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QWRF-Net: A Quantum-Wavelet Framework with Rectified Flow for Short-Term Precipitation Nowcasting
Zhuo Wang, Chaorong Li, Wenjie Luo, Chuanhu Deng
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Abstract
Abstract:Short-term precipitation nowcasting is important for hydrometeorological early warning, especially when intense convective rainfall may trigger urban flooding, flash floods, and other high-impact hazards. A key challenge in warning-oriented nowcasting is that radar precipitation fields contain strongly coupled multi-scale structures, while forecast quality often degrades at later lead times, making it difficult to preserve intense precipitation cores and their spatial organization over the full warning-relevant horizon. To address this problem, we propose QWRF-Net, a quantum-wavelet framework with rectified flow for short-term precipitation nowcasting. The core idea is to improve the conditional representation of precipitation by explicitly decomposing latent features into wavelet sub-bands and then performing differentiated quantum-inspired modulation in the decomposed latent space, before generating future sequences through a rectified-flow-based non-autoregressive decoder. Experiments on the KNMI radar and SEVIR benchmarks under a unified evaluation protocol show that QWRF-Net achieves favorable overall performance, with relatively consistent gains at medium-to-high precipitation thresholds, on an extreme-event subset, and in preserving intense precipitation cores and fine-scale structures. Ablation results further indicate that wavelet-based scale disentanglement, differentiated sub-band modulation, and flow-based generation provide complementary benefits within the proposed framework. Overall, these results suggest that jointly enhancing multi-scale precipitation representation and stable multi-step generation is a promising direction for warning-oriented short-term precipitation nowcasting. The observed improvements may also provide a more useful precipitation basis for downstream hydrological and warning-related applications.
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QWRF-Net: A Quantum–Wavelet Framework with Rectified Flow for Short-Term Precipitation Nowcasting Zhuo Wang a,b , Chaorong Li a,∗ , Wenjie Luo b and Chuanhu Deng b a School of Computer Science and Technology (School of Artificial Intelligence), Yibin University, , Yibin, 644000, Sichuan, China b College of Computer Science and Engineering, Chongqing University of Technology, , Chongqing, 400054, China A R T I C L E I N F O Keywords: Short-term precipitation nowcasting Hydrometeorological early warning Hydrometeorological forecasting Wavelet decomposition Quantum-inspired modulation Rectified flow A B S T R A C T Short-term precipitation nowcasting is important for hydrometeorological early warning, especially when intense convective rainfall may trigger urban flooding, flash floods, and other high-impact hazards. A key challenge in warning-oriented nowcasting is that radar precipitation fields contain strongly coupled multi-scale structures, while forecast quality often degrades at later lead times, making it difficult to preserve intense precipitation cores and their spatial organization over the full warning-relevant horizon. To address this problem, we propose QWRF-Net, a quantum–wavelet framework with rectified flow for short-term precipitation nowcasting. The core idea is to improve the conditional representation of precipitation by explicitly decomposing latent features into wavelet sub-bands and then performing differentiated quantum-inspired modulation in the decomposed latent space, before generating future sequences through a rectified-flow-based non-autoregressive decoder. Experiments on the KNMI radar and SEVIR benchmarks under a unified evaluation protocol show that QWRF-Net achieves favorable overall performance, with relatively consistent gains at medium-to- high precipitation thresholds, on an extreme-event subset, and in preserving intense precipitation cores and fine-scale structures. Ablation results further indicate that wavelet-based scale disentanglement, differentiated sub-band modulation, and flow-based generation provide complementary benefits within the proposed framework. Overall, these results suggest that jointly enhancing multi-scale precipitation representation and stable multi-step generation is a promising direction for warning- oriented short-term precipitation nowcasting. The observed improvements may also provide a more useful precipitation basis for downstream hydrological and warning-related applications. 1. Introduction 1.1. Background and challenges In the context of global climate change, the increasing frequency and intensity of extreme weather events continue to pose substantial risks to human society [1, 2]. In par- ticular, short-term intense precipitation triggered by local convection is closely associated with urban flooding, flash floods, landslides, and other high-impact hydrometeorolog- ical hazards. Because such events often develop rapidly and evolve within a limited time window, effective early-warning systems require timely and reliable precipitation forecasts [3]. Consequently, accurate short-term precipitation now- casting has become an important component of hazard- oriented weather warning and short-term risk mitigation. For flash-flood and urban inundation warning in particular, forecast value depends not only on whether rainfall occurs, but also on whether intense precipitation cores are correctly located and maintained over the warning-relevant lead time. Such properties may also be relevant when nowcasts are used as upstream precipitation inputs for downstream hydrologi- cal assessment and warning-related analysis. ∗ Corresponding author. 240503wj@stu.cqut.edu.cn (Z. Wang); lichaorong88@163.com (C. Li); lwj018@stu.cqut.edu.cn (W. Luo); onlyiyou@stu.cqut.edu.cn (C. Deng) ORCID(s): 0000-0001-8336-2661 (C. Li) 1 This work was supported in part by the Major Project of Yibin Univer- sity under Grant 2025XJZD01, and in part by the Science and Technology Program of the Yibin Municipal Science and Technology Bureau under Grant 2025JC008. From both scientific and operational perspectives, pre- cipitation nowcasting remains challenging. Although nu- merical weather prediction (NWP) models [4] have achieved considerable success in synoptic- and mesoscale forecasting, their application to rapid convective-scale nowcasting is often constrained by the complexity of physical modeling and the high computational cost of data assimilation [5]. Strongly nonlinear convective processes may initiate, in- tensify, merge, or dissipate within minutes, making them difficult to represent accurately in time-critical forecasting scenarios [6]. In warning-oriented settings, this challenge is especially important because localized errors in short lead- time rainfall prediction may affect the timing and usefulness of flood-related response. This issue is particularly critical in short-fuse warning situations, where errors in the 30–60 min range may directly reduce the effective preparation window for emergency response. Deep learning provides a practical data-driven route for precipitation nowcasting [7] by learning spatiotemporal evolution patterns directly from large radar archives. Com- pared with computationally intensive physics-based fore- casting, such models can offer much faster inference in short lead-time settings. However, current data-driven nowcast- ing methods still face two closely related challenges [8]. First, radar precipitation fields contain intertwined multi- scale structures, including broad precipitation organization, localized intense cores, and fine-scale boundaries, which are not always easy to represent adequately within a sin- gle feature space. From a warning-oriented hydrometeoro- logical perspective, these structures do not play identical Wang et al.: Preprint submitted to ElsevierPage 1 of 16 arXiv:2608.01626v1 [cs.LG] 3 Aug 2026 QWRF-Net for short-term precipitation nowcasting roles: broad precipitation organization is relevant to the overall spatial extent of rainfall, whereas localized intense cores and sharp gradients are more closely associated with short-duration high-impact events. From a hydrological per- spective, such large-scale organization provides the rain- fall background for runoff generation, whereas localized intense cores more directly influence where short-duration flood-triggering rainfall is concentrated. Second, multi-step forecasting remains vulnerable to progressive degradation, where small prediction errors may accumulate over time and lead to blurred structures, weakened intensities, and reduced stability at later lead times [9]. For short-term warning, this issue is particularly important because degraded later lead- time forecasts may reduce the effective response window available for emergency decision-making. These two difficulties are closely coupled in practice: in- sufficient conditional representation makes future-sequence generation more difficult, while unstable generation may further obscure precipitation structures that are critical to short-term warning. This motivates a nowcasting framework designed to jointly improve multi-scale precipitation repre- sentation and future-sequence generation [10]. 1.2. Research lineage Existing precipitation nowcasting methods have evolved from motion extrapolation [11] to discriminative prediction [12] and, more recently, to generative forecasting [13]. This progression reflects a gradual shift from modeling precip- itation displacement alone to modeling both precipitation structure and future evolution [14]. Early nowcasting methods mainly relied on motion ex- trapolation, such as optical-flow-based approaches [15] and semi-Lagrangian schemes [16]. These methods can be ef- fective when precipitation evolves smoothly, but they are often less suitable for convective systems involving rapid deformation, growth, merging, and dissipation. In warning- oriented applications, this limitation is important because the rapid emergence or decay of localized convective cores may strongly affect short-term hazard estimates. As a result, purely extrapolative methods may be less reliable when warning decisions depend on the rapid emergence, displace- ment, or dissipation of localized high-intensity rainfall. This limitation motivated the development of deep dis- criminative models that learn future precipitation directly from historical observations. Representative examples in- clude convolutional encoder–decoder models, recurrent now- casting models, and more recent spatiotemporal prediction architectures [17, 18, 19, 20, 21, 22]. While these models have substantially advanced precipitation nowcasting, fore- casts trained with point-estimation objectives may smooth intense echoes and fine-scale morphology, and recursive multi-step prediction can still amplify small errors over time [23]. For warning-oriented hydrometeorological forecasting, such smoothing may reduce fidelity in the location and structure of intense rainfall cores. This loss of structural fidelity is particularly problematic for warning-oriented applications because small spatial shifts in intense cores may lead to large differences in local hazard relevance. To alleviate the limitations of deterministic prediction, recent studies have increasingly explored generative models [24] that learn a distribution over future precipitation states rather than a single point estimate. GAN-based methods such as DGMR [25] and more recent approaches such as NowcastNet [26] indicate that generative formulations are well suited to modeling complex precipitation evolution. Diffusion-based methods such as PreDiff [27], DiffCast [28], and related conditional diffusion models [29] further show strong generation quality, although their iterative denoising procedures may still introduce non-negligible inference cost in time-sensitive settings. In operational hydrometeorologi- cal warning, such inference cost may become a practical lim- itation when frequent forecast updates are required. Flow- based formulations provide an alternative by learning a con- tinuous velocity field and generating future states through ODE-based sampling [30]. These developments suggest that improving future-sequence generation is important, but gen- eration quality also depends on how precipitation structures are organized before decoding. 1.3. Our proposed method: QWRF-Net To address the above issues, we propose QWRF-Net, a conditional generative framework for short-term radar-based precipitation nowcasting. As illustrated in Fig. 1, QWRF- Net combines a wavelet-decomposed bottleneck with a flow- based decoder to improve scale-aware conditional represen- tation and multi-step future prediction. From a hydrometeorological forecasting perspective, the central idea is to first organize precipitation information in a way that better reflects its multi-scale warning rele- vance, and then generate future sequences using a mecha- nism that is less vulnerable to lead-time degradation. The framework therefore follows a representation-to-generation strategy: it first separates precipitation information by scale, then enhances decomposed components in a differentiated manner, and finally generates future sequences through a non-autoregressive flow-based decoder. In this sense, the proposed framework is designed not only to improve aver- age prediction accuracy, but also to better preserve those rainfall structures that are most consequential for short- term hydrometeorological warning and potentially relevant to downstream hydrological use. Specifically, a discrete wavelet transform (DWT) [31] is introduced at the bottleneck to reorganize mixed latent features into frequency-specific sub-bands, thereby sepa- rating low-frequency background information from high- frequency structural details. This step converts an entangled latent representation into structurally differentiated com- ponents and provides an explicit basis for distinguishing broad precipitation organization from local warning-relevant sharp structures. After this scale disentanglement, each sub- band is modulated by a learnable quantum-inspired transfor- mation, simulated on classical hardware, so that nonlinear enhancement is performed in a frequency-aware latent space Wang et al.: Preprint submitted to ElsevierPage 2 of 16 QWRF-Net for short-term precipitation nowcasting 6×288×288 12×288×288 Velocity Loss Zt+dt=Zt+Vdt Overwrite Zt with Zt+dt Repeat until t = 1 12×288×288 bottleneck condition-integratedGatedFusion Noisy Image Zt Figure 1: Overall architecture of QWRF-Net for radar-based nowcasting. Given the past 6 frames (30 minutes) as condition, the model generates the next 12 frames (60 minutes). The encoder extracts multi-scale features, the quantum–wavelet bottleneck refines scale-aware precipitation representation, and the flow-based decoder generates the future sequence through ODE-based sampling. rather than on the original mixed feature map. Here, the quantum-inspired module is used as a classically simulated structured nonlinear operator for sub-band-specific modu- lation rather than as evidence of practical quantum advan- tage. Based on the resulting conditional representation, a rectified-flow-based formulation [32] is adopted to learn a conditional velocity field for non-autoregressive future- sequence generation. During inference, the model predicts the target sequence through ODE-based integration rather than recursive frame-by-frame rollout, which is expected to reduce accumulated degradation across the forecast horizon. Overall, the proposed framework is intended to jointly improve the representation of historical precipitation struc- tures and the generation of future precipitation sequences over multiple lead times. In this way, wavelet decompo- sition, differentiated sub-band modulation, and flow-based generation serve as sequentially connected components for improving both structural preservation and forecast stability in warning-relevant short-term nowcasting scenarios [33]. 1.4. Contributions The main contributions of this study are summarized as follows: 1. We formulate short-term precipitation nowcasting as a joint problem of conditional precipitation represen- tation and future-sequence generation, with emphasis on preserving multi-scale structures that are relevant to warning-oriented hydrometeorological forecasting. 2. We introduce a quantum–wavelet bottleneck that reor- ganizes latent precipitation features into wavelet sub- bands and performs differentiated structured mod- ulation in the decomposed latent space, aiming to improve the representation of both broad precipitation organization and localized intense structures. 3. We integrate the refined conditional representation with a rectified-flow-based non-autoregressive decod- ing strategy for multi-step precipitation nowcasting, with the goal of reducing forecast degradation over later lead times that are particularly relevant to short- term warning. 4. Under a unified evaluation protocol on the KNMI and SEVIR benchmarks, we find that the proposed Wang et al.: Preprint submitted to ElsevierPage 3 of 16 QWRF-Net for short-term precipitation nowcasting framework provides relatively more consistent gains in medium-to-high precipitation regimes, later lead times, and challenging extreme-event cases that are especially relevant to warning-oriented applications. 2. Related work 2.1. Wavelet-based multi-scale representation Radar precipitation fields exhibit intertwined multi-scale structures, ranging from broad precipitation organization to localized convective cells with sharp spatial gradients [34]. Preserving such scale diversity is important for represent- ing both the overall organization of precipitation systems and the fine-scale morphology of intense echoes. Although convolutional neural networks can expand receptive fields through hierarchical downsampling, their scale aggregation is often implicit, which may make the preservation of high- frequency details more difficult in challenging nowcasting scenarios [35]. The discrete wavelet transform (DWT) provides an explicit decomposition of spatial features into frequency- specific sub-bands [36]. In two dimensions, DWT decom- poses a feature map into four components, namely L, LH, HL, and H. Among them, L mainly captures coarse-scale background information, whereas LH, HL, and H retain directional high-frequency structures such as boundaries, local gradients, and abrupt intensity variations. This de- composition is well aligned with radar precipitation fields because it separates broad background information from high-frequency structural details in an interpretable manner. Wavelet-based representations have been explored in deep models for improving compactness, denoising ability, and robustness. More relevant to radar-related tasks, recent studies suggest that wavelet-driven designs can help preserve sharp boundaries and high-intensity structures. For exam- ple, WaveC2R [37] introduces a wavelet-driven coarse-to- refined hierarchical framework for radar retrieval and shows that frequency-specific modeling can help decouple large- scale intensity patterns from boundary details on SEVIR- related benchmarks [38]. These observations suggest that explicit frequency decomposition may also be useful for precipitation nowcasting, where both broad precipitation organization and localized structural details need to be rep- resented. From a hydrometeorological perspective, explicit fre- quency separation may be useful because broad background precipitation and localized intense convective structures may play different roles in warning-oriented forecasting. This potential is particularly relevant in hydrological warning because rainfall background extent and localized convective concentration may contribute differently to runoff response and hazard triggering. However, many existing wavelet- based designs mainly emphasize decomposition itself, while its role in conditional generative nowcasting remains less explored. 2.2. Quantum-inspired representation for structured nonlinear enhancement Quantum neural networks and variational quantum cir- cuits (VQCs) [39] have attracted increasing attention as structured nonlinear transformations for hybrid quantum– classical learning [40]. In many recent studies, such modules are used not as replacements for classical deep networks, but as compact nonlinear operators embedded within larger hybrid architectures. From a representation perspective, quantum-inspired modules can be interpreted as structured nonlinear operators acting on compact latent descriptors. This property is poten- tially relevant to precipitation nowcasting, where different latent components may correspond to different structural roles across scales. In particular, once precipitation features have been decomposed into wavelet sub-bands, differenti- ated nonlinear modulation may help enhance components associated with localized boundaries and intensity varia- tions. In this work, we adopt a quantum-inspired module sim- ulated on classical hardware rather than relying on physical quantum devices [41]. Its role is not to replace conventional feature extraction, but to provide structured nonlinear mod- ulation after wavelet-based scale disentanglement. Accord- ingly, the quantum-inspired component in our framework is best understood as a classically simulated sub-band-specific modulation operator rather than as evidence of practical quantum-computing advantage. 2.3. Generative modeling for precipitation nowcasting Generative modeling has become an important direction in precipitation nowcasting because it can better represent forecast uncertainty and often produces sharper precipitation structures than deterministic point-estimation methods. A representative early example is DGMR [25], which showed that deep generative radar nowcasting can achieve skillful and realistic precipitation prediction. More recently, Now- castNet demonstrated strong performance on intense pre- cipitation events by combining physical evolution modeling with deep generative prediction. These studies suggest that generative formulations are well suited to modeling complex spatiotemporal precipitation evolution [24]. Among recent generative paradigms, diffusion-based models have shown strong generation quality in precipitation nowcasting. Diffusion-based methods such as PreDiff [27], DiffCast [28], and related conditional diffusion models [29] further show strong generation quality, although their itera- tive denoising procedures may still introduce non-negligible inference cost in time-sensitive settings. In operational hy- drometeorological warning, such inference cost may become a practical limitation when frequent forecast updates are required. These developments indicate that the choice of gen- erative formulation can substantially affect forecast sharp- ness, realism, and computational practicality. At the same time, generation quality also depends on how conditional Wang et al.: Preprint submitted to ElsevierPage 4 of 16 QWRF-Net for short-term precipitation nowcasting precipitation information is represented before decoding, which makes the design of the conditional representation particularly relevant. For warning-oriented hydrometeoro- logical forecasting, realistic-looking outputs alone are not sufficient if intense precipitation structures and later lead- time stability are not adequately preserved. Accordingly, a warning-relevant generative nowcasting framework should be judged not only by perceptual realism, but also by its ability to preserve high-impact rainfall structures over op- erational lead times. 2.4. Flow-based generative modeling for future-sequence generation Flow-based generative formulations provide an alterna- tive by learning a continuous velocity field and generating samples through ODE-based transport. Flow matching [42] and related rectified or straightened flow [43] methods opti- mize such velocity fields under continuous-time objectives and have recently shown favorable efficiency–fidelity trade- offs in high-dimensional generation tasks. These properties are particularly relevant to precipitation nowcasting, where rapid inference is often desirable in operational settings. Recent studies have begun to introduce flow-based for- mulations into meteorological nowcasting. In particular, FlowCast applies conditional flow matching (CFM) [44] to radar nowcasting and shows that a flow-matching objective can produce high-fidelity forecasts with fewer sampling steps than diffusion objectives under similar backbone de- signs. MeanFlow further proposes a related one-step gen- erative formulation based on average velocity, providing a useful perspective on reducing the number of function eval- uations. These studies suggest that flow-based generative modeling is a promising direction for efficient precipitation forecasting. Our work is related to these methods in that it also adopts a flow-based formulation for non-autoregressive future-sequence generation. The main distinction lies in the conditional representation used by the generative decoder. Instead of relying on a standard latent conditioning pathway, QWRF-Net introduces a wavelet-decomposed and quantum- inspired bottleneck to organize low-frequency background information, high-frequency structural details, and struc- tured nonlinear enhancement before flow-based generation. Therefore, the contribution of the proposed framework lies not only in the use of a flow-based decoder, but also in its integration with a scale-aware conditional representa- tion. This combination is particularly relevant to warning- oriented forecasting, where both structural preservation and later lead-time stability are important. 3. Methodology QWRF-Net is a conditional generative framework for short-term radar-based precipitation nowcasting. As illus- trated in Fig. 1, the framework contains two key com- ponents: a wavelet-decomposed bottleneck for scale-aware precipitation representation and a flow-based decoder for non-autoregressive future-sequence generation. Given the previous 6 radar frames (30 minutes) at 5-minute intervals, the model generates the next 12 frames (60 minutes). 3.1. Overall architecture and notation QWRF-Net adopts a U-Net-style encoder–decoder back- bone to extract multi-scale spatial features from histori- cal radar observations. Skip connections preserve higher- resolution information during up-sampling, while the deep- est latent representation is further refined by the proposed wavelet-decomposed bottleneck. For SEVIR, we use VIL as the prediction target, while for KNMI we use the cor- responding radar-based precipitation field under the same nowcasting protocol. For both datasets, the target values are normalized to [0, 1] during training. Let 퐵 denote the batch size. The historical input se- quence and future target sequence are denoted by 푋 in ∈ ℝ 퐵×푇 in ×퐻×푊 , 푋 tar ∈ ℝ 퐵×푇 out ×퐻×푊 , (1) where 푇 in = 6, 푇 out = 12, and (퐻,푊 ) = (288, 288). Here, 푇 in and 푇 out denote the numbers of input and target frames, respectively, while 퐻 and 푊 denote the spatial height and width of each frame. For flow-based generation, an initial Gaussian noise sample 푍 0 ∼ (0,퐼) is drawn with the same shape as 푋 tar . We denote the continuous-time latent state by 푍(푡) and the learned conditional velocity field by 푣 휃 (⋅). Under this formulation, QWRF-Net parameterizes a time-dependent conditional velocity field 푣 휃 (푍(푡),푡,푋 in ) = QWRF-Net(푍(푡),푡,푋 in ;휃), (2) where푡 ∈ [0, 1] is embedded using sinusoidal time encoding and injected into the network blocks. The historical sequence 푋 in provides the condition that guides future-sequence gen- eration. To inject historical context throughout the encoder, multi-scale conditioning features extracted from 푋 in are fused into the main pathway through a gated fusion operator. This mechanism adaptively balances the main feature stream and the conditioning branch across spatial scales, allowing historical observations to influence both shallow and deep representations. In this way, the historical sequence serves not only as a global condition for generation, but also as guidance for organizing multi-scale latent features before de- coding. The resulting deepest latent feature is then processed by the wavelet–quantum bottleneck. 3.2. Quantum–wavelet bottleneck for scale-aware precipitation representation As illustrated in Fig. 2, the quantum–wavelet bottleneck is placed at the deepest level of the U-Net, where the latent representation is relatively compact and therefore suitable for structured transformation. Let the bottleneck feature be 퐹 ∈ ℝ 퐵×퐶×퐻 푏 ×푊 푏 , where 퐶 denotes the channel dimension, and 퐻 푏 and 푊 푏 denote the spatial height and width of the bottleneck feature Wang et al.: Preprint submitted to ElsevierPage 5 of 16 QWRF-Net for short-term precipitation nowcasting B×C×H×W Quantum- Enhanced Layer + + + + Conv 1×1 Conv 1×1 Conv 1×1 Conv 1×1 Quantum- Enhanced Layer Quantum- Enhanced Layer Quantum- Enhanced Layer IDWT B×C×H×W + Conv 1×1 DWT Discrete Wavelet Transform IDWT Inverse Discrete Wavelet Transform L (Low–Low): Low-pass × Low-pass LH (Low–High): Low-pass × High-pass HL (High–Low): High-pass × Low-pass H (High–High): High-pass × High-pass + Residual Connection LN LN LN LN DWT linear projection (features qubits ) Input Angular Embedding VQC×3 RZ Gate Linear CNOT Cyclic CNOT PauliZ linear reconstruction (qubits features) Output Quantum- Enhanced Layer RY GateRX Gate Figure 2: Structure of the quantum–wavelet bottleneck. The bottleneck feature is decomposed into four wavelet sub-bands (L, LH, HL, and H) through DWT. Each sub-band is processed by an independent quantum-inspired transformation followed by pointwise projection and normalization. The transformed sub-bands are then fused through IDWT and residual fusion to form the output bottleneck representation. map, respectively. The bottleneck consists of three stages: wavelet decomposition for scale disentanglement, quantum- inspired sub-band transformation for structured nonlinear enhancement, and reconstruction with residual fusion. The key idea is to apply structured nonlinear modulation after scale disentanglement rather than before it. Accord- ingly, the quantum-inspired operator is applied to wavelet sub-bands instead of the original mixed latent feature map, so that low-frequency background information and high- frequency structural details can be modulated in a differen- tiated manner. A single-level 2D discrete wavelet transform is first applied to decompose 퐹 into four wavelet sub-bands: (퐹 퐿 ,퐹 퐿퐻 ,퐹 퐻퐿 ,퐹 퐻 ) = DWT(퐹).(3) Here, 퐹 퐿 mainly captures low-frequency background in- formation, whereas 퐹 퐿퐻 , 퐹 퐻퐿 , and 퐹 퐻 retain directional high-frequency structural details such as boundaries, local gradients, and abrupt intensity variations. This decompo- sition explicitly reorganizes the latent representation into coarse-scale and fine-scale components before nonlinear modulation. Such decomposition may also be relevant to warning-oriented forecasting because broad precipitation organization and localized intense structures may play dif- ferent roles in short-term hazard-related prediction. From a hydrological interpretation standpoint, the L component can be viewed as carrying broad rainfall-background infor- mation related to the spatial extent of precipitation, whereas the higher-frequency components are more closely related to intense-core boundaries, localized gradients, and abrupt structural changes. Such explicit separation may be useful when warning relevance depends more strongly on preserv- ing localized convective organization than on reproducing only the average rainfall field. For each sub-band tensor 퐹 sub ∈ 퐹 퐿 ,퐹 퐿퐻 ,퐹 퐻퐿 ,퐹 퐻 ,(4) we apply an independent learnable transformation(⋅) im- plemented by a variational quantum circuit simulated on classical hardware. The transformation starts by compress- ing the spatial feature map into a compact channel descriptor through global average pooling, 푢 sub = GAP(퐹 sub ) ∈ ℝ 퐵×퐶 ,(5) so that the sub-band is represented by a low-dimensional summary rather than by the full spatial grid. This de- sign allows the quantum-inspired module to operate as a lightweight structured nonlinear operator on compact sub- band descriptors, rather than replacing spatial feature extrac- tion by the encoder–decoder backbone itself. The descriptor Wang et al.: Preprint submitted to ElsevierPage 6 of 16 QWRF-Net for short-term precipitation nowcasting is then projected into a qubit-aligned latent vector, 휶 sub = 푊 enc 푢 sub + 푏 enc ∈ ℝ 퐵×푁 ,(6) where휶 sub denotes the angle vector used for quantum state encoding,푊 enc and푏 enc are learnable projection parameters, and 푁 is the number of qubits. The vector휶 sub is used as the angular input of the variational quantum circuit. In this way, the classical sub-band descriptor is encoded into a quantum state by angular embedding, |휓 enc (휶 sub )⟩ = 푈 enc (휶 sub ) |0⟩ ⊗푁 ,(7) where |0⟩ ⊗푁 denotes the initial all-zero state and 푈 enc (⋅) denotes the angle-embedding operator. The encoded state is then processed by a trainable variational circuit, |휓 out ⟩ = 푈(휽) |휓 enc (휶 sub )⟩ = 푈(휽)푈 enc (휶 sub ) |0⟩ ⊗푁 , (8) where 푈(휽) is parameterized by learnable circuit parameters 휽. In practice, this circuit is composed of parameterized single-qubit rotation gates and entangling operations. To return to the classical feature space, the output quan- tum state is measured through Pauli-푍 expectations, 푦 푖 = ⟨휓 out |푍 푖 |휓 out ⟩, 푖 = 1, ...,푁,(9) where 푍 푖 denotes the Pauli-푍 observable acting on the 푖-th qubit, yielding a classical vector 푦 sub = [푦 1 , ...,푦 푁 ] ∈ ℝ 퐵×푁 .(10) This vector is then projected back to the original feature dimension and used as a sub-band-specific modulation term. The overall transformed sub-band is written as 퐹 ′ sub = ( 퐹 sub +(퐹 sub ) ) ,(11) where(퐹 sub ) denotes the quantum-inspired modulation reconstructed from푦 sub , and (⋅) denotes a 1×1 convolution followed by layer normalization. The quantum-inspired transformation can be viewed as a classically simulated structured nonlinear operator that maps each decomposed sub-band descriptor to a sub-band-specific enhancement term. In the proposed framework, its role is to provide differentiated modulation after wavelet-based scale disentanglement rather than to act as an independent pre- dictor. Under this interpretation, the role of the sub-band- specific modulation is to enhance structurally differentiated precipitation information after decomposition rather than to introduce complexity for its own sake. This property may be useful for warning-oriented forecasting, where not all latent precipitation components contribute equally to the identification of intense short-duration rainfall. This design is particularly suitable after wavelet de- composition because low-frequency background informa- tion and high-frequency structural details no longer play identical roles once the bottleneck feature has been reorga- nized into sub-bands. As further illustrated in Fig. 2, the transformed wavelet sub-bands are fused back into the spatial domain through the inverse discrete wavelet transform and a residual connection: 퐹 out = Conv 1×1 ( IDWT(퐹 ′ 퐿 ,퐹 ′ 퐿퐻 ,퐹 ′ 퐻퐿 ,퐹 ′ 퐻 ) + 퐹 ) . (12) Here, IDWT restores cross-sub-band interactions in the spa- tial domain, while the residual addition with the original bottleneck feature helps preserve the underlying latent rep- resentation during reconstruction. This reconstruction stage also helps maintain the overall spatial continuity of the pre- cipitation field after differentiated sub-band enhancement. 3.3. Rectified-flow-based future-sequence generation After the conditional representation is refined by the wavelet–quantum bottleneck, the future sequence is gen- erated through a rectified-flow-based formulation, so that representation refinement and non-autoregressive genera- tion are connected within the same pipeline. Under this framework, QWRF-Net learns a conditional velocity field that transports an initial Gaussian sample toward the future precipitation sequence. Let 푍 1 = 푋 tar and sample 푍 0 ∼ (0,퐼). For a random time 푡 ∼ (0, 1), the interpolation state is defined as 푍 푡 = 푡푍 1 + (1 − 푡)푍 0 .(13) This interpolation can be interpreted as a continuous tran- sition from noise to the target precipitation field, providing a natural training pathway for learning temporally coherent precipitation evolution. Such a formulation is also compati- ble with the view that precipitation evolution is a temporally continuous process, rather than a collection of disconnected frame-wise states. QWRF-Net is trained to match the corresponding condi- tional velocity field using (휃) = 피 푍 0 ,푍 1 ,푡 [ ‖ ‖ 푣 휃 (푍 푡 ,푡,푋 in ) − (푍 1 − 푍 0 ) ‖ ‖ 2 2 ] . (14) This objective encourages the model to learn how the noisy latent state should evolve toward the target future sequence under the condition provided by the historical observations. From a forecasting perspective, this learning objective en- courages a continuous evolution process rather than a se- quence of independently generated steps, which may help preserve temporal stability over later lead times. At inference time, the future sequence is obtained by solving the conditional ordinary differential equation 푑푍 푑푡 = 푣 휃 (푍(푡),푡,푋 in ), 푍(0) = 푍 0 ,(15) and taking the final state as 푋 pred = 푍(1).(16) Unless otherwise stated, we use a forward Euler solver with 50 integration steps for evaluation and visualization. In this Wang et al.: Preprint submitted to ElsevierPage 7 of 16 QWRF-Net for short-term precipitation nowcasting Table 1 Quantitative comparison on the KNMI dataset. CSI and HSS are reported at rainfall thresholds of 0.5, 2, 5, 10, and 30 m/h. MAE, RMSE, and SSIM are also reported. Higher is better for CSI, HSS, and SSIM, while lower is better for MAE and RMSE. The best results are marked in bold, and the second-best results are marked by underlining. Models CSI↑HSS↑ MAE↓ RMSE↓ SSIM↑ r≥0.5r≥2r≥5r≥10r≥30r≥0.5r≥2r≥5r≥10r≥30 ConvLSTM[21]0.6621 0.4236 0.3458 0.1202 0.1049 0.4299 0.4179 0.2416 0.1532 0.0357 6.284 7.5610.565 RainNet[19]0.6645 0.4793 0.3129 0.1198 0.0596 0.5675 0.4432 0.2345 0.0964 0.0236 7.573 9.2510.531 SmaAt-UNet[20]0.6733 0.4689 0.3196 0.1207 0.0698 0.5689 0.4369 0.2449 0.0987 0.0567 6.254 8.6520.545 SimVP[22]0.6809 0.4788 0.3094 0.1076 0.0661 0.5619 0.3967 0.2578 0.1463 0.0672 6.321 8.2160.556 DiffCast[28]0.6856 0.49630.3196 0.12250.1096 0.5746 0.4375 0.25860.1763 0.0596 6.578 7.4430.567 CoDiCast[29]0.6878 0.4869 0.35960.1220 0.1101 0.5733 0.4385 0.2536 0.1799 0.06896.491 7.1250.571 NowcastNet[26]0.6864 0.4928 0.3607 0.1232 0.11050.58110.4412 0.2581 0.18020.0673 5.9777.0310.573 QWRF-Net (Ours) 0.6963 0.4997 0.3610 0.1236 0.1112 0.5869 0.4484 0.2597 0.1812 0.0691 5.967 7.001 0.585 Table 2 Quantitative comparison on the SEVIR dataset. CSI and HSS are reported on the original VIL intensity scale at thresholds 16, 74, 133, 160, 181, and 219. MAE, RMSE, and SSIM denote the continuous and structural metrics. Higher is better for CSI, HSS, and SSIM, while lower is better for MAE and RMSE. The best results are marked in bold, and the second-best results are marked by underlining. Models CSI↑HSS↑ MAE↓ RMSE↓ SSIM↑ x≥16x≥74x≥133x≥160x≥181x≥219x≥16x≥74x≥133x≥160x≥181x≥219 ConvLSTM[21]0.6191 0.5147 0.3185 0.2361 0.2285 0.1067 0.4151 0.3147 0.3120 0.2211 0.1826 0.1064 8.4699.5870.551 RainNet[19]0.5893 0.4731 0.2991 0.2423 0.2101 0.0699 0.3496 0.2886 0.2112 0.1685 0.1563 0.0721 10.312 13.542 0.523 SmaAt-UNet[20]0.6375 0.5563 0.3121 0.2651 0.2230 0.0967 0.4508 0.4231 0.3101 0.2257 0.1789 0.0964 9.564 11.258 0.536 SimVP[22]0.6496 0.5645 0.3256 0.2756 0.2159 0.0996 0.4501 0.4322 0.3256 0.2311 0.1686 0.1023 8.5689.5680.535 DiffCast[28]0.6596 0.5789 0.3696 0.2629 0.2564 0.1302 0.46880.4126 0.3316 0.25360.1903 0.1033 8.4819.6210.549 CoDiCast[29]0.6687 0.5796 0.3626 0.2789 0.25790.1413 0.4710 0.4267 0.34660.2479 0.2030 0.11208.441 9.5490.554 NowcastNet[26]0.66910.58610.3681 0.2761 0.2571 0.14560.4661 0.43290.3456 0.2531 0.2123 0.1118 8.463 9.2810.568 QWRF-Net (Ours) 0.6773 0.5869 0.3726 0.27630.2581 0.1524 0.4612 0.4331 0.3479 0.2579 0.21220.1131 8.4609.3140.571 Table 3 Performance on the extreme-event subset of SEVIR, defined by peak VIL≥ 219 and exceedance ratio of pixels with VIL > 219 over the 12-frame target stack≥ 2%. ModelsMAE↓ RMSE↓ SSIM↑ RainNet[19]30.241 41.215 0.103 SmaAt-UNet[20]29.426 40.584 0.146 SimVP[22]30.544 39.337 0.169 ConvLSTM[21]29.781 38.918 0.149 DiffCast[28]28.587 36.4430.171 CoDiCast[29]33.248 37.668 0.176 NowcastNet[26]29.131 36.554 0.172 QWRF-Net (Ours)28.054 33.281 0.181 way, the model generates the full target sequence jointly rather than through recursive frame-by-frame prediction. This non-autoregressive generation mechanism is expected to reduce error accumulation across time and is therefore particularly relevant to maintaining forecast usefulness over the 60-minute warning-critical horizon considered in this study. 4. Experiments We evaluate QWRF-Net on two public precipitation nowcasting benchmarks, KNMI and SEVIR [38], using both categorical and continuous metrics. The experiments are designed to assess not only overall forecasting ac- curacy, but also structural fidelity, behavior under high- intensity precipitation conditions, and the usefulness of the proposed representation-to-generation design in warning- relevant short-term nowcasting under a unified evaluation setting. 4.1. Datasets and preprocessing We evaluate QWRF-Net on two public precipitation nowcasting datasets, KNMI and SEVIR, which play comple- mentary roles in this study. KNMI provides a regional radar- based nowcasting setting that is closer to practical short- term warning applications, whereas SEVIR offers a larger- sample benchmark for examining structural preservation and robustness under diverse convective conditions, including high-intensity and extreme-event cases. In this sense, the two datasets are used here to assess warning-relevant precipi- tation nowcasting performance from both a regional radar perspective and a broader benchmark perspective. The KNMI dataset consists of ground-based radar obser- vations over the Netherlands and surrounding regions, with a temporal resolution of 5 minutes and a spatial resolution of 288 × 288. In our experiments, the past 6 frames (30 minutes) are used to predict the next 12 frames (60 min- utes). This setting is consistent with the short lead times that are particularly relevant to operational warning-oriented forecasting. To reduce the dominance of non-precipitating samples, sequences without meaningful precipitation signals Wang et al.: Preprint submitted to ElsevierPage 8 of 16 QWRF-Net for short-term precipitation nowcasting are filtered out so that the models focus on learning the spatiotemporal evolution of precipitation events that are more relevant to short-term hazard-related applications. SEVIR is a large-scale storm event imagery dataset for radar and satellite meteorology. We use its vertically integrated liquid (VIL) product with a temporal resolution of 5 minutes. After removing invalid or incomplete samples, 17,321 valid sequences are retained. The original spatial resolution of 384×384 is resized to 288×288 for consistency with the KNMI setting and to control computational cost. Under the same forecasting protocol, the past 6 frames are used as input and the subsequent 12 frames are used as prediction targets. In the present work, SEVIR is primarily used to examine model behavior under a standardized large- sample setting and to assess whether the proposed frame- work remains effective in preserving intense precipitation structures under more challenging convective scenarios. For both datasets, input and target sequences are normal- ized to [0, 1] during training. For SEVIR, threshold-based categorical scores and extreme-event analysis are addition- ally reported on the original VIL intensity scale in order to better characterize performance under stronger convec- tive conditions. It should be noted that the use of KNMI and SEVIR in this study is intended to support evaluation of warning-relevant precipitation nowcasting performance, rather than to directly assess downstream hydrological re- sponse such as rainfall–runoff, flood routing, or inundation simulation. 4.2. Implementation details QWRF-Net is implemented in PyTorch and uses PennyLane and pytorch_wavelets for the quantum-inspired transforma- tion and wavelet decomposition, respectively. All experi- ments are conducted on a multi-GPU server with NVIDIA A6000 GPUs using distributed data parallel (DDP). Unless otherwise stated, the model takes the past 6 frames as input and predicts the next 12 frames at a spatial resolution of 288 × 288. We use the AdamW optimizer with an initial learning rate of 1 × 10 −4 and a batch size of 6 per GPU. In the flow-based generation module, the number of sampling steps is set to 10 during training and 50 during evaluation and visualization. The best model checkpoint is selected according to validation loss. For reproducibility, all compared models are trained and evaluated under the same forecasting protocol, including the same data split, spatial resolution, input–output setting, and preprocessing pipeline. When adapting baseline methods to the unified 6→12 setting, we keep their overall architectures as close as possible to their original implementations while adjusting only the components necessary for compatibility with the common experimental setup. Model selection is performed using the same validation criterion for all meth- ods. 4.3. Evaluation metrics We evaluate model performance using both categorical and continuous metrics. For categorical verification, we report the critical success index (CSI) [45] and Heidke skill score (HSS) [46]: CSI = TP TP + FP + FN ,(17) HSS = 2(TP⋅ TN − FP⋅ FN) (TP + FN)(FN + TN) + (TP + FP)(FP + TN) , (18) where TP, FP, FN, and TN denote true positives, false positives, false negatives, and true negatives, respectively. In warning-oriented forecasting, CSI is particularly rele- vant because it reflects successful detection of threshold- exceeding precipitation events, while HSS provides a skill- based assessment beyond chance agreement. To complement threshold-based evaluation, we addi- tionally report mean absolute error (MAE) [47], root mean squared error (RMSE) [48], and structural similarity index measure (SSIM) [49], which quantify intensity accuracy and structural consistency. Given the predicted sequence 푋 pred and the ground-truth sequence 푋 tar , MAE and RMSE are defined as MAE = 1 푁 푁 ∑ 푖=1 | | | 푋 (푖) pred − 푋 (푖) tar | | | ,(19) RMSE = √ √ √ √ 1 푁 푁 ∑ 푖=1 ( 푋 (푖) pred − 푋 (푖) tar ) 2 ,(20) where 푁 denotes the total number of evaluated pixels over all forecast frames. MAE and RMSE quantify intensity errors that may be relevant when considering the potential downstream use of precipitation nowcasts in rainfall-driven hydrological applications. For structural similarity, we adopt SSIM, defined as SSIM(푥,푦) = (2휇 푥 휇 푦 + 퐶 1 )(2휎 푥푦 + 퐶 2 ) (휇 2 푥 + 휇 2 푦 + 퐶 1 )(휎 2 푥 + 휎 2 푦 + 퐶 2 ) , (21) where 휇 푥 and 휇 푦 are the mean intensities of the prediction and ground truth, 휎 2 푥 and 휎 2 푦 are their variances, 휎 푥푦 is the covariance, and 퐶 1 , 퐶 2 are stabilization constants. For warning-relevant precipitation forecasting, SSIM is partic- ularly useful because preserving intense core location and boundary structure may matter more than mean intensity agreement alone. For KNMI, CSI and HSS are computed at rain-rate thresholds of 0.5, 2, 5, 10, and 30 m/h, following com- mon evaluation settings. For SEVIR, threshold-based scores are computed on the original VIL intensity scale using thresholds 16, 74, 133, 160, 181, 219, covering precipita- tion regimes from weak echoes to extreme convective inten- sity. To further assess model behavior under high-impact precipitation, we define an extreme-event subset on SEVIR. Wang et al.: Preprint submitted to ElsevierPage 9 of 16 QWRF-Net for short-term precipitation nowcasting 0 5 10 15 20 25 30 T-30minT-25minT-20minT-15minT-10minT-5min Input(X) Ground Truth(Y) Ours CoDiCast DiffCast NowcastNet RainNet SmaAt-UNet SimVP ConvLSTM T+10minT+20minT+30minT+40minT+50minT+60min T-30minT-25minT-20minT-15minT-10minT-5min Input(X) Ground Truth(Y) Ours CoDiCast DiffCast NowcastNet RainNet SmaAt-UNet SimVP ConvLSTM T+10minT+20minT+30minT+40minT+50minT+60min 100 50 0 150 200 255 (a) KNMI radar dataset.(b) SEVIR VIL dataset. Figure 3: Visual comparison of QWRF-Net with representative methods on two benchmark datasets. (a) KNMI radar dataset. (b) SEVIR VIL dataset. In each panel, the first row shows the input sequence, the second row shows the ground truth, and the remaining rows show the predictions produced by different models from T+10 min to T+60 min. A sample is regarded as extreme if, over the 12-frame target stack, the peak VIL intensity is at least 219 and the exceedance ratio of pixels with VIL > 219 is no less than 2%. 4.4. Baselines and fair comparison protocol We compare QWRF-Net against representative discrim- inative baselines, including RainNet, SmaAt-UNet, SimVP, and ConvLSTM, as well as strong generative baselines, including DiffCast, CoDiCast, and NowcastNet. These base- lines were selected to represent several commonly used families of data-driven nowcasting models, including recur- rent, convolutional encoder–decoder, and recent generative approaches. To improve comparability, all models are trained and evaluated under the same data split, spatial resolution, input– output setting (6→12), and preprocessing pipeline. For base- line methods whose original implementations were not de- signed exactly for this setting, we adapt them to the unified protocol while preserving their main architectural charac- teristics. Hyperparameters are adjusted within a comparable training setting, and the best checkpoint of each method is selected using the same validation criterion. We note that the compared generative baselines differ in their original optimization and sampling configurations. Therefore, our goal is not to reproduce every method under its task-specific best-case setting, but to assess their behavior under a common and controlled nowcasting protocol. Under this setting, all methods are compared using the same train- ing/validation split, input and prediction horizon, and eval- uation pipeline, so that the relative differences are more di- rectly attributable to model design rather than to mismatched experimental conditions. The purpose of this comparison is not only to compare predictive accuracy across model families, but also to examine which design choices appear more favorable for preserving warning-relevant precipitation structures under a common short-term nowcasting setting. 4.5. Quantitative results We first report quantitative results from both categori- cal verification and continuous/structural assessment so as to examine detection performance, intensity accuracy, and morphological consistency under a unified setting. Table 1 reports the categorical and continuous/structural results on KNMI. QWRF-Net achieves the strongest over- all results under the present setting, including the highest Wang et al.: Preprint submitted to ElsevierPage 10 of 16 QWRF-Net for short-term precipitation nowcasting Figure 4: Lead-time curves of CSI and HSS for different models on the KNMI dataset. CSI and HSS values across the reported thresholds, to- gether with the lowest MAE and RMSE and the highest SSIM. Although the margins over the strongest baselines are moderate for some metrics, the gains are relatively consis- tent across threshold-based verification and reconstruction- oriented evaluation. From a hydrometeorological forecasting perspective, the advantage of QWRF-Net becomes more visible at medium and high rain-rate thresholds, where prediction is gener- ally more difficult and where preserving strong precipi- tation cores is particularly important for warning-relevant nowcasting. The favorable SSIM, together with the im- provements at higher thresholds, further suggests that the proposed representation-to-generation design helps preserve structural details over the forecast horizon. Lower intensity errors and improved structural consistency may provide a more useful precipitation basis for downstream hydrological use than less stable nowcasts. For warning-oriented use, the improvements at 푟≥ 10 and 푟≥ 30 are particularly note- worthy because these thresholds are more closely associated with high-impact short-duration rainfall than low-threshold background precipitation alone. In this sense, the gains of QWRF-Net are not limited to average reconstruction quality, but also extend to rainfall regimes that are more relevant to flood-triggering conditions. Table 2 reports the categorical and continuous/structural results on SEVIR. QWRF-Net achieves favorable perfor- mance at medium-to-high VIL thresholds and attains the highest SSIM, while remaining competitive in MAE and RMSE. Compared with strong baselines such as NowcastNet and CoDiCast, the gains are generally moderate in absolute Wang et al.: Preprint submitted to ElsevierPage 11 of 16 QWRF-Net for short-term precipitation nowcasting Table 4 Ablation results on the KNMI dataset. CSI and HSS are reported at rainfall thresholds of 0.5, 2, 5, 10, and 30 m/h. MAE, RMSE, and SSIM denote the continuous and structural metrics. Higher is better for CSI, HSS, and SSIM, while lower is better for MAE and RMSE. The best results are marked in bold. Models CSI↑HSS↑ MAE↓ RMSE↓ SSIM↑ r≥0.5r≥2r≥5r≥10r≥30r≥0.5r≥2r≥5r≥10r≥30 QW-Net0.6812 0.4421 0.2933 0.0822 0.0651 0.4355 0.3622 0.2215 0.1133 0.0515 6.812 8.2360.548 QWRF-Net-A0.6581 0.4533 0.3011 0.0911 0.0722 0.4422 0.3711 0.2311 0.1211 0.0311 6.954 8.4870.541 QWRF-Net-B0.6811 0.4801 0.3301 0.1011 0.0815 0.5701 0.4211 0.2401 0.1501 0.0511 6.421 7.8840.559 QWRF-Net-C0.6755 0.4855 0.3355 0.1055 0.0911 0.5655 0.4255 0.2455 0.1555 0.0601 6.318 7.7010.563 QWRF-Net-D0.6701 0.4888 0.3411 0.1151 0.1051 0.5601 0.4301 0.2501 0.1701 0.0651 6.184 7.5020.569 QWRF-Net-E0.6901 0.4955 0.3501 0.1101 0.1001 0.5801 0.4401 0.2555 0.1601 0.0611 6.072 7.2110.576 QWRF-Net (Ours) 0.6963 0.4997 0.3610 0.1236 0.1112 0.5869 0.4484 0.2597 0.1812 0.0691 5.967 7.001 0.585 Table 5 Ablation results on the SEVIR dataset. CSI and HSS are reported on the original VIL intensity scale at thresholds 16, 74, 133, 160, 181, and 219. MAE, RMSE, and SSIM denote the continuous and structural metrics. Higher is better for CSI, HSS, and SSIM, while lower is better for MAE and RMSE. The best results are marked in bold. Models CSI↑HSS↑ MAE↓ RMSE↓ SSIM↑ x≥16x≥74x≥133x≥160x≥181x≥219x≥16x≥74x≥133x≥160x≥181x≥219 QW-Net0.6768 0.5122 0.3155 0.2411 0.2133 0.0822 0.3422 0.2933 0.2244 0.1733 0.1544 0.1094 8.972 10.441 0.529 QWRF-Net-A0.6322 0.5211 0.3211 0.2488 0.2211 0.0988 0.3611 0.3011 0.2311 0.1811 0.1622 0.0811 9.154 10.862 0.522 QWRF-Net-B0.6611 0.5701 0.3501 0.2601 0.2401 0.1201 0.4501 0.4101 0.3201 0.2301 0.1901 0.1001 8.714 9.9440.548 QWRF-Net-C0.6555 0.5755 0.3555 0.2655 0.2455 0.1301 0.4533 0.4155 0.3301 0.2401 0.1955 0.1051 8.603 9.7780.553 QWRF-Net-D0.6501 0.5788 0.3601 0.2701 0.2501 0.1451 0.4488 0.4201 0.3355 0.2501 0.2051 0.1101 8.521 9.6020.561 QWRF-Net-E0.6701 0.5801 0.3655 0.2688 0.2551 0.1401 0.4555 0.4255 0.3401 0.2455 0.2001 0.1088 8.493 9.4970.564 QWRF-Net (Ours) 0.6773 0.5869 0.3726 0.2763 0.2581 0.1524 0.4612 0.4331 0.3479 0.2579 0.2122 0.1131 8.460 9.314 0.571 magnitude, but they are more consistent at higher intensity thresholds and in structural-fidelity-related evaluation. This observation is important because average perfor- mance alone may obscure model behavior under stronger convective activity. Under the present setting, the advantage of QWRF-Net is more evident in regimes where preserv- ing intense structures and maintaining boundary sharpness become increasingly difficult. Such behavior is particularly relevant to short-term hazard-oriented forecasting, where the location, continuity, and intensity of convective precipitation cores may matter more than average reconstruction quality alone. Therefore, the SEVIR results support the view that the proposed framework is potentially useful for maintaining structural consistency under challenging precipitation con- ditions rather than only improving easier or low-intensity cases. Such behavior may be particularly relevant when precipitation nowcasts are considered as potential upstream inputs for warning-related or hydrological applications that are sensitive to the location and continuity of intense rainfall structures. Table 3 reports MAE, RMSE, and SSIM on the extreme- event subset of SEVIR. Since average metrics over the full test set may mask model behavior under high-impact precipitation, this subset provides a more focused evaluation of challenging convective cases with strong intensity and sufficient spatial extent. On this subset, QWRF-Net achieves the lowest MAE and RMSE together with the highest SSIM. These results suggest that the proposed framework remains relatively robust when the prediction target contains more intense precipitation cores and sharper structural variations, which is particularly relevant to warning-oriented nowcast- ing. This behavior is important because extreme-event cases are often the most consequential for flash-flood and urban inundation warning, while also being the cases in which structural distortion is most damaging to forecast usefulness. The improved robustness of QWRF-Net on this subset there- fore further suggests its potential relevance for high-impact short-term warning and related downstream use. 4.6. Practical relevance for warning-oriented nowcasting Although this study focuses on precipitation nowcasting rather than downstream hydrological simulation, the ob- served improvements are potentially relevant to hydrome- teorological early warning. In particular, gains at medium- to-high precipitation thresholds, better preservation of in- tense precipitation cores, and relatively slower degradation at later lead times are all desirable properties in warning- oriented applications. These characteristics may provide a more useful precipitation basis for subsequent flood-related analysis and hydrological modeling. In particular, structure- preserving nowcasts may be more suitable as precipita- tion inputs for distributed hydrological or inundation-related models than forecasts that achieve similar average error but lose intense-core organization. 4.7. Qualitative results To provide a compact visual comparison, the qualitative results on KNMI and SEVIR are organized into a unified figure, where the two datasets are shown as separate pan- els for direct comparison. Representative cases from the Wang et al.: Preprint submitted to ElsevierPage 12 of 16 QWRF-Net for short-term precipitation nowcasting T-30minT-25minT-20minT-15minT-10minT-5min Input(X) Ground Truth(Y) Ours QWRF-Net-A QWRF-Net-B QWRF-Net-C QWRF-Net-D QWRF-Net-E QW-Net T+10minT+20minT+30minT+40minT+50minT+60min (a) KNMI radar dataset. 0 5 10 15 20 25 30 T-30minT-25minT-20minT-15minT-10minT-5min Input(X) Ground Truth(Y) Ours QWRF-Net-A QWRF-Net-B QWRF-Net-C QWRF-Net-D QWRF-Net-E QW-Net T+10minT+20minT+30minT+40minT+50minT+60min (b) SEVIR VIL dataset. 100 50 0 150 200 255 Figure 5: Visual comparison of QWRF-Net and its ablation variants on two benchmark datasets. (a) KNMI radar dataset. (b) SEVIR VIL dataset. In each panel, the first row shows the input sequence, the second row shows the ground truth, and the remaining rows show the predictions of the full model and different ablation variants from T+10 min to T+60 min. two benchmark datasets are shown in Fig. 3. As shown in Fig. 3(a), corresponding to the KNMI radar dataset, QWRF- Net better preserves the morphology and intensity distribu- tion of the main precipitation body, especially at middle and later lead times. As shown in Fig. 3(b), corresponding to the SEVIR VIL dataset, QWRF-Net produces predictions that are visually more consistent with the ground truth in core location, boundary sharpness, and structural continuity. Compared with representative discriminative baselines and strong generative baselines such as DiffCast, CoDiCast, and NowcastNet, the proposed method shows clearer advan- tages in maintaining intense precipitation cores and fine- scale structures in the illustrated cases. These qualitative observations are consistent with the quantitative improve- ments at medium-to-high thresholds and further suggest that the proposed framework may be useful for preserving pre- cipitation structures that are relevant to short-term warning. From a hydrometeorological perspective, better preservation of core location and boundary sharpness may be particularly important where localized intense rainfall governs short- term warning relevance and may also be relevant to the potential downstream use of such nowcasts. 4.8. Lead-time analysis Fig. 4 presents the lead-time curves of CSI and HSS on the KNMI dataset. As the forecast horizon increases, QWRF-Net maintains strong performance and exhibits a relatively slower degradation trend than the compared base- lines. This behavior is broadly consistent with the design motivation of the non-autoregressive flow-based generation mechanism. From an operational perspective, stable behavior across the full forecast horizon is often more valuable than isolated gains at a single lead time. In practical warning settings, fore- cast usefulness depends not only on early lead-time accuracy but also on maintaining reliable information throughout the operational forecast window. In particular, the 40–60 minute range is often critical for short-term preparedness and is also where many models show substantial structural degra- dation. Overall, Fig. 4 provides supportive evidence that the proposed framework can maintain relatively stable forecast quality at later lead times under the current evaluation set- ting. This later lead-time stability is especially relevant in practice, because forecast usefulness for warning support often depends more on whether quality remains acceptable across the full lead-time window than on isolated gains at the earliest frames. 5. Ablation study To further examine the effectiveness of the main com- ponents in QWRF-Net, we conduct ablation experiments on both KNMI and SEVIR. The purpose is not only to Wang et al.: Preprint submitted to ElsevierPage 13 of 16 QWRF-Net for short-term precipitation nowcasting test whether each component contributes to the final perfor- mance, but also to examine whether the proposed design is beneficial for preserving structurally important precipitation information before multi-step generation. 5.1. Ablation setup We construct the following ablation variants: • QWRF-Net-A (Simple Bottleneck – No Wavelet, No Quantum): This variant retains the overall U- Net-style architecture and the rectified-flow genera- tion mechanism, but replaces the quantum–wavelet bottleneck with a standard convolutional bottleneck. It is used to assess the contribution of the proposed bottleneck design as a whole. • QWRF-Net-B (Wavelet-Only – No Quantum): This variant preserves the DWT-based decomposition and reconstruction, but replaces the quantum-inspired trans- formation with standard convolutional sub-band pro- cessing. It is used to isolate the role of explicit wavelet decomposition. • QWRF-Net-C (Wavelet + Classical MLP): This variant preserves the wavelet decomposition, but re- places the quantum-inspired transformation with clas- sical MLP-based mappings. It is used to examine whether differentiated sub-band modulation provides benefits beyond conventional nonlinear mixing. • QWRF-Net-D (Shared Quantum Processor): This variant uses both DWT and quantum-inspired pro- cessing, but all four sub-bands share the same quan- tum processor rather than using independent proces- sors. It is used to test the necessity of sub-band- specific processing after decomposition. • QWRF-Net-E (Quantum-Only – No Wavelet): This variant removes DWT/IDWT and applies the quantum- inspired transformation directly to the bottleneck fea- ture map. It is used to evaluate whether nonlinear enhancement without explicit scale disentanglement is sufficient. • QW-Net (Without Rectified Flow): This variant re- tains the quantum–wavelet bottleneck but replaces the rectified-flow generation mechanism with a con- ventional discriminative prediction head. It is used to evaluate the contribution of the flow-based non- autoregressive generation strategy. In addition to CSI and HSS, we also report MAE, RMSE, and SSIM in the ablation study so as to examine whether the observed differences among variants are consistent in terms of intensity accuracy and structural fidelity. 5.2. Analysis of ablation results The ablation results in Tables 4 and 5 lead to several observations. First, the complete QWRF-Net achieves the best overall results on both datasets, particularly at medium-to-high pre- cipitation thresholds. This suggests that the full combination of wavelet-based scale disentanglement, differentiated sub- band modulation, and rectified-flow-based future-sequence generation is more effective than the corresponding partial variants under the present setting. From a warning-oriented perspective, this is especially important because improve- ments at higher thresholds are more relevant to intense precipitation regimes. Second, replacing the quantum–wavelet bottleneck with a standard convolutional bottleneck (QWRF-Net-A) leads to a clear performance drop on both datasets, indicating that the proposed bottleneck contributes meaningfully to the quality of the conditional representation before generative decoding. Third, the comparisons among QWRF-Net-B, QWRF- Net-C, QWRF-Net-D, and QWRF-Net-E help rule out sev- eral simpler explanations. QWRF-Net-B shows that explicit wavelet decomposition alone is beneficial, but not sufficient to match the full model. QWRF-Net-C indicates that the gain is not merely due to inserting a generic nonlinear map- ping after decomposition. QWRF-Net-D shows that using a shared processor across all sub-bands is less effective than using sub-band-specific modulation, suggesting that the decomposed components indeed play different roles and are better handled in a differentiated manner. The comparison between QWRF-Net-E and the full model further suggests that nonlinear enhancement is more effective after wavelet- based scale disentanglement than when it is directly imposed on the original mixed bottleneck feature. Taken together, these results support a more specific interpretation of the proposed bottleneck design: the ob- served benefit does not arise simply from adding wavelet decomposition, inserting a generic nonlinear operator, or increasing architectural complexity. Rather, the improve- ment is associated with the intended sequence of opera- tions, namely decomposition first and structured sub-band- specific modulation afterward. This suggests that explicit organization of precipitation information by scale may be an important prerequisite for enhancing warning-relevant structural features within the present framework. Fourth, the comparison with QW-Net highlights the role of the rectified-flow generation mechanism. QW-Net remains competitive on some lower-threshold metrics, but the advantage of the full QWRF-Net becomes more visible at higher thresholds, especially on SEVIR at x≥219 and on KNMI at r≥10 and r≥30. This trend is consistent with the role of flow-based generation in maintaining forecast quality under more challenging precipitation regimes and later lead times. The visual comparisons in Fig. 5 are broadly consis- tent with the quantitative ablation results. As illustrated in Fig. 5(a) and Fig. 5(b), on both KNMI and SEVIR, the predictions of the complete QWRF-Net remain closer to the ground truth in morphology, intensity distribution, and spatial continuity of strong precipitation cores, particularly Wang et al.: Preprint submitted to ElsevierPage 14 of 16 QWRF-Net for short-term precipitation nowcasting at middle and late forecast stages. In contrast, several abla- tion variants exhibit more noticeable smoothing, structural distortion, or loss of local detail, which further supports the effectiveness of the full design. Overall, the ablation results support the design logic of QWRF-Net, namely that differentiated sub-band modulation is more effective when applied after wavelet-based scale disentanglement within the present framework. This finding is relevant because preserving intense, structured precipita- tion information is especially important in warning-oriented short-term nowcasting. 6. Conclusion In this work, we presented QWRF-Net, a quantum– wavelet framework with rectified flow for short-term precip- itation nowcasting. The framework is designed to address two closely related challenges in nowcasting: representing intertwined multi-scale precipitation structures and reducing degradation in multi-step future prediction. To this end, QWRF-Net combines wavelet-based latent decomposition, quantum-inspired sub-band modulation, and rectified-flow- based future-sequence generation within a unified frame- work. Experimental results on KNMI and SEVIR show that QWRF-Net provides favorable overall performance under the unified 6→12 setting. In addition to improving aver- age predictive quality, the proposed model shows relatively more consistent gains in structurally challenging regimes, in- cluding medium-to-high precipitation thresholds, later lead times, and an extreme-event subset. The ablation results are broadly consistent with the intended design logic, indicating that wavelet-based decomposition, differentiated sub-band modulation, and flow-based generation provide complemen- tary benefits when organized in the proposed sequence. From a hydrometeorological perspective, these findings suggest that jointly improving conditional precipitation rep- resentation and future-sequence generation is a useful di- rection for warning-relevant short-term precipitation fore- casting, especially when preserving intense precipitation structures and later lead-time stability is important. These improvements may also provide a more useful precipitation basis for subsequent warning-related and hydrological appli- cations. Several limitations should also be noted. The present study focuses on a 60-minute forecasting horizon, and the conclusions should therefore be interpreted within this set- ting. In addition, the quantum-inspired module is simulated on classical hardware and should be understood as a struc- tured nonlinear operator rather than as evidence of practi- cal quantum-computing advantage. The current bottleneck design also does not yet model richer hierarchical cross- scale interactions, and the study does not directly assess how any improvement in nowcast quality may translate into downstream hydrological response. Future work will examine whether the proposed frame- work remains effective under longer forecast horizons, higher spatial resolutions, and more diverse regional precipitation datasets. It will also investigate the coupling of the predicted precipitation with distributed hydrological or inundation- related models to assess its practical value for warning- oriented decision support more directly. 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