model on observational GRDC river discharge data in Sec. 4.2. Flood thresholds are determined using return periods for individual points and are calculated from the long-term data. The thresholds allow for the identification of flood when the threshold is surpassed.
7

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Evaluation metrics. We evaluate the performance of RiverMamba on both GloFAS reanalysis and GRDC, where diagnostic GRDC stations are available (3366 stations). For evaluation, we use common metrics like the coefficient of determination (R2), Ling-Gupta efficiency (KGE), and the averaged Fl-score for floods with return periods of 1.5 to 20 years. Details about these metrics can be found in the suppl. material. We train on the years 1979-2018, validate on 2019-2020, and test on 2021-2222222 1-204.. All evaluation points are gauged stations and temporally out-of-sample. Results on ungauged stations are also available in the suppl. material. The metrics are calculated on the time series at single grid points and then averaged over all points.
Baselines. We compare RiverMamba to persistence, climatology, and the state-of-the-art deep learning Encoder-Decoder LSTM of Google's operational flood forecasting system [24]. For the LSTM model, we followed the same protocol as originally proposed in [24]. which considers only temporal context but does not include any spatial connections. The space filling curves are thus not used in combination with the LSTM baseline. To ensure consistent evaluation, we train LSTM on the same input data as RiverMamba. All results in the paper are obtained with our trained LSTM. comparison with the published reforecasts by Google's LSTM (24) is also available in the suppl. material. For evaluation on GRDC observations, we additionally compare our approach to the reforecast version of the state-of-the-an operational GloFAS forecasting system operated by ECMWF material.
[5 [6]. More details about dataset, evaluation metries and baselines are provided in the suppl.
4.1 Experiments on GloFAS river discharge reanalysis
The quantitative results are shown in Table I As can be seen, the climatology baseline performs poorly, as the dynamic in local river discharge varies lot over time, highlighting the difficulty in predicting flows. We therefore exclude it in Fig. 5 (a) that shows F1-score for floods with a 1.5-year return period and (b) KGE for river discharge for different lead times from 24 to 168 hours. The boxes show distribution quartiles and the evaluation points are represented as points along the y-axis. Fig. (d) shows the Fl-score averaged over return periods of 1.5 to 20 years and (e) shows the median R2 for river discharge. The persistence baseline predicts the future discharge as the same value of the discharge at time L. This achieves good prediction for the short-term forecast, however, the prediction skill drops with lead time. While LSTM outperforms the persistence baseline, RiverMamba outperforms all baselines and methods on all metrics as shown in Table [ In particular for lead times above 48 hours, the performance gap between RiverMamba and LSTM is large. We attribute this to the receptive field and the spatio-temporal modeling of RiverMamba. Fig. (c) plots the Fl Fc-se averaged over 24 to 168 hours lead time for different flood return periods. The results show that RiverMamba outperforms the other approaches both for more frequent floods and rare severe floods that occur statistically only every 500 years. More results are in the suppl. material. In the following, we discuss set of ablation studies that are not performed globally but over Europe.
Objective functions. In Table (a), we evaluate the impact of the weighting factor in the loss which is based on ② Eq. 8 and é. The results show that both terms improve the results. w is
L's yeur
Guata
[toun] parted
time [toun]
Averrgedd TLacon lndd
Averged Tlanzw over 1.520 setrr
Madian with
LSTe
1STM
Exed Intor (ears)
Figure 5: Results on GloFAS reanalysis across lead times and flood return periods.
8

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Table 1: Results on GloFAS-Reanalee (+) denotes the standard deviation for 3 runs.
Validation (2019-2020)
Test (2021-2024)
Model R2 (1)
KGE (t)
F1 (t)
R2 (t)
KGE (1)
Fl (1)
Climatology 0.1175
0.2618
0,1352
0.2449
Persistence 0.6778
0.8380
0.3138
0.6833
0.8412
0.3223
LSTM 0.8539:10.00331 0.000000000000100000000000001113
0.351 0.8485110.0021 0.8924 0.3582:10.0058
RiverMamba 0.8803
0.4540:10.0056 0.8728::0.0013 0.9120::0.000000 0.4589:00.0080
Table 2: Ablation studies on the validation set over Europe.
(a) Objective function (b) Location Embedding
(c) Forecasting strategy
KGE FI (t)
LOAN (hind) LOAN
KGE FI (t)
S-HRES T-HRES
KGE FI (t)
X X 0.9086 0.2236
x
x
0.9183 I 00.2790
X
/
0.8862 I 0.2030
/ X 0.9127 0.28559
x
0,9160 I 0.2827
0,8869 0.2268
X / 0.9136 0.2593
X
V
0.9166
0.9205 0.2875 /
I 0.2931
/
0.9205 0.2875
/ 0.9205 0.2875
important to focus rare and more severe floods, increasing the Fl metric substantially (second row). à gives more weight to the forecast in the near future where NH is more reliable, which is important due the sequential structure of the forecast module. Using only û (third row) improves the results on both KGE and F1 metrics. Using both and â (fourth row) gives the best results.
Location embedding. In Table 2 (b), we show the benefit of using LOAN. In the first row, duplicate the static features along the dimension and concatenate them with the dynamic input. Using the LOAN layer in the hindcast (second row) or forecast blocks (third row) increases the Fl score but decreases KGE. Using LOAN in both hindcast and forecast blocks balances the metrics (fourth row).
Forecasting strategy. Table (c) evaluates the impact of spatio-temporal modeling in the forecast module. In the first row, we remove the spatial relations in the forecast module by replacing the forecast blocks by point-wise MIPs. In this way, the data processed after the last hindcast layer temporally but not spatially. This makes the model unaware of the spatial biases in the meteorological forcing XHRES. The second row denotes a setup where the forecast blocks do not get the features from the previous forecast block (Fig. 2 but directly from the last hindcast layer. In this case, we forecast river discharge for each lead time independently. The results show that both cases the performance drops compared to our approach (third row), demonstrating the importance of spatio-temporal modeling. More ablation studies can be found in the suppl. material.
4.2 Experiments on GRDC observational river discharge
Table reports the performance on GRDC river discharge observations at gauged stations, which also includes the physics-based GloFAS reforecast model. As previously, Fig. 6 coomprees the forecast performance across multiple lead times and flood return periods. Compared to the results on GloFAS reanalysis (Table T). all models show noticeable drop performance when evaluated on GRDC observations (Table 3 This decline likely stems from the fact that GloFAS simulates primarily naturalized discharge, with simplified representations of major reservoirs
32 95 whereas GRDC reflects fully regulated flow, influenced by complex and unobserved human activities, such as dam operations and irrigation. This introduces biases that models cannot learn, especially in the absence of globally available data representing human water management, highlighting the challenge of predicting discharge under human- modiiied conditions. The results show that traditional baselines such as Climatology and Persistence perform poorly. GloFAS performs much better than the baselines, but the R2 and KGE values are rather low due to the mentioned differences physics-based models and observations. RiverMamba consistently outperforms the other methods for all metrics. Notably, RiverMamba shows less degradation Fl F1-score with increasing lead time, highlighting its strength in medium-rane range flood forecasting. More results are in the suppl. material.

---

GEPAA DOMMY
GROAA (OOWA))
51 scere Nr your dout peroiiveets Sattr DNN PAX Statoos
King Supli ofoonn mesic
paterrs
(oors]
Aecragol 1l lesc (oumppai
4B Prcsapol Maanc la 20 ICUMUORAb por koallan
Moll R2 lang
Bhatkante
LSTM
LSTH
0.13
0.50
103
123
10
350
Figure 6: Results on gauged GRDC observations across lead times and flood return periods.
Table 3: Results on GRDC gauged stations. (#) denotes the standard deviation for 3 runs.
Validation (2019-2020)
Test (2021-2023)
Model R2 (1)
KGE (1)
Fl (1)
R2 (t)
KGE (1)
Fl (t)
Climatology -0.0002
0.1342
-0.0013
0.0870
Persistence 0,1682
0.4569
0.1626
0.0660
0.3918
0.1462
GloFAS 0.3713
0.5412
0.2135
0,2892
0.4944
0.2044
I.TTM 0.5437:t0.0025
0.4615+-0.0039
0.6141 0.0014
RiverMamba 01944880.00660000155000000000..0
0.5057:10.002
0.6612:10.0110 0.0027
5 Conclusions and limitations
We introduced RiverMamba, a novel deep learning approach for global, medium-range river discharge and flood forecasting. Due to its efficient structure and specialized scanning paths, RiverMamba main- tains a very large receptive field, while scaling linearly with respect to the number of sampled points. As a result, RiverMamba capable of forecasting high-resolution (0.05") global river discharge maps. Further. the spatio-tempont modeling of the forecast blocks incorporates metcorological forcing and ensures consistent forecast through space and time. Our analysis reveals that RiverMamba outperforms operational state-of-the-att deep learning and physics-based models on both reanalysis and observational data. While the results show major advancements in river discharge and flood forecasting, the approach has some limitations. For a real operational setting, only data can be used that is available until the current day For instance, ERA5-Land is publicly available after days whereas we assumed that ERAS-Land is already available after day, i.e., -- 1. LR-Laaand, however, could be substituted by other near real-time reanalysis data that is earlier available or analysis data until day l. It also needs to be mentioned that observational data are affected by human interventions like dams and there is a need to integrate such interventions in the model. As it is the case for operational systems, floods are not always correctly forecast. The causes of the errors need to be analyzed more in detail. The forecast errors can be caused by human interventions, errors in the weather forecast for metcorological forcing river attributes, the rarity of floods, or bias in the data and re-analysis. Given such errors, it is desirable to extend the model such that it estimates its uncertainty for the forecast well.
Besides these limitations, RiverMamba has the potential for an operational medium-range river discharge and flood forecasting system that predicts flood risks, in particular extreme floods, more accurately and at higher resolution than existing systems. This is essential for stakeholders to make decisions for an effective flood risk mitigation strategy and an early warning system to protect citizens.
10

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6 Acknowledgments and Disclosure of Funding
This work was supported by the Federal Ministry of Research, Technology, and Space under grant 16IS24075C RAINA and by the Deutsche Forschungsgemeinsccaatfee (DFG, German Research Foundation) - SFB 1502/1- (CRC) for the project Regional Climate Change: Disentangling the Role of Land Use and Water Management (DETECT). We acknowledge EuroHPC Joint Undertaking for awarding us access to Leonardo at CINECA, Italy, through EuroHPC Regular Access Call proposal No. EHPC-REG- 2025R01-218. The authors also gratefully acknowledge the granted access to the Marvin cluster hosted by the University of Bonn. Furthermore, we acknowledge the ESM Testprojekt project for supporting this study by providing computing time on the esmtst partition of the supercomputer JUWELS-BOOSTER Jülich Supercomputing Centre (JSC). Finally, we thank Lars Doorenbos for proofreading the manuscript. The Mamba logos were generated with Microsoft Designer.
project no. 450058266 within the Collaborative Research Center
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23


Reviews:
[{"review_id": "TgiOzjruoP", "reviewer": "Reviewer_Ci8G", "summary": "This paper introduces a genuinely interesting forecasting approach that builds upon a global hydrological model, called GloFAS, by integrating information over a (extremely) wide space. Traditional approaches always orient themselves on the physical conception of catchments and hence try to physical delineation thereof. This means that a lot of spatial information is not accounted for here. This is where RiverMamba comes in. It leverages state space models to integrate the spatial data pixelwise (and avoids paying the quadratic cost per additional pixel) and build a new forecast out of the existing reanalysis.", "questions": "I happily increase my score if the rebuttal addresses my questions and improves on the readability aspect. \n\n- I do not find the motivation for a global receptive field to account for uncertainty in the meteorological variables is convincing.  Why would ERA5-Land runoff, snow and soil moisture in a river of Siberia be a useful feature for a short-term (7-day) forecast in a reach of the Amazon River. While there is uncertainty in the precise location (and occurrence/magnitude) of precipitation forecasts, there is certainly no real-world meaning in such a receptive field. Additionally, why would a pixel in their sequence of p in P somewhere in Siberia be more informative to river discharge in a reach of the Amazon than the direct neighbors and upstream pixels in that basin (many of which are not included due to the random sampling). P denotes not even 5% of all landmass pixels. This seems particularly off since the localized ablation suggests for me that mostly local information is used to get high predictive capacity. Hence, I would recommend to the authors to instead frame the whole in a more traditional machine learning fashion. Something in the line of: Traditional models, like GloFas do not account for wide ranging spatial correlation. We can exploit that with Machine Learning. To do so we use a lot of data and let the model learn the spatial correlations rather than to set them a-priori (in this regard, you might want to refer to the bitter lesson or something too).  \n- The paper emphasizes in multiple passages that RiverMamba can be used in an operational setting (as a matter of fact, the comparison is made against two operational models). However, the model relies on ERA5-Land which is not available in real-time but has a ~30 day lag. \n- L44. Not entirely true. a) The Google Model runs globally at 300k locations (but only a few thousand are verified to be good). b) [Yang et al.](https://www.google.com/url?q=https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2024WR039764&sa=D&source=docs&ust=1751387338408298&usg=AOvVaw1VAQb4SomBzB6JgQVARGBh) already have a global gridded model.\n- L89 There is a quite some literature missing (e.g. [1](https://arxiv.org/abs/2405.19836), [2](https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2023WR036170), [3](https://www.google.com/url?q=https://essopenarchive.org/users/810569/articles/1227435-high-resolution-national-scale-water-modeling-is-enhanced-by-multiscale-differentiable-physics-informed-machine-learning&sa=D&source=docs&ust=1751387497840100&usg=AOvVaw1VwvPCwSSlHswiQ6jqLVw7), [4](https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2023WR035337), [5](https://egusphere.copernicus.org/preprints/2025/egusphere-2024-3649/) to name a few)\n- L121. This must be a misunderstanding from my side but why is RiverMamba not including any information from the nowcast timestep but only up to t-1 and then starting on t+1? \n- L123. I struggle to understand the sentence about the “additional” shift to GloFAS, ERA5, and CPC. According to your notation, you only consider data until t-1, with t being the date that the forecast is issued. Why another shift by 2 days for CPC and 1 day for GloFAS and ERA5?\n- Figure 4 appears before Fig 3 (which is interesting, I did not even know that Latex allows for that)\n- Eq 2. It does seem to met that the dimensions listed in the text below do not work with this equation? \n- Eq 2. Why GELU? Have you tried different activations functions or is there any motivation to it? The LOAN reference does not (yet) seem to use GELU.\n- In general, but I noted it especially around L236ff: The terminology is a bit off. There is a difference between a flood and an event of a given return period. A 1.5 year return period does not necessarily mean any flooding. In most places in North America/Europe, not even a 10/20 year return period should necessarily mean flood.\n- L238. where do these ranges come from? Is something you chose?\n- L247. I couldn’t find the results on the ablation study of their loss weighting.\n- Suppl. L190. In many operational settings you compute return periods separately in the observed space (i.e. long-term records of streamflow measurements) and in model climatology (i.e. long-term reanalysis/reforecasts of the model). The important point to measure here is if the model predicts the correct return period and not, how well the predictions match the observations. For example imagine your model gives perfect predictions but shifted down by 100 cms. For flood forecasting, to know when to trigger an alert, it is only important to know if your model thinks the upcoming event will be larger than some threshold (usually in return period space). If the return period thresholds are computed separately for observations and model climatology, you would get 100% accuracy with such a model, even though your absolute predictions are constantly off by 100 (which is not important if your task is operational flood warnings/forecasts).\n- Suppl. Tab 5. The table is still showing P=245954 for GRDC finetuning. Is the loss only computed for those p in P that are associated to a GRDC station or also on all other points (here then on dis24 from GloFAS)?\n- Suppl F2. How can Glofas be dropped here?\n\nLastly, I am mainly mentioning the following because it came up in some other reviews that I was involved in and because Fig 13 in the Supplementary. This figure shows F1 scores over lead time for different return periods. If I understand the explanations correctly, this should essentially be the same information as Fig3 in Nearing et al. (2024). However, the figures show very different values. There might be misalignment in the data when computing the metrics, since Nearing et al. (2024) provided the data right-labeled, while GRDC data is left-labeled. E.g., note from Zenodo:\n\n*“Model outputs are daily and timestamps are right-labeled, meaning that model outputs labeled, .e.g., 01/01/2020 correspond to streamflow predictions for the day of 12/31/2019.”*", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Albeit I do in the following mainly focus on the weaknesses, I would like to emphasize that the overall contribution is — in my view — quite strong. The idea is good, the evaluation is sufficient for what the authors want to show, and ablations are thorough. Still, I would like to start my critique with a meta-point: The current form of the paper is rather hard to read. At some points it is even confusing. Many parts are not explained well enough and readers need to make inferences about what actually happens. For example, it is unclear how the LSTM baseline is trained and used. Is the LSTM baseline also trained on sequences of multiple hundred thousand timesteps (if yes, this is far beyond what LSTMs usually can work with)? Similarly, it took me unnecessarily long to understand that the model is still trained and used with only a small-subset of the available pixels. In short, I think with some love the readability of the manuscript could be greatly improved. As a consequence most of my critique consists of what I would normally consider minor comments or so. As a matter of fact even my major point is related to language: \n\nMy main point is that with the current formulation readers will get the impression that the LSTM baseline is the one from Nearing et al. (2024). But, as far as the provided description lets me infer, the one used as baseline has nothing in common with it besides the general architecture (decoder-encoder LSTM). The task of the LSTM in the original publication is to integrate meteorological information over longer time-horizons and provide a streamflow simulation. In contrast, the task from RiverMamba is to provide a post-processor for such a streamflow simulation model — namely GloFAS.  As a matter of fact, the LSTM from Nearing et al (2024) could very well be used as a stand-in backbone for the hydrological model, which would provide a more apt comparison. As an example of how the used language can be misleading take Table 3. First, an LSTM as proposed in Nearing et al. (2024) in a gauged setting commonly achieves median $R22$ of $> 0.7$ in the test period. Second, most results and simulations provided by Nearing et al. 2024 are for an ungauged setting (i.e., the GRDC stations were not included in the training), which, if compared to gauged, is obviously worse. \nSimilarly, different sequence lengths can be used if you feed in the states (snow, soil moisture) and current runoff to the model compared to a model that has to simulate everything (e.g., snow accumulation during the winter to predict snow melt in the spring/summer) just from weather inputs. This is because the states and the streamflow integrate the meteorological signal of the past already. Hence, sentences like the following example can easily give the wrong impression:\n\n*“In [6], an input sequence length of 365 days was used. In our experiments, we also trained the LSTM model using a range of input sequence lengths from 4 to 90 days. We observed only marginal performance gains beyond a certain point, and identified 14 days as an optimal input sequence length.”*", "was_revised": true, "final_justification": "This contribution is technically excellent and proposes an approach that does not only have the potential to improve hydrological predictions but land-surface models in general (and is perhaps even of interest for weather forecasting). My concerns about the paper where from the start about language and positioning --- and the authors very good job at explaining how they will improve the papers in this regard.", "rebuttal": "Thank you for the detailed review and the thoughtful feedback. We appreciate your time and we are glad that you found our approach interesting and the contribution strong.\n\n> It is unclear how the LSTM baseline is trained and used.\n\nWe describe the details of the LSTM baseline in Section G.3 of the suppl. As in Nearing et al. (2024), we do not use spatial connections for the LSTM. The sequence length for the LSTM is 14 days, which performed better than using a longer sequence length. We will state this clearly in the revised version. \n\n> The LSTM baseline from Nearing et al. (2024).\n\nThe original model from Nearing et al. (2024) is not publicly available. We thus built the encoder-decoder LSTM from the neuralhydrology repository and followed the model structure as described in Nearing et al. (2024). The LSTM model is trained similarly to Nearing et al. (2024) but on a gauged setting (Section G.3 in Suppl.). For a fair comparison of the methods, we also use the same input to the LSTM model and RiverMamba, which is different to Nearing et al. (2024). We will clarify this in the revised manuscript and in the tables, in particular in Table 3. We do not think that a model should achieve a median $R^2>0.7$. The metric is affected by many factors like the length of the evaluation set (length of the extrapolation), lead time, input data, number of gauged points, resolution, region of study, etc. \n\n> Different sequence lengths can be used if you feed in the states and current runoff to the model compared to a model that has to simulate everything just from weather inputs.\n\nThank you for this clarification. We will integrate this into the manuscript to make it clearer. \n\n> The motivation for a global receptive field.\n\nWe will revise the formulation since the term \"global\" might be misleading. As mentioned in the suppl. material on page 16, we split the Earth into smaller domains with 311K nearest points for each. We thus do not connect points from the Amazon to points in Siberia. However, we give the network the possibility to consider a very large spatio-temporal context. For instance, river networks like Amazon can be very large and providing a model that can handle a very large spatio-temporal context is thus very intuitive.         \nFinally, we present a general backbone model that is not limited to medium-range river discharge forecast and specific input variables or task. For instance, the model can be used for seasonal discharge forecasting. Furthermore, weather forecast and climate modeling generally require a large receptive field to preserve the dynamic over lead time and RiverMamba is a promising backbone for such tasks. \n\n> The model relies on ERA5-Land which is not available in real-time but has a $\\sim30$ day lag.\n\nPlease kindly note that ECMWF states: \"The ERA5-Land dataset is available for public use for the period from 1950 to 5 days before the current date.\" ... \"The ERA5-Land-T version delivers non-checked close to Near-Real-Time (NRT) daily updates. ERA5-Land-T is synchronized with the close to NRT daily updates provided by the ERA5 climate reanalysis (ERA5T).\", so there is no risk of having a 30-day lag. In the RiverMamba framework, ERA5-Land can be also replaced by an analysis or ERA5 similar to GloFAS. We will revise the manuscript to make this issue clear.\n\n> L44. Not entirely true. a) The Google Model runs globally at 300k locations. b) Yang et al. already have a global gridded model.\n\na) We will rephrase the sentence. We wanted to highlight here the limited spatial modeling of the LSTM.\n\nb) Please see L91-L93 and ref [60], we already discuss the preprint version by Yang et al. We will update the reference and text based on the published version. Thank you for the note. \n\n> L89 There is a quite some literature missing.\n\nThank you for this note. We will briefly discuss the mentioned methods in the related works. Kindly note that the first reference [1] is already mentioned in the manuscript.\n\n> L121. Why is RiverMamba not including any information from the nowcast timestep?\n\nRiverMamba intentionally excludes the analysis data (t=0) from the input, and instead starts forecasting from t+1 using only past data up to t–1. The rationale behind this design is to ensure broader applicability, since many weather forecast systems especially ML models provide only lead time $t>0$ and we wanted to make the model more generic so it can work without nowcasting or a specific type of forecast (IFS-HRES). However, adding nowcasting to the model is straightforward and can be added optionally. We will mention this explicitly in the manuscript.\n\n> L123. Why another shift by 2 days for CPC and 1 day for GloFAS and ERA5?\n\nWe will revise this sentence and remove the word \"shift\" since we do not shift data. To our knowledge, CPC data are available with 2 days lag. Consequently, we only consider data until t-2. \n\n> Figure 4 appears before Fig 3.\n\nWe will correct it.\n\n> The dimensions in Eq 2.\n\nThank you for this note. We will correct it. PyTorch handles the dimensions for different operations, i.e., $\\sigma$ and $\\mu$ will be duplicated $K$ times along the last dimension to match $\\textbf{X}$.\n\n> Eq 2. Why GELU?\n\nWe were motivated by two things: first, GELU avoids the dying ReLU problem and improves optimization. Second, it has been shown that a learned activation function initialized as ReLU, ends up in a smooth variant shape similar to GELU (Teney et al., \"Do We Always Need the Simplicity Bias? Looking for Optimal Inductive Biases in the Wild\", CVPR'25).\nWe conducted an additional experiment (see Table below). The model is trained over Europe for the years 1979-2018 and tested on the validation set (2019-2020). Shown are (KGE $\\mid$ F1) averaged for the return periods 1.5-20 years on reanalysis data.\n\n| ReLU               | GELU               |\n|---------- |--------- |\n| 91.43 $\\mid$ 28.33 | 92.05 $\\mid$ 28.75 |\n\nUsing GELU performs slightly better.\n\n> L236ff: The terminology is a bit off.\n\nThank you for pointing out the imprecise usage of terminology. We agree that a return period e.g., 1.5 years does not necessarily imply actual flooding in all regions, particularly in highly regulated or flood-resilient areas. A high return period event simply reflects statistical rarity in streamflow magnitude, and should not be equated with a flood event without additional context (e.g., thresholds, inundation).\nIn the revision, we will clarify it and emphasize that the return period is used as a proxy indicator of hydrological extremity, rather than a direct definition of flood severity. \n\n> L238. where do these ranges come from?\n\nThe return periods are used in GloFAS and operated by ECMWF.\n\n> L247. I couldn’t find the results on the ablation study of their loss weighting.\n\nThe ablation study regarding the weighting is provided in Table 2 (a).\n\n> Suppl. L190. In many operational settings you compute return periods separately in the observed space and in model climatology.\n\nThank you for this insightful comment. You are correct that in many operational settings, thresholds are computed from the model’s own climatology (e.g., long-term reforecasts), and what matters is whether the model correctly identifies exceedance relative to its own statistical distribution, rather than matching the exact values of the reference. As described in Suppl. L190–L194, we calculated return period thresholds separately from both the GRDC observations and the GloFAS reanalysis. This allows us to evaluate each dataset relative to its own climatology. However, we didn't compute return periods from the trained ML models reforecast as this would require generating a long reforecast climatology to fit a statistical extreme value distribution. This was beyond the scope of the current study. We acknowledge that this approach penalizes model that has a systematic bias but still captures the correct return period, but a systematic bias is also not desirable. We will discuss this issue.\n\n> Suppl. Tab 5. Is the loss only computed for those p in P that are associated to a GRDC station or also on all other points (here then on dis24 from GloFAS)?\n\nFor GRDC finetuning, P=245954 is the number of input points per sample. The loss is computed only on 3366 points where GRDC observations are available. We do not use the dis24 GloFAS here to compute the loss. We will make this clearer in the revision.\n\n> Suppl F2. How can Glofas be dropped here?\n\nWe only drop GloFAS from the input and keep the data as a target to train the model. During inference, we still use the last step of GloFAS-Reanalysis and add it to $\\Delta \\textbf{X}$ to generate the discharge. This ensures consistency within the table and isolates the impact of input GloFAS-Reanalysis on the model. RiverMamba still works without taking GloFAS as input. This highlights that the model is more than a post-processor of discharge data and can in fact be used as a backbone for the hydrological modeling. However, if we want to drop GloFAS completely, we need to change the objective function, e.g.,  by predicting the absolute value of river discharge or the change of discharge w.r.t. climatology.\n\n> Fig 13 in the Supplementary.\n\nThe GRDC observational time series, which are originally left-labeled, were explicitly converted to right-labeled time series to ensure a temporal consistency with the right-labeled predictions from the GloFAS simulations, RiverMamba, LSTM baseline, and Google reforecast dataset. \nThe F1 scores reported in Fig. 13 are based on synchronized detection windows between model predictions and observations. We will highlight the label alignment step in the revision to avoid potential confusion. Regarding the observed differences between our Fig. 13 and Fig. 3 in Nearing et al. (2024), we note that although both figures present F1 scores by lead time and return period, they differ in several aspects like thresholding strategy, data sampling, and station filtering (evaluation domain)."}, {"review_id": "9Kj0zpSEpz", "reviewer": "Reviewer_yDqB", "summary": "In this paper, the authors propose RiverMamba, a novel deep learning model that leverages Mamba blocks—a type of bidirectional state space model—to efficiently model hydrological dynamics at a global scale. RiverMamba integrates diverse data sources, including reanalysis datasets (ERA5-Land, GloFAS), meteorological forecasts (ECMWF HRES), static river attributes, and sparse in-situ gauge observations. The model produces global river discharge forecasts at a fine 0.05° resolution, with lead times of up to 7 days, and is capable of predicting extreme flood events across a wide range of return periods.", "questions": "The written quality of the paper would benefit from further refinement. \n1. When evaluation metrics such as R², KGE, and F1-score are first introduced in the main text, it would be helpful to briefly define them or, at the very least, direct readers to where the definitions can be found (e.g., in the appendix).\n\n2. The presentation of results in Table 1 is confusing and potentially misleading. The reported values for R², KGE, and F1-score all exceed 1, which is unconventional and suggests a transformation has been applied. Upon checking the appendix, it appears that KGE has been multiplied by 100, and it is reasonable to assume the same was done for R² and F1-score—though this is not clearly stated. Rather than burying this detail in the appendix, I strongly recommend that the authors explicitly mention this scaling in the main text, ideally in the caption or title of Table 1. This kind of transformation is non-standard, and without proper explanation, it risks confusing readers and misrepresenting the model’s performance.", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "The paper addresses a critical gap in global-scale, high-resolution river discharge and flood forecasting—an area where most existing deep learning models fall short due to their localized focus and limited ability to capture spatial dependencies across river networks.\nOne of the key innovations of this work is its multi-source data fusion architecture combined with an efficient spatio-temporal modeling strategy. RiverMamba stands out as one of the first deep learning frameworks capable of generating high-resolution (0.05°) global river discharge maps. It moves beyond localized predictions by explicitly modeling spatial connectivity across river systems. The use of space-filling curves (such as Gilbert and Sweep) to serialize river points into 1D sequences is particularly creative, enabling scalable sequence modeling using Mamba blocks. Additionally, the model introduces Location-Aware Adaptive Normalization (LOAN) to condition dynamic inputs on static river attributes, further enhancing its ability to generalize across diverse hydrological settings.\nFor operational forecasting, RiverMamba integrates ECMWF HRES meteorological forecasts and accounts for their uncertainties through robust spatio-temporal modeling. Experimental results demonstrate that it outperforms both physics-based models (like GloFAS) and AI baselines (like LSTM), especially in predicting extreme flood events across a wide range of return periods—from 1.5 to 500 years.", "was_revised": true, "final_justification": "Thank you to the authors for their time and detailed responses during the rebuttal. I’ve reviewed all comments and appreciate the effort made to address the concerns. I would like to maintain my original score.", "rebuttal": "Thank you for your time and the recognition of the novelty of this work. We are glad that you found our work creative and addresses a critical gap for future research.\n\n> When evaluation metrics such as R², KGE, and F1-score are first introduced in the main text, it would be helpful to briefly define them or, at the very least, direct readers to where the definitions can be found (e.g., in the appendix).\n\nThank you for the suggestion. We described the metrics in the Supplementary due to the limited space for the main text. We will follow your suggestion and direct the readers to where the definitions can be found.\n\n> The presentation of results in Table 1 is confusing and potentially misleading. The reported values for R², KGE, and F1-score all exceed 1, which is unconventional and suggests a transformation has been applied. Upon checking the appendix, it appears that KGE has been multiplied by 100, and it is reasonable to assume the same was done for R² and F1-score—though this is not clearly stated. Rather than burying this detail in the appendix, I strongly recommend that the authors explicitly mention this scaling in the main text, ideally in the caption or title of Table 1. This kind of transformation is non-standard, and without proper explanation, it risks confusing readers and misrepresenting the model’s performance.\n\nThank you for this comment. We agree with you about the metrics definition. Following your comment, we will remove the transformation and report the metrics in their conventional values, to be consistent with the values reported in the figures. Note that we still use the transformation in the rebuttal for consistency with the paper."}, {"review_id": "EkqjEyRID9", "reviewer": "Reviewer_V2mj", "summary": "The authors frame the streamflow, and flood forecasting problem as image level tasks with each pixel being mapped to a unique geographical location, covering 5 arc-seconds in both directions. In this setting, they propose an encoder-decoder architecture where the encoder integrates past spatio-temporal maps in conjunction with static information into a hidden representation. Using this encoded information alongside forecasted spatio-temporal data, the decoder predicts for each point on the map the changes to the river discharge values relative to the mean of the encoder input data. \nTo produce predictions at scale, the authors propose the usage of Mamba layers with their linear space and time complexity. A set of space-filling curves serialise these geographically organised data. Through alternation of these curves, different spatial points will be close in the serialised sequence, helping the model to learn different spatial correlations. \nA novel normalisation layer facilitates the incorporation of static attributes, like the river channel network, into the hidden representation at each step in the encoder. It does that by linearly transforming the static attributes, activating them using GeLU and additively overlaying these activations with the z-score normalised hidden representation at that point. \nWith this architecture, the authors demonstrate superior performance compared to existing state of the art models (Google's operational LSTM) as well as physics-based models (GloFAS) when evaluated on both reanalysis and observational data. This performance increase is measured on multiple metrics, $R^2$, KGE, F1-score, on a global forecasting scale.\nNotably, RiverMamba is the first architecture capable of producing global river-discharge forecasts with 7 day lead time on a spatial resolution of 5 arc-seconds.", "questions": "- Does weighting of no-flood events equally in equation (8) to the ones with a one year return period not skew the results to the no-flood case? Weighting floods not just by their return period but also augmenting it with an additive flood offset (let's say 1) might help the flood scarcity problem a bit, which also has been mentioned in the conclusion. \n- Could you provide computational time comparisons to better position the model in the landscape of operational forecasting along Google's LSTM and GloFAS?\n- Is there an architectural reason for not training on quantile regression, thereby providing a way of estimating the uncertainty of the model's predictions?\n- Could you evaluate the model's performance with larger temporal gaps between training and test data (e.g., 5-10 years) to assess robustness to climate change impacts on flood drivers? This would help establish the model's long-term operational viability.", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "## Originality \nApplying state space models—including the necessary usage of space filling curves for serialisation—to the global hydrological forecasting task is, to the reviewer's knowledge, novel. Repeatedly adding linearly transformed and GeLU activated static attributes to the normalised hidden embeddings provides a clever way of informing the model of static spatial relationships. Additionally, their composed weighting factors that balance the recency of the input with the return period represent a thoughtful approach to addressing the dual challenges of temporal decay in forecast reliability and the relative importance of rare flood events in the training objective.\n## Quality -- Strengths\nThe authors provide a thorough evaluation of RiverMamba across multiple dimensions, including systematic ablation studies on location embedding approaches, space filling curve alternatives, weighting factors in the objective function, the impact of exchanging static attributes from LISFLOOD-derived to HydroRIVERS-derived sources, input feature importance analysis, and the effects of pretraining versus training from scratch. In addition to temporal out-of-sample settings, the extended evaluation in the appendix also tests spatial generalization and compares the model not only against the leading data-driven model from Google but also against the physics-based model GloFAS. Furthermore, the authors effectively contextualize their work by contrasting related approaches in each section against their proposed methodology, demonstrating a clear understanding of how their contributions advance the field.\n## Quality -- Weaknesses\nThe model produces only point forecasts without uncertainty estimates. These, however, provide important additional information decision makers can use in the operational flood forecasting context.\nThe ablation studies mentioned in the main text and summarised in Table 2 leave out one possible combination preventing assessment of any separate impact of one hyperparameter from possible synergistic effects. Specifically, sub-tables (a) and (b) lack results for using only the recency factor or LOAN exclusively in the forecast block. This omission prevents assessment of whether the observed performance improvements are independent effects or result from synergistic interactions between the return period weighting and LOAN placement in different blocks. \nThe authors do not provide inference time comparisons on the global scale, particularly against the LSTM baseline, which would help assess the practical computational advantages claimed for the Mamba architecture. \nAdditionally, there is a partially incorrect statement about Flash-Attention in the appendix (line 261) claiming linear complexity; while this accurately describes the space complexity improvement, Flash-Attention's time complexity remains quadratic in the input length, which undermines the claimed efficiency comparison.\n## Clarity\nThe main part of the paper clearly describes the key components of the architecture, highlighting the intended effects of each design element.\nHowever, some presentation issues hinder clarity. The sentence spanning the lines 137-140 is overly long and complex, making it difficult to follow on first reading. \nThe relationship between the number of hindcast layers and the chosen temporal input dimension is not clearly explained in the main text, though the former seems to be dependent on the latter. Additionally, Figure 4's layout is somewhat ambiguous -- it is difficult to discern whether the first serialisation layer belongs to the hindcast block, and including it within the outer shaded region would clarify this organizational structure. \nFinally, while the appendix describes how the authors set up and trained a version of Google's LSTM, it does not explicitly clarify how this relates to the LSTM results shown in the figures versus results obtained directly from Google's system.\n\nSome typos were found during reading the paper including the appendix:\n- Main paper: Line 65 \"saptio-temporal\" -> \"spatio-temporal\"\n- Appendix: Line 167 \"see\" -> \"sea\"\n## Significance \nThe model demonstrates significant practical value by effectively detecting very rare floods that might be missed by existing LSTM approaches as impressively shown in Figure 47 for example. However, the model's spatial generalization capabilities appear limited based on the results in appendix section J, where performance on spatially out-of-sample ungauged basins does not significantly differ from the LSTM baseline and regresses quickly with increasing return periods.", "was_revised": true, "final_justification": "I thank the authors for their thorough response and for running additional experiments, which have clarified several points. However, as my concerns regarding the ablation studies and spatial generalization limitations persist, I will maintain my initial rating.", "rebuttal": "Thank you for the detailed and clear summary you have provided about this work. We are glad that you found our work novel and the evaluation thorough.\n\n> The model produces only point forecasts without uncertainty estimates. These, however, provide important additional information decision makers can use in the operational flood forecasting context.\n\nAs mentioned on page 9, extending the model to output a probabilistic forecast is an interesting future direction.\n\n> The ablation studies mentioned in the main text and summarized in Table 2 leave out one possible combination preventing assessment of any separate impact of one hyperparameter from possible synergistic effects. Specifically, sub-tables (a) and (b) lack results for using only the recency factor or LOAN exclusively in the forecast block.\n\nThere might be some misunderstanding about Table 2. Table 2 represents actually 3 distinctive tables (a), (b), and (c). Table 2 (b) evaluates exclusively the impact of LOAN. We will revise it to make it clearer.\n\n> There is a partially incorrect statement about Flash-attention in the appendix (line 261) claiming linear complexity; while this accurately describes the space complexity improvement, Flash-attention's time complexity remains quadratic in the input length, which undermines the claimed efficiency comparison.\n\nThank you for the note. We will correct it and make it more clear if we refer to runtime or memory. In Fig. 6 in the appendix, we compare both.   \n\n> The sentence spanning the lines 137-140 is overly long and complex, making it difficult to follow on first reading.\n\nWe will revise the sentence.\n\n> The relationship between the number of hindcast layers and the chosen temporal input dimension is not clearly explained in the main text, though the former seems to be dependent on the latter.\n\nThank you for this comment. In our implementation, we chose T=4 as for the GloFAS operational system and a temporal down-sampling of 2. Consequently, we defined 3 layers to encode the input (the first layer doesn't use down-sampling). For example, when T=8 and down-sampling is 2, one would need 4 hindcast layers. The Table below shows the temporal resolution for each layer w.r.t. the input temporal dimension T.\n\n| Layer | $$1^{st}$$ | $$2^{nd}$$ | $$3^{rd}$$ | $$4^{th}$$ | \n| :-----| :----------|:---------- |:-----------|:-----------|\n| T=2   | 2 | 1 | | |\n| T=4   | 4 | 2 | 1 | |\n| T=8   | 8 | 4 | 2 | 1 |\n\n> Figure 4's layout is somewhat ambiguous -- it is difficult to discern whether the first serialisation layer belongs to the hindcast block, and including it within the outer shaded region would clarify this organizational structure.\n\nThank you for this suggestion. We will modify the figure accordingly.\n\n> While the appendix describes how the authors set up and trained a version of Google's LSTM, it does not explicitly clarify how this relates to the LSTM results shown in the figures versus results obtained directly from Google's system.\n\nAll results shown in experiments are based on the trained Google's LSTM on our dataset except the results shown in suppl. section J pages 23-28 which are obtained directly from the published Google reforecast. We will make this clear in the paper.\n \n> Some typos were found during reading the paper.\n\nThank you for the careful reading. We will fix the typos and check the paper for any other ones.\n\n> The model demonstrates significant practical value by effectively detecting very rare floods that might be missed by existing LSTM approaches as impressively shown in Figure 47 for example. However, the model's spatial generalization capabilities appear limited based on the results in appendix section J, where performance on spatially out-of-sample ungauged basins does not significantly differ from the LSTM baseline and regresses quickly with increasing return periods.\n\nAs described in the suppl. section J, there are plausible reasons behind this observation:\n\nWe do not use nowcasting, i.e. weather forecast at $t=0$, as input. We expect that this would substantially improve the results at early lead time and it is the main reason for the close performance at early lead time. Other differences are: The Google model (Nearing et al. 2024) was trained on ($\\sim5680$) stations compared to ($3366$) for RiverMamba. The ungauged streamflow forecast becomes better when the number of stations increases.\nThere are also differences in the input initial conditions, i.e., Google's LSTM uses precipitation estimates from the NASA Integrated Multi-satellite Retrievals for GPM (IMERG) early run as input. In addition, Google's LSTM uses an ensemble of three separately trained LSTMs (Nearing et al. 2024). The results in Section J are thus not directly comparable, but we added them for completeness. We expect that using nowcasting and IMERG as input and an ensemble would improve the results of RiverMamba on ungauged basins further. For the other results in the paper, we used the same training and evaluation setup for all methods to ensure a fair comparison.        \n\n> Does weighting of no-flood events equally in equation (8) to the ones with a one-year return period not skew the results to the no-flood case? Weighting floods not just by their return period but also by augmenting it with an additive flood offset (let's say 1) might help the flood scarcity problem a bit, which also has been mentioned in the conclusion.\n\nAs suggested, we conducted an additional experiment. To this end, we trained a model with weighted flood events by their return periods + flood offset of 1. The F1 results are shown below for the reanalysis dataset and different return periods:\n\n| Return period | 1.5   | 2.0   | 5.0   | 10.0  | 20.0  |\n|--------------|-------|-------|-------|-------|-------|\n| **Validation (2019-2020)**|\n| w/ offset    | 48.20 | 37.60 | 23.58 | 17.90 | 11.81 |\n| w/o offset   | 48.70 | 37.67 | 25.16 | 20.15 | 12.08 |\n| **Test (2021-2024)** |\n| w/ offset    | 61.14 | 50.80 | 31.25 | 24.86 | 16.56 |\n| w/o offset   | 61.22 | 50.72 | 30.31 | 24.34 | 16.69 |\n\nAdding an offset does not improve the results.  \n\n> Could you provide computational time comparisons to better position the model in the landscape of operational forecasting along Google's LSTM and GloFAS?\n\nNeither Google (Nearing et al. 2024) nor GloFAS (Harrigan et al. 2023) provided the compute time for the operational forecast.\nThe inference time for RiverMamba is reported in supp. Fig. 6.\nIn the table below, we report the inference time (seconds) w.r.t. the number of input points for our model with 4 days as a hindcast (first row), a trained version of Google's LSTM with 4 days as a hindcast (second row), and a Google's LSTM version as in Nearing et al. (2024) with one year hincast (third row). We use one A100 GPU for all runs. All machine learning approaches are very fast. We expect that GloFAS is by several magnitudes slower, which is a practical advantage of machine learning approaches for this task.\n\n| Model                  | 10K   | 20K   | 40K   | 80K   | 160K  | 300K  | 600K  | 1500K |\n|------------------------|-------|-------|-------|-------|-------|-------|-------|-------|\n| RiverMamba             | 0.026 | 0.044 | 0.086 | 0.190 | 0.423 | 0.874 | 1.914 | 4.739 |\n| LSTM                   | 0.005 | 0.009 | 0.015 | 0.027 | 0.053 | 0.098 | -     | -     |\n| LSTM (one-year hindcast)| 0.069 | -     | -     | -     | -     | -     | -     | -     |\n\n> Is there an architectural reason for not training on quantile regression, thereby providing a way of estimating the uncertainty of the model's predictions?\n\nThere is no architectural reason that prevents the training using a quantile loss. An ensemble of different models can be trained with different quantiles. We agree that an ensemble and estimating the uncertainty of the model are an interesting direction for future work, but we focused on deterministic forecast to thoroughly analyze and evaluate the design of the network architecture. We think that the results demonstrate the strong capabilities of RiverMamba for large scale river discharge forecast. Using an ensemble not only increases the computational cost for running all ablation studies, but it also requires a different evaluation framework, e.g, adding Continuous Ranked Probability Score (CRPS) and spread/skill ratio metrics. Given that we have already 54 pages for the suppl. material, adding an ensemble and uncertainty estimation is out of scope, but an interesting future research direction.   \n\n> Could you evaluate the model's performance with larger temporal gaps between training and test data (e.g., 5-10 years) to assess robustness to climate change impacts on flood drivers?\n\nIn the Table below, we report the evaluation for each year in the test dataset separately. The model is trained over Europe for the years 1979-2018 and shown are averaged (KGE $\\mid$ F1) for the return periods 1.5-20 years for both reanalysis and GRDC data. \n\n| Year     | 2019          | 2020          | 2021          | 2022          | 2023          | 2024          |\n|:----------|---------------|---------------|---------------|---------------|---------------|---------------|\n| Reanalysis | 90.80 $\\mid$ 30.09 | 91.75 $\\mid$ 20.57 | 90.32 $\\mid$ 24.42 | 90.76 $\\mid$ 20.54 | 91.05 $\\mid$ 34.57 | 90.41 $\\mid$ 38.66 |\n| GRDC (obs) | 76.63 $\\mid$ 10.77 | 76.31 $\\mid$ 12.74 | 69.33 $\\mid$ 11.79 | 71.41 $\\mid$ 08.94 | 71.73 $\\mid$ 19.88 | 52.32 $\\mid$ 14.53 |\n\nNote that the evaluation is highly dependent on the ratio of the flood events that happened during a specific year and on the dataset. On the observational data the modeling of the discharge time series (KGE) decreases with time while the model stays robust regarding flood detection (F1). This is probably due to anthropogenic intervention, as mentioned in the manuscript. Reanalysis data has more data points to train on them and the model shows a good generalization ability with a larger gap between training and testing."}, {"review_id": "3hMaVj1rxR", "reviewer": "Reviewer_ugtP", "summary": "RiverMamba forecasts river discharge up to 7 days in the future based on land surface variables, meteorological forecasts and static river attributes. \nThe data is serialized with space filling curves and fed into a Mamba block. \nPaired with a sophisticated encoding and decoding, the method achieves promising results.", "questions": "Related work uses GNNs to model the spatio-temporal relationships. Why did you opt for space filling curves combined with Mamba?", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "## Strengths\n - Detailed description of the training procedure and model architecture\n - Very good results compared to GloFAS (Global Flood Awareness System)\n - Some engineering decisions were validated by ablation studies\n\n## Weaknesses\n - The only machine learning model among the baselines is a LSTM. \n   Space filling curves might be well-suited for Mamba, but it is not clear whether this is the right approach for a LSTM. \n   (Graph)convolutional networks would be a more interesting baseline.\n - Limited reproducibility (no code provided)", "was_revised": true, "final_justification": "See comment", "rebuttal": "Thank you for your time and appreciating the detailed descriptions in the paper, the thorough ablation studies and the promising results.\n\n> The only machine learning model among the baselines is a LSTM. Space filling curves might be well-suited for Mamba, but it is not clear whether this is the right approach for a LSTM. (Graph) convolutional networks would be a more interesting baseline.\n\nThere seems to be some misunderstanding about the LSTM baseline. To train the LSTM, we followed the same protocol as originally proposed in Nearing et al (2024), which considers only temporal context but does not include any spatial connections. The space filling curves are thus not used in combination with the LSTM. As pointed out, an LSTM would also not be able to handle such long curves. The baselines are described in more details in the suppl. (page 17). In addition, we note that LSTM is the most popular backbone for river discharge forecasting. Recent GNN models for hydrology still use LSTM in their backbone for the temporal modeling e.g. (Gauch et al., \"Towards Deep Learning River Network Models\", EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-9768, 2025) and many studies use LSTM to resolve the spatial modeling e.g. (Yu. et al., \"Enhancing long short-term memory (LSTM)-based streamflow prediction with a spatially distributed approach\", Hydrol. Earth Syst. Sci. 28, 2024).\nNote that real-world gridded data like the GloFAS dataset has a spatial resolution of 7000 × 3200 (suppl. A.7 page 7) and we consider 4 time steps as input. A spatio-temporal graph would consist of 7000 × 3200 × 4 = 89,600,000 nodes, which would be computationally very expensive. To the best of our knowledge, such a GNN baseline does not exist since GNNs are only proposed in the literature at local scales or coarse resolution, i.e., basin level analysis. Note that we compare to a Transformer architecture with flash attention in Figure 6 and Tables 6 and 7 of the supp. \n\n\n> Limited reproducibility (no code provided)\n\nThank you for the comment. The code will be made publicly available upon publication as we mention in the NeurIPS Paper Checklist regarding ``Open access to data and code'' and in the suppl. on page 53.\n\n> Related work uses GNNs to model the spatio-temporal relationships. Why did you opt for space filling curves combined with Mamba?\n\nThe main motivation is that we aim toward developing a model that operates at grid scale and achieves a high accuracy. Mamba avoids the computational cost of the GNNs (see above clarification about GNNs) and Transformers (see Section F.1 in suppl. material). The space-filling curves allow the model to learn the spatial relations adaptively without the complexity of a graph structure."}]

Author rebuttal:

Meta-review: The paper studies the river discharge and flood forecasting problem and proposes a Mamba-based model to achieve 0.05 high-resolution forecasting. Reviewers all appreciate the novelty from the application side but have concerns about the baselines, uncertainty quantification, and reproducibility. After reading the paper, the initial reviews, and the author-reviewers discussions, the AC agrees that the paper studies an important problem and comes up with a solid method. While I suggest the acceptance of the work, I strongly suggest the authors to opening all the datasets and codes, and provide more baselines from the Spatial-temporal forecasting domain (e.g., refer to PredBench).
Decision: Accept (poster)