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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, Pengfei Duan

arXiv:2609.04864v1cs.AI

TL;DR

Station-level precipitation nowcasting is limited by weak physics-guided organization of meteorological variables and severe zero inflation. MZ-Rain addresses both through moisture-budget-guided process pathways and adaptive Tweedie modeling with auxiliary occurrence supervision, achieving consistent improvements over strong baselines across diverse stations and precipitation regimes.

  • Problem

    Station-level precipitation nowcasting must handle heterogeneous atmospheric processes and severe zero inflation, while conventional methods often treat meteorological variables homogeneously.

  • Method

    MZ-Rain uses moisture-budget-guided process-specific pathways together with adaptive Tweedie modeling and auxiliary precipitation-occurrence supervision.

  • Results

    MZ-Rain consistently improves rainfall-event discrimination and quantitative precipitation estimation over strong baselines across six diverse stations and maintains robust heavy-rain performance.

  • Takeaways & Limitations

    The results support combining physically organized process modeling with zero-inflated statistical modeling for station-level precipitation nowcasting.

Abstract

from arXiv · show

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 \textbf{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.

I. INTRODUCTION

Station-level precipitation nowcasting is important but challenged by insufficient physics-guided modeling and severe zero inflation. MZ-Rain addresses these challenges by organizing precipitation processes into moisture-budget-guided pathways and combining adaptive Tweedie modeling with auxiliary occurrence supervision.

  • Station-level nowcasting supports disaster prevention, flood control, and real-time operational decision-making for localized rainfall evolution.
  • Existing methods entangle heterogeneous atmospheric processes and struggle with dry-period dominance caused by severe precipitation zero inflation.
  • Experiments across six geographically and climatically diverse stations show consistent improvements over strong baselines in event discrimination and quantitative precipitation estimation.The evaluation uses CSI, FAR, MSE, and MAE, with robust performance under heavy-rain conditions.
  • MZ-Rain organizes moisture storage, transport and convergence, surface evaporation, and precipitation persistence into dedicated process-specific pathways.
  • Adaptive Tweedie modeling estimates rainfall amounts while separate occurrence supervision provides complementary wet-dry discrimination signals.
  • MZ-Rain introduces physical knowledge directly into representation structure rather than relying only on auxiliary losses, equation residuals, or dynamical regularization.

C. Zero-Inflated Modeling

The paper formulates station-level precipitation nowcasting as multivariate-to-univariate forecasting and models precipitation’s mixed zero-positive distribution with process-organized inputs and a Tweedie distribution. The data pipeline combines GNSS, IMERG, and ERA5 observations, with diagnosed moisture transport retained for station-level prediction.

  • Station-level nowcasting predicts a future precipitation sequence from historical meteorological variables and observed precipitation.
  • B. Moisture Budget Equation: The moisture budget motivates separate storage, transport, and evaporation branches that represent moisture storage change, horizontal transport, and surface moisture supply.
  • C. Tweedie Distribution: The Tweedie distribution models precipitation as a point mass at zero with continuous, right-skewed positive values, using mean µ, dispersion ϕ, and variance power p.For 1 < p < 2, it has a compound Poisson–Gamma form and Var(Y) = ϕµ^p.
  • Dataset: RainfallBench integrates GNSS atmospheric observations, IMERG precipitation, and ERA5 reanalysis across six geographically and climatically diverse stations.
  • C. Zero-Inflated Modeling: MZ-Rain reorganizes inputs into moisture-storage, moisture-transport and convergence, surface-evaporation, and precipitation-persistence pathways.These use PWV and its temporal difference, moisture-flux convergence, surface evaporation, and historical precipitation, respectively.
  • C. Zero-Inflated Modeling: Moisture-flux convergence is diagnosed from surrounding gridded water-vapor fluxes before interpolation to the target station, preserving spatial transport information.

2) Split, Windowing, and Leakage Control:

The study uses 24-hour histories to forecast 2-, 4-, and 6-hour precipitation horizons across six geographically and climatically diverse stations, with chronological splitting and leakage controls.

  • Windowing: Each sample uses the previous L = 24 hourly observations to predict precipitation over subsequent H ∈ 2, 4, 6 hours.
  • Split and leakage control: Data are chronologically divided into training, validation, and test subsets using a 7:1:2 ratio.
  • Split and leakage control: Windows are constructed separately within each split, preventing future periods from entering model training.
  • Split and leakage control: Checkpoint selection, validation-dependent thresholds, and hyperparameter tuning use only validation data, while testing is reserved for final evaluation.
  • Missing-value treatment: Short gaps in continuous atmospheric variables are linearly interpolated, whereas windows with missing precipitation targets are excluded.
  • Study stations: The six stations provide broad geographic and climatic coverage for precipitation forecasting evaluation.

IV. METHOD

MZ-Rain combines moisture-budget-guided process organization with dedicated temporal pathways and a precipitation-persistence signal for station-level nowcasting.

  • Framework overview: MZ-Rain organizes atmospheric information into moisture-storage, moisture-transport and convergence, surface-evaporation, and precipitation-persistence components.
  • Process-specific inputs: The moisture-storage pathway uses precipitable water vapor, its first-order temporal difference, and surface pressure.
  • Process-specific inputs: The transport pathway uses moisture-flux convergence diagnosed from vertically integrated horizontal moisture flux rather than a local wind-speed proxy.
  • Process-specific inputs: Surface evaporation represents upward moisture supply, while historical precipitation supplies a complementary persistence signal for short-term forecasting.

C. Process-Specific Multi-Branch Temporal Encoding

The multi-branch sLSTM encoder models heterogeneous atmospheric processes separately, then fuses them with adaptively weighted rainfall memory.

  • Process-specific encoding: Dedicated sLSTM branches encode moisture storage, moisture transport and convergence, and surface evaporation instead of sharing one temporal backbone.
  • Moisture storage pathway: The storage branch represents precipitable water vapor, its short-term tendency, and surface pressure through an embedded temporal sequence.
  • Moisture transport pathway: A PWV-guided gate lets the moisture-storage state modulate the transport and convergence pathway.
  • Surface evaporation pathway: A transport-dependent gate adaptively modulates the surface-evaporation representation according to the prevailing transport regime.
  • Pathway fusion: The process-specific representations are concatenated and projected into a unified moisture-budget-guided representation.
  • Precipitation persistence: A separate persistence branch uses recent precipitation and an adaptive memory gate to combine rainfall continuity with the fused atmospheric representation.

D. Adaptive Tweedie Modeling for Zero-Inflated Precipitation

MZ-Rain uses adaptive Tweedie modeling and auxiliary occurrence supervision to address intermittent, zero-inflated precipitation while estimating future rainfall amounts.

  • Framework overview: The adaptive Tweedie multi-task framework combines quantitative precipitation modeling with auxiliary rainfall-occurrence learning.
  • Adaptive Tweedie modeling: For 1 < p < 2, the Tweedie family accommodates nonnegative precipitation with a point mass at zero and continuous positive outcomes.
  • Adaptive Tweedie modeling: A data-dependent modulation coefficient adjusts the positive rainfall-amount candidate to produce the final nonnegative mean prediction.
  • Quantitative prediction: The quantitative forecast used for inference is the final mean prediction, ˆyτ = ˆµτ.
  • Occurrence-aware learning: The occurrence branch predicts future rainfall probability and supplies wet-dry supervision without directly entering the quantitative forecast.
  • Occurrence-aware learning: The two tasks provide complementary supervision: amount estimation for quantitative accuracy and occurrence learning for dry-wet discrimination.

E. Training Objective

MZ-Rain jointly models wet-dry occurrence, Tweedie-inspired precipitation amounts, and pointwise regression through a unified objective.

  • The training objective jointly optimizes wet-dry occurrence discrimination, Tweedie-inspired quantitative precipitation modeling, and pointwise regression.
  • The binary rainfall occurrence label uses a dry-wet threshold of δ = 0.1 mm/h.
  • The objective uses ϵ = 10^-6 for numerical stability and α = 0.1 and β = 0.3 as loss-balancing coefficients.

V. EXPERIMENTS

The experiments evaluate MZ-Rain across diverse stations, forecast horizons, model families, and precipitation-specific metrics, including dedicated tests for extreme rainfall.

  • The evaluation uses two evidence chains testing moisture-budget process information and the contributions of Tweedie modeling, adaptive mean modulation, and occurrence supervision.
  • Datasets contain six years of hourly precipitation observations from six geographically and climatically diverse GNSS stations.Each sample uses a 24-hour history to forecast 2-, 4-, and 6-hour horizons.
  • Baselines span general time-series architectures, precipitation-specific models, and statistical zero-inflated models.The statistical group includes ZIP and Hurdle-Gamma models.
  • Deep-learning baselines use official optimal configurations to support fair comparison.
  • Evaluation covers MSE and MAE for pointwise accuracy and CSI and FAR for wet-dry event discrimination.Higher CSI and lower FAR indicate better event-level forecasting skill.
  • Extreme-precipitation evaluation separates heavy precipitation, 10 ≤ y_t < 50, from very extreme precipitation, y_t ≥ 50.Range-specific squared and absolute errors are computed for both severity levels.

4) Implementation and Statistical Protocol:

Across six stations and 2-, 4-, and 6-hour horizons, MZ-Rain consistently leads competing methods on macro-averaged and station-level precipitation metrics.

  • Cross-Station Average Performance: MZ-Rain ranks first in CSI, FAR, MSE, and MAE at every horizon, with an average rank of 1.0 across twelve horizon-metric combinations.
  • Cross-Station Average Performance: At 2 h, MZ-Rain achieves MAE 0.2367, MSE 1.2762, CSI 0.4412, and FAR 0.4358.Relative to the best competing result for each metric, the reductions are 5.7%, 1.8%, and 20.7% for MAE, MSE, and FAR, while CSI improves 20.4%.
  • Cross-Station Average Performance: At 4 h, MZ-Rain obtains MAE/MSE 0.2690/1.4855 and CSI/FAR 0.3627/0.5407.The corresponding best competing results are 0.2780, 1.5199, 0.3135, and 0.6098.
  • Cross-Station Average Performance: At 6 h, MZ-Rain remains best on all four metrics, achieving MAE 0.2841, MSE 1.5929, CSI 0.3243, and FAR 0.5895.Its CSI advantage over the strongest competitor remains 0.0553 at 6 h.
  • Station- and Horizon-Specific Performance: MZ-Rain achieves the best value in 62 of 72 station-horizon-metric comparisons across six stations, three horizons, and four metrics.
  • Station- and Horizon-Specific Performance: At 6 h, MZ-Rain has the highest CSI and lowest MAE at all six stations, while localized MSE exceptions occur at P095 and BFTA.At P095, ZIP's lower FAR accompanies CSI 0.0379, versus 0.2429 for MZ-Rain, indicating under-detection.

C. Analysis of Moisture-Budget-Guided Process Modeling

MZ-Rain organizes forecasting around moisture-budget processes whose predictive relevance is empirically supported, while ablations show complementary roles for atmospheric pathways, precipitation persistence, and contextual gating.

  • Physical Motivation and Empirical Verification: The moisture-budget formulation represents storage, horizontal transport, surface supply, and precipitation persistence as distinct forecasting pathways.Historical precipitation captures persistence and system life cycle, while atmospheric terms describe complementary moisture processes.
  • Physical Motivation and Empirical Verification: Moisture-flux convergence shows the strongest persistent association with future rainfall, with Spearman correlations of 0.345–0.368 and AP of 0.410–0.509.The AP values exceed the wet-event base rate of 0.154.
  • Physical Motivation and Empirical Verification: The combined diagnostic's Spearman correlation with observed precipitation rises from approximately 0.40 at 1 h to 0.62 at 6 h.The result supports complementary and temporally predictive information without implying exact budget closure.
  • Process-Input Ablation: Removing any process input degrades performance, with moisture convergence producing the largest event-detection deterioration: CSI falls from 0.3243 to 0.2961 and FAR rises from 0.5895 to 0.6254.
  • Process-Input Ablation: Removing precipitation persistence causes the largest continuous-metric deterioration, increasing MAE from 0.2841 to 0.3015 and MSE from 1.5929 to 1.6842.This indicates different roles for historical precipitation and atmospheric pathways.
  • Representation Organization: The process-specific organization outperforms both a shared encoder and a generic multi-branch design using comparable inputs and capacity.
  • Contextual Gating: Removing all contextual gates increases MAE to 0.2988 and MSE to 1.6942, lowers CSI to 0.2989, and raises FAR to 0.6245.The larger degradation than single-gate removals indicates complementary gating effects.

D. Analysis of Adaptive Tweedie-Based Multi-Task Learning

MZ-Rain combines Tweedie modeling, auxiliary occurrence supervision, and adaptive mean modulation to address zero-inflated precipitation. Ablations show complementary gains across amount and event-detection metrics, with modulation acting mainly on dry-to-moderate conditions.

  • Model formulation: MZ-Rain combines a Tweedie objective, occurrence-aware auxiliary learning, and state-dependent mean modulation for zero-inflated precipitation forecasting.The occurrence probability supervises wet-dry discrimination without directly multiplying the final precipitation mean.
  • Component-wise ablation: Replacing point regression with Tweedie modeling reduces MAE from 0.3048 to 0.2962 and MSE from 1.7246 to 1.6657, while CSI rises from 0.2891 to 0.3028.FAR also decreases from 0.6328 to 0.6164.
  • Component-wise ablation: Adding occurrence supervision increases CSI from 0.3028 to 0.3165 and decreases FAR from 0.6164 to 0.6008.Its primary contribution is distinguishing atmospheric states associated with precipitation occurrence rather than directly estimating rainfall amount.
  • Component-wise ablation: Adaptive modulation reduces MAE from 0.2962 to 0.2889 and MSE from 1.6657 to 1.6172 relative to Tweedie-only learning.It primarily refines conditional precipitation magnitude by suppressing inappropriate means under unfavorable atmospheric states.
  • Component-wise ablation: The full formulation achieves the best performance across all four metrics, reducing MAE and MSE by approximately 6.8% and 7.6% relative to point regression.CSI increases from 0.2891 to 0.3243 and FAR decreases from 0.6328 to 0.5895; the two mechanisms provide complementary improvements.
  • Regime-dependent modulation: Adaptive modulation reduces dry-condition positive bias from 0.071 to 0.034 mm/h and MAE from 0.079 to 0.050 mm/h, while its heavy-rain effect remains limited.The peak ratio changes from 0.94 to 0.92 under heavy rain, indicating state-dependent rather than uniform mean shrinkage.
  • Occurrence supervision: The occurrence head achieves a Brier score of 0.086, an AUCPR of 0.612, and an ECE of 0.028; removing its supervision worsens all four precipitation metrics.Without occurrence supervision, MAE increases from 0.2841 to 0.2889 and CSI decreases from 0.3243 to 0.3116.

E. High-Intensity Precipitation Evaluation

MZ-Rain is evaluated on heavy and extreme precipitation through conditional intensity analyses and qualitative regime comparisons. The results show stronger magnitude preservation in high-intensity events, while qualitative examples also show reduced dry-event false positives and less smoothing.

  • Evaluation protocol: Heavy precipitation is defined as observed rainfall of 10–50 mm/h, while extreme precipitation exceeds 50 mm/h; evaluations use observation-selected samples shared across methods.The heavy-rain analysis uses fixed thresholds across stations.
  • Heavy-precipitation intensity accuracy: MZ-Rain achieves the lowest heavy-rain errors at five of six stations, reducing J340 MAE from 9.9672 to 9.4417 and MSE from 121.2693 to 115.3476 relative to sLSTM.ZIMM is the main exception, so the benefit is not uniform across all stations.
  • Extreme-precipitation intensity accuracy: At ARTA, MZ-Rain reduces extreme-rain MAE from 69.5046 to 68.8169 and MSE from 5452.9663 to 5377.7040 relative to the strongest baselines.Because extreme-rain samples are available only at ARTA, this is an exploratory single-station analysis.
  • Overall high-intensity findings: Across conditional evaluations, MZ-Rain improves precipitation-magnitude estimation in both heavy and extreme regimes beyond the dominant dry and light-rain samples.The paper frames this as an extension of the overall forecasting advantage into the high-intensity tail.
  • Qualitative regime comparisons: In a dry event, MZ-Rain stays near zero and suppresses false positives, whereas baselines generate spurious rainfall signals.This qualitative comparison uses a representative station-level dry sequence.
  • Qualitative regime comparisons: For moderate rainfall, MZ-Rain tracks temporal variation more faithfully, while baselines over-smooth predictions and underestimate fluctuations.FilterTS, BFPF, and TimeFilter are described as especially damped.
  • Qualitative regime comparisons: During a heavy event with a sharp peak, MZ-Rain better captures peak magnitude while competing methods exhibit regression-to-the-mean behavior and reduced intensity.The comparison concerns a highly dynamic rainfall sequence.
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