MZ-Rain: Moisture-Budget-Guided Zero-Inflated Model for Station-Level Precipitation Nowcasting

Yifang Zhang; Shengwu Xiong; Henan Wang; Wenjie Yin; Yuqiang Zhang; Chen Zhou; Hua Chen; Qile Zhao

cs.AISep 4, 2026

MZ-Rain: Moisture-Budget-Guided Zero-Inflated Model for Station-Level Precipitation Nowcasting

Authors: Yifang Zhang, Shengwu Xiong, Henan Wang, Wenjie Yin, Yuqiang Zhang, Chen Zhou, Hua Chen, Qile Zhao, +1 more

Organizations: Sanya Science and Education Innovation Park, Wuhan University of Technology, Sanya, 572000, China · School of Computer Science and Artificial Intelligence, Wuhan University of Technology, Wuhan 430070, China · School of Earth and Space Science and Technology, Wuhan University, Wuhan 430072, China · School of Water Resources and Hydropower Engineering, Wuhan University, Wuhan 430062, China · GNSS Research Center, Wuhan University, Wuhan 430062, China

Abstract

Accurate station-level precipitation nowcasting is critical for agriculture, water resource management, and disaster prevention, which typically is formulated as a time series forecasting problem. However, conventional time-series modeling techniques face two major challenges in addressing station-level precipitation nowcasting: (1) Lack of Physics-Guided Modeling}, where meteorological variables are treated as a homogeneous set without accounting for their distinct roles in precipitation formation, leads to predictions that deviate from the physical processes governing precipitation. (2) Severe zero inflation in precipitation, where dry intervals dominate the dataset, obscuring meaningful precipitation patterns and complicating the predictive modeling. To address these challenges, we propose MZ-Rain, a moisture-budget-guided zero-inflated sLSTM framework for station-level precipitation nowcasting. Guided by the moisture budget equation, MZ-Rain decomposes the precipitation formation process into process-specific pathways corresponding to moisture storage, moisture transport, surface evaporation, and precipitation persistence, and captures their temporal evolution through dedicated sLSTM branches. To account for the zero-inflated nature of precipitation, MZ-Rain introduces an adaptive Tweedie modeling strategy that adaptively modulates the rainfall mean while jointly learning precipitation occurrence as an auxiliary task, enabling the model to better balance dry-wet discrimination and quantitative precipitation estimation. Extensive experiments across diverse geographical and climatic regimes demonstrate that MZ-Rain consistently outperforms strong baselines on multiple evaluation metrics, including CSI, FAR, MSE, and MAE. In particular, the model exhibits superior skill in forecasting heavy precipitation events, while benefiting from physically grounded process modeling.

Figures & tables

Fig. 1: Motivation of the proposed MZ-Rain, highlighting the two key challenges and their corresponding solutions.

Variable	Description	Source	Pathway
$W_{t}$	Precipitable water vapor	GNSS	ms
$\Delta W_{t}$	Temporal difference of PWV	GNSS-derived	ms
$P_{t}^{\mathrm{sfc}}$	Surface pressure	ERA5 Reanalysis	ms
$C_{t}$	Moisture-flux convergence	ERA5-derived	tr
$E_{t}$	Surface evaporation	ERA5 Reanalysis	ev
$y_{t}$	Historical precipitation	IMERG	pr

TABLE I: Input variables used by MZ-Rain and their corresponding data sources and process pathways.

Fig. 2: Geographical distribution of the six GNSS stations used in this study. The selected stations span diverse geographic locations and climatic conditions, providing broad spatial coverage for precipitation forecasting evaluation.

Fig. 3: Architecture of MZ-Rain. The left side shows four process-specific pathways for moisture storage, moisture transport and convergence, surface evaporation, and precipitation persistence. The right side shows adaptive Tweedie modeling for quantitative precipitation estimation together with auxiliary rainfall-occurrence supervision.

Model	2 h				4 h				6 h				Avg. Rank
Model	MAE $\downarrow$	MSE $\downarrow$	CSI $\uparrow$	FAR $\downarrow$	MAE $\downarrow$	MSE $\downarrow$	CSI $\uparrow$	FAR $\downarrow$	MAE $\downarrow$	MSE $\downarrow$	CSI $\uparrow$	FAR $\downarrow$	Avg. Rank
sLSTM	0.2909	1.3102	0.2999	0.6748	0.3311	1.5199	0.2567	0.7186	0.3547	1.6203	0.2370	0.7438	6.67
FilterTS	0.2732	1.3985	0.3428	0.5839	0.3033	1.6486	0.2904	0.6373	0.3127	1.7699	0.2603	0.6671	5.58
TimeFilter	0.2510	1.3726	0.3577	0.5658	0.2794	1.6178	0.3002	0.6210	0.2941	1.7262	0.2641	0.6686	3.75
TimeKAN	0.2559	1.3848	0.3625	0.5535	0.2796	1.6200	0.3060	0.6098	0.2945	1.7386	0.2690	0.6511	3.67
xPatch	0.2517	1.4010	0.3664	0.5493	0.2780	1.6162	0.2984	0.6228	0.2928	1.7369	0.2657	0.6593	3.50

TABLE II: Cross-station macro-average performance at 2/4/6 h horizons. CSI

\uparrow

, FAR

\downarrow

, MSE

\downarrow

, and MAE

\downarrow

. Avg. Rank denotes the mean rank over all twelve horizon–metric combinations, where a lower value is better.

Fig. 4: Per-station detection performance at 2/4/6 h horizons. Each panel shows all ten models across the six GNSS stations (J340, ZIMM, P095, MTLA, ARTA, BFTA); the red solid line is MZ-Rain (Ours) . Top: CSI (

\uparrow

, higher is better). Bottom: FAR (

\downarrow

, lower is better). MZ-Rain attains the highest CSI at every station and every horizon and the lowest FAR in nearly all cases; at P095, the lower FAR of ZIP is accompanied by an extremely low CSI, indicating severe under-detection of precipitation events(cf. Figure 4 and Figure 5 ).

Fig. 5: Per-station intensity error at 2/4/6 h horizons. Top: MSE ((mm/h) 2 ,

\downarrow

). Bottom: MAE (mm/h,

\downarrow

). MZ-Rain (red) achieves the lowest MAE at all six stations and all horizons, and the lowest MSE in nearly all cases.

	$-\partial W/\partial t$		$C=-\nabla\!\cdot\!\mathbf{Q}$		$E$
$H$ (h)	Spear.	AP	Spear.	AP	Spear.	AP
1	0.286	0.387	0.354	0.509	0.172	0.257
2	0.309	0.401	0.368	0.506	0.186	0.271
4	0.321	0.405	0.368	0.465	0.201	0.282
6	0.307	0.382	0.345	0.410	0.194	0.274

TABLE III: Lead–lag relationship between moisture-budget components at time

t

and accumulated future precipitation

P_{t+1:t+H}

at J340. Spear. denotes Spearman correlation and AP denotes wet-event average precision. The wet-event base rate is approximately 0.154.

Variant	$\Delta W$	$C$	$E$	Persist.	MAE $\downarrow$	MSE $\downarrow$	CSI $\uparrow$	FAR $\downarrow$
Full	✓	✓	✓	✓	0.2841	1.5929	0.3243	0.5895
w/o storage	$\times$	✓	✓	✓	0.2887	1.6154	0.3132	0.6028
w/o convergence	✓	$\times$	✓	✓	0.2948	1.6537	0.2961	0.6254
w/o evaporation	✓	✓	$\times$	✓	0.2869	1.6068	0.3176	0.5978
w/o persistence	✓	✓	✓	$\times$	0.3015	1.6842	0.3040	0.6189

TABLE IV: Ablation of moisture-budget-related inputs and precipitation persistence at the 6 h horizon. Results are six-station macro averages.

Variant	MAE $\downarrow$	MSE $\downarrow$	CSI $\uparrow$	FAR $\downarrow$
Shared Encoder	0.3076	1.6812	0.3004	0.6018
Generic Multi-Branch	0.2918	1.6350	0.3110	0.6072
Process-Specific Organization	0.2841	1.5929	0.3243	0.5895

TABLE V: Comparison of different representation organizations at the 6 h forecasting horizon.

Variant	MAE $\downarrow$	MSE $\downarrow$	CSI $\uparrow$	FAR $\downarrow$
w/o PWV gate	0.2896	1.6217	0.3154	0.6018
w/o transport gate	0.2915	1.6359	0.3097	0.6108
w/o persistence gate	0.2924	1.6463	0.3168	0.6006
w/o all contextual gates	0.2988	1.6942	0.2989	0.6245
Full	0.2841	1.5929	0.3243	0.5895

TABLE VI: Ablation study of the contextual gating mechanism at the 6 h forecasting horizon. Results are macro-averaged over the six stations.

Variant	Tweedie	Mod.	Occ.	Output	MAE $\downarrow$	MSE $\downarrow$	CSI $\uparrow$	FAR $\downarrow$
Point regression	$\times$	$\times$	$\times$	$\tilde{\mu}$	0.3048	1.7246	0.2891	0.6328
Tweedie only	✓	$\times$	$\times$	$\tilde{\mu}$	0.2962	1.6657	0.3028	0.6164
Tweedie + occurrence	✓	$\times$	✓	$\tilde{\mu}$	0.2908	1.6294	0.3165	0.6008
Tweedie + modulation	✓	✓	$\times$	$\mu$	0.2889	1.6172	0.3116	0.6052
Full	✓	✓	✓	$\mu$	0.2841	1.5929	0.3243	0.5895

TABLE VII: Component-wise ablation of the adaptive Tweedie-based multi-task formulation at the 6h forecasting horizon. Results are macro-averaged over the six stations.

\tilde{\mu}

denotes the unmodulated mean prediction, while

\mu=g^{\mu}\tilde{\mu}+\epsilon

denotes the adaptively modulated mean. The occurrence prediction

q

is used only for auxiliary supervision and does not enter the final precipitation amount.

	Bias (mm/h)		MAE (mm/h)		Peak ratio
Regime	raw $\tilde{\mu}$	gated $\mu$	raw	gated	raw	gated
Dry	+0.071	+0.034	0.079	0.050	N/A	N/A
Light	+0.083	+0.032	0.196	0.174	1.18	1.08
Moderate	+0.061	+0.018	0.514	0.482	1.07	1.01
Heavy	-0.182	-0.205	1.218	1.226	0.94	0.92

TABLE VIII: Behavior of adaptive mean modulation across observed precipitation regimes on the six-station test set. Bias is defined as prediction minus observation. A peak ratio closer to one indicates better preservation of high-intensity precipitation.

Model	ARTA		BFTA		J340		MTLA		P095		ZIMM
Model	MAE $\downarrow$	MSE $\downarrow$	MAE $\downarrow$	MSE $\downarrow$	MAE $\downarrow$	MSE $\downarrow$	MAE $\downarrow$	MSE $\downarrow$	MAE $\downarrow$	MSE $\downarrow$	MAE $\downarrow$	MSE $\downarrow$
sLSTM	12.2241	185.1727	13.3234	203.5121	9.9672	121.2693	11.8161	163.0870	19.2073	593.6420	16.1272	332.9984
TimeFilter	12.7852	202.5680	13.4437	208.0682	10.0554	128.3993	12.2085	174.8581	19.1827	598.4038	15.7476	319.3812
TimeKAN	12.7985	202.5675	13.4795	209.8473	10.0872	129.2633	11.9936	170.6457	19.1857	598.1708	15.8169	321.3663
xPatch	12.8199	202.7773	13.4888	209.8547	10.1312	130.0660	12.1957	174.6668	19.1528	597.0271	15.8126	321.6467
FilterTS	13.1206	209.9214	13.3106	204.9712	10.0436	128.8823	12.0950	173.4394	19.2252	599.3501	15.6878	317.1874

TABLE IX: Conditional intensity accuracy for observed heavy precipitation (10–50mm/h) under the 24-to-6 prediction setting.

Model	Brier $\downarrow$	AUCPR $\uparrow$	ECE $\downarrow$	MAE $\downarrow$	MSE $\downarrow$	CSI $\uparrow$	FAR $\downarrow$
Full ( $q$ + BCE)	0.086	0.612	0.028	0.2841	1.5929	0.3243	0.5895
w/o occurrence task	N/A	N/A	N/A	0.2889	1.6172	0.3116	0.6052

TABLE X: Quality of the auxiliary occurrence prediction and its contribution to precipitation forecasting on the six-station test set. Brier score, AUCPR, and ECE evaluate the supervised occurrence probability

q

. N/A indicates that the metric is not applicable because the occurrence head is absent.

Model	MAE	MSE
sLSTM	69.9135	5475.8630
TimeFilter	69.5046	5452.9663
TimeKAN	69.9554	5499.4810
xPatch	69.9045	5491.0386
FilterTS	70.9552	5607.1426
BFPF	69.9475	5472.3105

TABLE XI: Conditional intensity accuracy for extreme precipitation (

>50

mm/h) at ARTA under the 24-to-6 prediction setting. This regime is reported as an exploratory evaluation because valid samples are available only at ARTA.

Panel of Figure 17 — Fig. 6: Qualitative forecasting comparisons under three representative precipitation regimes. (a) Dry event at Station J340 (2023-12-27 01:00–06:00): MZ-Rain maintains near-zero predictions and effectively suppresses false positives, while baselines produce spurious rainfall signals. (b) Normal precipitation event at Station ZIMM (2023-05-05 16:00–21:00): MZ-Rain tracks moderate temporal variations more faithfully, whereas baseline methods tend to over-smooth the signal and underestimate fluctuations. (c) Heavy precipitation event at Station ARTA (2024-05-24 12:00–17:00): MZ-Rain preserves sharp peak intensity, while competing models underestimate the event magnitude due to regression-to-the-mean effects.

Explore similar work

VMU-Diff: A Coarse-to-fine Multi-source Data Fusion Framework for Precipitation Nowcasting
May 14, 2026Chunlei Shi, Hao Li, Yufeng Zhu +6Precipitation Forecasting Probabilistic Forecasting
Department of Automation, Southeast University, Nanjing 210096, China
M3R: Localized Rainfall Nowcasting with Meteorology-Informed MultiModal Attention
Apr 15, 2026Sanjeev Panta, Rhett M Morvant, Xu Yuan +2Precipitation Nowcasting Spatiotemporal Forecasting
University of Louisiana at Lafayette, Lafayette, LA, USA · University of Delaware, Newark, DE, USA
Dense-Cast: A lightweight ensemble of deep learning architectures for precipitation nowcasting
Aug 6, 2026Gourav Jyoti Kalita, Hidam Kumarjit SinghPrecipitation Forecasting Deep Ensembles
Department of Electronics and Communication Technology, Gauhati University, Guwahati-781014, Assam, India

May 14, 2026J/K move · Enter open · S save

VMU-Diff: A Coarse-to-fine Multi-source Data Fusion Framework for Precipitation Nowcasting

Chunlei Shi, Hao Li, Yufeng Zhu, Boyu Liu+5

Department of Automation, Southeast University, Nanjing 210096, China

Precipitation Forecasting Probabilistic Forecasting Precipitation Nowcasting Diffusion Models

Open paper AskPDF arXiv

Precipitation nowcasting is a vital spatio-temporal prediction task for meteorological applications but faces challenges due to the chaotic property of precipitation systems. Existing methods predominantly rely on single-source radar data to build either deterministic or probabilistic models for extrapolation. However, the single deterministic model suffers from blurring due to MSE convergence. The single probabilistic model, typically represented by diffusion models, can generate fine details but suffers from spurious artifacts that compromise accuracy and computational inefficiency. To address these challenges, this paper proposes a novel coarse-to-fine Vision Mamba Unet and residual Diffusion (VMU-Diff) based precipitation nowcasting framework. It realizes precipitation nowcasting through a two-stage process, i.e., a deterministic model-based coarse stage to predict global motion trends and a probabilistic model-based fine stage to generate fine prediction details. In the coarse prediction stage, rather than single-source radar data, both radar and multi-band satellite data are taken as input. A spatial-temporal attention block and several Vision mamba state-space blocks realize multi-source data fusion, and predict the future echo global dynamics. The fine-grained stage is realized by a spatio-temporal refine generator based on residual conditional diffusion models. It first obtains spatio-temporal residual features based on coarse prediction and ground truth, and further reconstructs the residual via conditional Mamba state-space module. Experiments on Jiangsu SWAN datasets demonstrate the improvements of our method over state-of-the-art methods, particularly in short-term forecasts.

Abstract

Explore similar work

VMU-Diff: A Coarse-to-fine Multi-source Data Fusion Framework for Precipitation Nowcasting

M3R: Localized Rainfall Nowcasting with Meteorology-Informed MultiModal Attention

Dense-Cast: A lightweight ensemble of deep learning architectures for precipitation nowcasting