Rainfall interception, the temporary storage of rainfall on vegetation and its subsequent evaporation (Ei), plays a crucial role in the surface water balance. Ei buffers rainfall intensity, redistributes surface water, and provides rapid moisture feedbacks to the atmosphere. Understanding Ei is essential because it directly influences soil water availability for vegetation, impacting ecosystem functions, particularly in water-stressed regions. Biases in Ei estimations also propagate to other key eco-hydrological parameters like the ratio of plant transpiration to total evapotranspiration (ET). Current methods for estimating Ei, primarily site-level measurements of the difference between gross and net rainfall, are limited in spatial and temporal coverage. While site-level studies show Ei variations (10-50% of gross rainfall) depending on vegetation, rainfall regime, and evaporative demand, they cannot be scaled globally. Global flux tower networks offer continuous eddy-covariance (EC) measurements of water and energy fluxes, but these don't directly measure Ei. Existing global Ei mapping relies on process-based models that often oversimplify the interception process due to a lack of mechanistic understanding and reliable observation-based estimates for model benchmarking. The potential to partition Ei from EC measurements remains underexplored, despite Ei occurring exclusively under wet canopy conditions, making it a primary component of ET during and shortly after rain events. Previous attempts using empirical EC-based methods were effective in specific rainforests but lacked generalizability.

The literature extensively documents the importance of rainfall interception in the hydrological cycle. Studies have highlighted the significant variability in interception loss (Ei) across different vegetation types and rainfall regimes. Site-level measurements have provided valuable insights into the factors influencing Ei, including plant functional types (PFTs), leaf area index (LAI), and rainfall characteristics. However, these measurements are limited in spatial and temporal scale, hindering the ability to assess Ei at larger scales. Process-based models have attempted to address this limitation, but often lack detailed mechanistic representation of the interception process and struggle to adequately capture the complexity of real-world scenarios. There is a significant gap in observation-based, large-scale estimates of Ei, limiting model development and validation. Previous research using eddy covariance (EC) data has shown some promise, but methodologies have lacked generalizability across diverse ecosystems and climatic conditions. This paper addresses the need for a robust, scalable method for estimating Ei globally.

This study developed a novel approach to estimate global rainfall interception (Ei) using a hybrid machine learning (ML) model combined with physical constraints. The methodology involved several key steps: 1. **Data Acquisition:** The study utilized eddy covariance (EC) measurements from the FLUXNET2015 Tier 2 database, encompassing various vegetation types and climates. These data included latent heat flux (LE), sensible heat flux (H), air temperature (Ta), precipitation (P), vapor pressure deficit (VPD), net solar radiation (Rn), ground heat flux (G), wind speed (WS), PFTs, and LAI. 2. **Data Preprocessing:** Rigorous data filtering was applied to ensure data quality. This included removing negative LE values, poor-quality data, and data from sites where site-level PFT did not match satellite-retrieved PFTs. Hourly LE data were corrected for potential biases related to relative humidity (RH) and rainfall intensity using a neural network (NN) approach. A Bowen ratio method was applied to address incomplete energy balance closure. 3. **Model Development:** A hybrid model, combining physics-based and ML components, was developed to estimate LE. Two models were trained: HMwet (trained with data from wet conditions during and after rainfall events) and Hmdry (trained with data from dry conditions). Both models use common predictors (Ta, VPD, Rn, WS, PFT, LAI), with HMwet additionally incorporating a canopy water storage (CWS) parameter inferred from a neural network using vegetation attributes and rainfall characteristics. The difference between LE predicted by HMwet and Hmdry provides an indirect estimate of Ei. 4. **Model Validation:** The hybrid models demonstrated good performance in reproducing site-level LE observations (r² > 0.75, RMSE < 60 mm). The Ei estimates were further validated against independent ground-based in situ measurements, showing good agreement (r = 0.76, p < 0.05). 5. **Global Upscaling:** The hybrid models were used to upscale Ei estimations to a global scale using gridded meteorological variables from ERA5 reanalysis data, LAI from MOD15A2H, and PFT from MCD12C1. The study considered the spatial heterogeneity of rainfall within grids, using a linear interpolation method to estimate Ei for light rain events. Annual Ei and Ei/P were calculated for the period 2000-2020. 6. **Analysis of Rainfall Regime Changes:** The study analyzed temporal changes in Ei and Ei/P over the 2000-2020 period, examining the relationships with changes in rainfall frequency and intensity. Rainfall frequency was defined as the fraction of wet hours (excluding intensely raining hours), and rainfall intensity as the fraction of intensely raining hours (above the 90th percentile of rainfall amounts).

The study's key findings include: 1. **Global Ei Estimate:** The global average annual Ei was estimated to be 84.1 ± 1.8 mm, accounting for 8.6 ± 0.2% of total rainfall during 2000-2020. This percentage varies significantly across regions and biomes. 2. **Drivers of Ei/P:** Rainfall characteristics (total amount, maximum and average hourly rainfall) were the primary determinants of Ei/P, with more intense rain events leading to lower Ei/P ratios. The relationship between Ei/P and LAI was weak, suggesting that rainfall intensity overshadows vegetation effects at large scales. 3. **Spatial Patterns of Ei:** The highest Ei values were found in wet, densely vegetated tropical regions. Ei did not increase proportionally with precipitation across all regions; the Ei/P ratio increased with rainfall amount in dry regions but decreased in humid regions, highlighting the trade-off between vegetation cover and rainfall characteristics. 4. **Comparison with Existing Models:** The data-driven estimates of Ei and Ei/P differed from those generated by the Gash model (GLEAM) and land surface models (LSMs). The data-driven approach resulted in higher Ei estimates, particularly in humid regions, suggesting potential limitations in the parameterizations of existing models. The data-driven approach better captured the spatial structure of Ei/P. 5. **Temporal Trends in Ei and Ei/P:** Global annual Ei significantly decreased by 4.9% during 2000-2020, resulting in a 6.7% decline in Ei/P. This decrease was primarily attributed to less frequent and more intense rainfall events. Rainfall frequency was found to be the most significant factor influencing changes in Ei, while rainfall intensity primarily influenced changes in Ei/P. 6. **Spatial Heterogeneity of Ei Changes:** The spatial patterns of Ei and Ei/P changes showed strong heterogeneity, with decreasing trends dominating in many tropical and extratropical regions. The spatial variation in Ei trend was largely controlled by changes in rainfall frequency, while Ei/P trend was more strongly influenced by rainfall intensity changes.

The findings highlight the importance of considering rainfall interception in global water balance assessments. The data-driven approach presented here offers a more accurate representation of Ei compared to existing process-based models, especially in humid regions where the effect of rainfall intensity is substantial. The observed decline in global Ei and Ei/P is a significant result, indicating that changes in rainfall patterns under climate change are altering the partitioning of rainfall into different components of the hydrological cycle. This shift towards more soil moisture and runoff could have both beneficial (increased water availability for ecosystems) and detrimental (increased flood risk) consequences. The study's results emphasize the need for improved representation of rainfall interception in land surface models and hydrological forecasts, especially given the projected increases in rainfall extremes and decreases in rainfall frequency under climate change.

This study provides a robust, data-driven estimate of global rainfall interception (Ei) over the past two decades, revealing a significant decline driven by changes in rainfall regimes. The findings highlight the importance of rainfall characteristics (frequency and intensity) in determining Ei and Ei/P. The developed hybrid modeling framework offers a significant advancement in estimating Ei, surpassing the accuracy of existing models, particularly in humid regions. Future research should focus on better incorporating long-term vegetation changes and improving the representation of sub-daily rainfall variability in models. The observed decline in Ei has implications for water resource management, ecosystem functions, and flood risk assessment, underscoring the need for further investigation into these interconnected aspects.

The study acknowledges several limitations. The assumption that relationships between LE and predictors built during dry periods can be applied to wet periods might introduce biases, particularly in situations where intercepted water affects transpiration. The model might not fully capture the effects of slowly evolving factors such as LAI on Ei. The spatial resolution of the global data used (0.5° × 0.5°) could limit the accuracy of capturing fine-scale spatial variations in Ei. The validation against in situ measurements was limited by the availability of comparable datasets. Despite these limitations, the findings provide valuable insights into the global patterns and drivers of rainfall interception and its response to changing rainfall regimes.