The study, authored by Hongye Cao of Xianyang Normal University and the China Jikan Research Institute of Engineering Investigation and Design, presents a model named VMD-DSTCN-GA, which stands for a variational mode decomposition-based dual-stream temporal convolutional network with gated attention. Evaluated on thirty years of daily hydro-meteorological observations from the Jingcun hydrological station on China’s Jing River, the framework achieved a coefficient of determination of 0.9872 and a Nash–Sutcliffe efficiency of 0.9631 during the independent evaluation period from 2010 to 2019, outperforming a suite of established benchmark models including deep learning hybrids and the widely used physically based SWAT model.

The central innovation of the work lies in how it disentangles two fundamentally different kinds of signal. Rivers possess a kind of internal dynamic memory: water stored in the subsurface, in snowpack and in channel banks is released slowly, producing smooth, slowly varying components of flow. Superimposed on this are abrupt responses to external forcing, when a rainstorm delivers a pulse of energy and water to the catchment and the hydrograph spikes within hours. Conventional single-stream neural networks must learn both behaviours simultaneously from raw inputs, which often blurs the distinction between the two regimes. The new architecture instead decomposes the historical runoff record using variational mode decomposition, a signal-processing technique that adaptively splits a time series into a set of frequency-specific sub-series, or modes, each capturing oscillations at a characteristic scale.

Variational mode decomposition, first formalised by Dragomiretskiy and Zosso in 2014, differs from classical empirical decomposition methods by framing the decomposition as a variational optimisation problem, seeking the set of modes whose sum reproduces the input signal while each mode remains narrow-banded around its own centre frequency. This makes it considerably more robust to noise and mode mixing than older approaches, a property that matters greatly in hydrology, where observed flows carry measurement error and the underlying signal is anything but stationary. In the new framework, the decomposed runoff components are fed into what the author calls a runoff-state stream, a temporal convolutional network built from causal dilated convolutions and residual blocks.

Temporal convolutional networks have been gaining ground on the long short-term memory (LSTM) architectures that dominated hydrological machine learning for much of the past decade. Where LSTMs process sequences step by step through gated recurrent units, temporal convolutional networks apply one-dimensional convolutions across the time axis, using dilated kernels to expand their receptive field exponentially with network depth. The causal design ensures that predictions at any time step depend only on past information, avoiding future leakage, while residual connections stabilise training in deep stacks. The practical advantages are considerable: convolutions can be computed in parallel across the entire input window, making training dramatically faster, and the hierarchical receptive field allows the network to capture dependencies operating at multiple timescales, from the daily rhythm of rainfall events to the seasonal pulse of snowmelt.

The second stream of the network is dedicated entirely to meteorological forcing. Precipitation, maximum and minimum temperature, solar radiation, relative humidity and wind speed are processed through an independent encoder, so that the atmospheric drivers of runoff are represented in their own feature space rather than being forced to share a representation with the river’s internal state. Only after both streams have produced their encoded features are they combined, and the combination is far from a simple concatenation. A gated fusion mechanism learns, for each time step and each feature channel, how much weight to assign to the runoff-state representation versus the meteorological representation, effectively letting the model decide dynamically whether the river’s own memory or the prevailing weather matters more at any given moment.

On top of this gated fusion sits a temporal attention module, which reweights the contributions of different time steps in the input history, allowing the network to focus on the days that matter most for the forecast, such as the immediate aftermath of a storm. The authors also introduce a peak-sensitive loss function, deliberately penalising errors on high-flow events more heavily than errors during low-flow periods. This addresses a chronic weakness of machine learning hydrology models, which, trained on ordinary mean-squared error, tend to fit the abundant mid-range flows well and systematically underestimate the extreme peaks that matter most for flood risk.

The evaluation protocol was deliberately stringent. The model was trained on daily data from 1990 to 2009 at the Jingcun station and tested on the entirely withheld decade from 2010 to 2019. Against observed flows, VMD-DSTCN-GA recorded an R² of 0.9872, a root mean square error of 7.3734 cubic metres per second, a percent bias of 13.0314 percent, and a Nash–Sutcliffe efficiency of 0.9631, the latter being a standard measure in hydrology where values above roughly 0.75 are generally considered very good and values above 0.9 exceptional. Among all models evaluated, the new framework achieved the highest R², indicating the strongest ability to reproduce the full range of observed runoff variability.

The comparison with benchmarks was informative rather than one-sided. A CNN–LSTM–Attention hybrid achieved a slightly lower root mean square error of 6.6113 cubic metres per second and the highest NSE of 0.9703, while the physically based SWAT model produced the smallest absolute percent bias, reflecting its grounding in water-balance physics. These results suggest a nuanced picture: the proposed dual-stream architecture excels at capturing the shape and variability of the hydrograph, while purely physics-driven approaches retain an advantage in reproducing total volumes. When the same framework was applied at monthly resolution, its performance improved further, yielding an R² of 0.9929, an NSE of 0.9660 and an RMSE of 6.1879 cubic metres per second, a finding consistent with the general observation that aggregation smooths daily noise and makes underlying dynamics easier to learn.

The Jing River basin, a major tributary of the Yellow River, provides a demanding test case. The basin is subject to pronounced hydrological droughts whose propagation from meteorological drought has intensified under environmental change, and its semi-arid to semi-humid climate produces highly variable flows with episodic floods. Data for the study were drawn from the Chinese Hydrological Yearbook of the Yellow River Basin and the China National Meteorological Information Center, spanning the full suite of variables a modern forecasting system would need in operation.

The significance of the approach extends beyond one basin. Signal decomposition combined with machine learning has become one of the most active fronts in hydrological forecasting research, with recent studies pairing wavelet methods, CEEMDAN and empirical mode decomposition variants with gradient boosting, LSTMs and other learners. What distinguishes the new work is the architectural separation of internal state and external forcing, which mirrors how hydrologists conceptually understand catchment behaviour, and the explicit attention to peak flows through the loss function. In effect, the model encodes domain knowledge about the physics of runoff generation into its structure rather than hoping a sufficiently large generic network will discover it from data alone.

The author is candid about the framework’s limitations. A systematic volume bias of just over thirteen percent persists, meaning the model tends to misestimate the total water passing the gauge even as it tracks the timing and shape of flow variations closely. More importantly, the study evaluated the model at a single station; whether the architecture transfers across basins with different geology, land cover and climate remains an open question that will be essential for real-world deployment. Generalisation, or the lack of it, has long been the dividing line between models that impress in benchmarks and models that serve water managers.

Nevertheless, the results arrive at a moment when the demand for accurate streamflow prediction is intensifying. Climate change is amplifying hydrological extremes in many of the world’s major basins, stressing water allocation systems designed around the statistics of a more stable past. Hybrid frameworks that combine signal processing, deep learning and physically informed architectures offer a pragmatic path forward, and the demonstration that a dual-stream, attention-equipped temporal convolutional network can reach NSE values above 0.96 on out-of-sample daily data marks a genuine step in that direction. The work was supported by several Chinese research programmes, including projects from Sinomach Group, Xianyang City and Chang’an University’s Fundamental Research Funds, and the full technical details, along with supplementary material, are available in the journal article.

The stakes behind this technical comparison are considerable. River discharge forecasts support reservoir operations, irrigation planning, drought response, flood warnings, and the allocation of limited water resources. In regions where rainfall is highly variable and hydrological systems are influenced by complex terrain, seasonal climate patterns, and rapidly changing atmospheric conditions, a small forecasting error can have practical consequences. Traditional statistical models often struggle with nonlinear relationships and long-term dependencies in environmental data. Deep-learning systems can identify such relationships, but their effectiveness depends heavily on how they represent time, how they select relevant information, and how efficiently they learn from multiple interacting variables. The West Azerbaijan study focuses on that problem by testing recurrent and transformer architectures under the same multivariate forecasting framework.

The models were trained with daily measurements of precipitation, air temperature, relative humidity, evaporation, air pressure, and wind speed. These variables provide a compact description of the atmospheric conditions that influence the movement of water through a watershed. Rainfall can produce a rapid rise in discharge, while temperature affects snowmelt and evaporation; humidity, pressure, and wind help describe the broader meteorological setting in which precipitation and water loss occur. By combining these inputs, the researchers sought to move beyond single-variable forecasting based only on historical river flow. The approach is particularly relevant to ungauged or sparsely monitored basins, where meteorological observations may be more widely available than detailed information about every physical process occurring within the catchment.

At the heart of the comparison is the difference between recurrent neural networks and transformers. LSTM networks process a sequence step by step, carrying forward an internal memory that helps them connect current conditions with earlier events. Their gating system allows the network to retain or discard information, making LSTMs more capable than conventional recurrent networks of learning delayed hydrological responses. However, sequential processing can make it difficult to capture relationships across long time windows, and the model may devote too much capacity to information that is not equally important. Attention mechanisms address this limitation by assigning different weights to elements of the input sequence. Instead of treating every previous observation as equally influential, attention allows the model to emphasize the meteorological patterns most relevant to the discharge being predicted.

The Informer model extends the transformer concept for long-sequence time-series forecasting. Standard transformers rely on self-attention, a mechanism that compares each time step with others in the sequence to identify relationships. That procedure can become computationally expensive as the sequence grows. Informer reduces this burden through more efficient attention calculations and a strategy designed to identify the most influential patterns rather than processing every possible interaction with equal intensity. It also uses an encoder-decoder structure to transform historical observations into future predictions. In the study, the Attention-Informer architecture adds another layer of selective focus, allowing the system to concentrate on the meteorological signals and temporal features that matter most for streamflow dynamics.

The results presented by the researchers show a consistent advantage for A-Informer. Across the three rivers, the model achieved correlation coefficients above 0.90 and Nash–Sutcliffe efficiency values exceeding 0.88. The correlation coefficient measures how closely predicted and observed discharge vary together, while the Nash–Sutcliffe efficiency compares the model against a basic benchmark based on the mean observed flow. A value approaching one indicates that the forecasts reproduce the observed pattern with high skill. A-Informer also produced the lowest reported errors, with root mean square error values of approximately 1.53 to 3.33 and mean absolute error values of about 0.87 to 1.84, depending on the station. Because root mean square error gives greater weight to large mistakes, its reduction is especially important when forecasting flood-related peaks.

The study’s visual analyses add an important dimension to the numerical scores. According to the authors, A-Informer tracked both low-flow periods and extreme peaks more accurately than the competing architectures. This distinction matters because a model can achieve a strong average score while still smoothing away short-lived floods or exaggerating minor fluctuations. Low-flow prediction is essential for assessing water availability and ecological stress, whereas accurate peak detection is central to flood preparedness and infrastructure safety. The researchers also evaluated peak-flow agreement, deviation, and bias, finding that A-Informer showed the highest concordance and the smallest departures from observed peak events. In practical terms, the model was less likely to miss or misrepresent the timing and magnitude of the sharp rises that challenge operational forecasting systems.

The CEEMDAN-LSTM model included in the comparison represents a different strategy for improving recurrent forecasting. Complete Ensemble Empirical Mode Decomposition with Adaptive Noise, or CEEMDAN, separates a complex signal into components operating at different time scales before those components are processed by an LSTM. Such decomposition can reveal oscillations, trends, and irregular fluctuations that may be hidden in the original discharge series. Although this hybrid design can improve a recurrent model’s ability to handle nonstationary data, the reported results indicate that signal decomposition alone did not match the performance achieved by the attention-enhanced transformer. The comparison suggests that the capacity to identify relevant relationships directly across long sequences may be more valuable than relying primarily on pre-processing to simplify the streamflow signal.

The authors describe their work as a systematic evaluation of advanced deep-learning models in a heterogeneous hydrological environment, but the findings also highlight important limits. The study used existing observations rather than generating a new dataset, and the underlying data and code are not openly provided; the authors state that code may be requested from the corresponding author. Strong performance across three rivers in West Azerbaijan does not automatically guarantee the same results in basins with different climates, land cover, snow regimes, reservoir operations, or data quality. Transformer models can also require substantial computational resources and careful tuning, and high predictive accuracy does not by itself explain the physical causes of a flood. Even so, the results offer a compelling signal for water-management agencies: combining efficient long-sequence attention with multivariate meteorological information may provide a more responsive and dependable route to daily streamflow forecasting, particularly when the next forecast must capture not just the river’s usual rhythm, but its most dangerous departures from it.

Subject of Research: Comparative evaluation of deep-learning models for multivariate daily streamflow prediction in three rivers of West Azerbaijan Province, Iran.

Article Title: Comparative evaluation of attention-based and transformer deep learning models for multivariate daily streamflow prediction in rivers of West Azerbaijan, Iran

Article References: Keshavar, M. R., & Parvishi, A. (2026). “Comparative evaluation of attention-based and transformer deep learning models for multivariate daily streamflow prediction in rivers of West Azerbaijan, Iran.” Earth Science Informatics, 19, Article 165.

Image Credits: AI Generated

DOI: https://doi.org/10.1007/s12145-026-02212-9

Keywords: Daily streamflow prediction; deep learning; attention mechanism; transformer architecture; Informer; Attention-Informer; flood forecasting; hydrology