Changes in precipitation patterns significantly impact socioeconomic outcomes and human well-being. Global warming is expected to alter the pattern and magnitude of precipitation due to increased atmospheric water vapor. While the 'wet-get-wetter, dry-get-drier' paradigm applies in many regions, regional variations exist due to complex interactions of precipitation drivers. To predict future precipitation changes, a structural model representing the underlying physical processes is needed, allowing for the identification of contributing factors and their interactions. Previous studies have simplified the analysis of precipitation using atmospheric moisture budgets, quantifying distinct physical processes like dynamic and thermodynamic components and horizontal moisture advection. The dynamic process reflects contributions from atmospheric circulation, while the thermodynamic process is linked to changes in atmospheric water vapor content related to temperature. Horizontal moisture advection acts as a moisture source for precipitation. Prior research has focused on the relative importance of these processes, often neglecting their interplay. However, increased water vapor reduces the vertical motion required for precipitation of the same intensity, potentially leading to stronger precipitation with the same vertical motion, suggesting significant interplay among moisture budget processes. Time-averaged moisture budget analysis doesn't reveal these interactions; daily or sub-daily analysis is needed to understand atmospheric moisture dynamics and future precipitation changes.

Existing literature highlights the impact of global warming on precipitation variability and the 'wet-get-wetter, dry-get-drier' paradigm. However, the complexity of regional variations necessitates a deeper understanding of the interplay between dynamic and thermodynamic processes. Previous studies have utilized atmospheric moisture budgets to quantify individual processes, but often neglected their interactions. The Clausius-Clapeyron relationship, linking temperature and moisture availability, has been investigated, but its direct control on daily precipitation remains unclear. The need for a dynamically interactive model, accounting for instantaneous impacts and propagation of changes through the atmospheric moisture system, is highlighted to fully explain atmospheric moisture dynamics and predict future precipitation changes.

This study constructs a dynamically interactive atmospheric moisture model to explore the moisture budget balance. Precipitation (P) is expressed as a linear function of four processes: vertically-integrated vertical motion (dynamic process, DY), vertically-integrated moisture profile (thermodynamic process, TH), vertically-integrated horizontal moisture advection (HA), and evaporation (E). Daily outputs from ten coupled ocean-atmosphere general circulation models (CMIP5) are used for pre-industrial (PI), present (2006-2025), and future (2081-2100) climates under RCP4.5. The dynamic process is associated with vertical velocity at fixed specific humidity, and the thermodynamic process with constant vertical velocity and moisture content linked to ambient temperatures. A structural vector autoregression (SVAR) model is employed to capture the interactions among the five processes (P, DY, TH, HA, E). The SVAR estimates the system of interactions using time-lagged values of all processes, specifying physical links using Choleski decomposition. Impulse-response functions (IRFs) are computed to identify the propagation of perturbations through the moisture budget system. Time-averaged hydrological patterns and moisture budget components are examined, comparing time-averaged and instantaneous impacts of components on precipitation. Forecast error variance decomposition (FEVD) is used to quantify the overall relative contribution of each component to precipitation. Probability densities of the impacts of processes on precipitation are analyzed to examine the range of precipitation responses. The geographical distribution of impacts is also examined to understand regional variations. Spatial correlation among grids is tested by including neighboring grid data in the SVAR regression, but it is found to be insignificant. The residual from the moisture budget equation is calculated to evaluate the model output consistency.

The time-averaged analysis reveals that the dynamic and thermodynamic components contribute almost equally to precipitation, but the IRF analysis reveals a stark contrast. Perturbations in the dynamic component have the largest impact on same-day precipitation, decreasing on subsequent days. Perturbations in the thermodynamic component have a smaller immediate impact, lasting for two days. Horizontal advection's impact is delayed, peaking the next day. Evaporation's maximum impact is on the first day. The time-averaged moisture budget masks the dynamic component's dominating influence and the delayed effect of horizontal advection. FEVD analysis confirms the dynamic component's dominating influence (47.6%), far exceeding the thermodynamic component (3.5%). In all climate states, components show increased impact on precipitation, with the dynamic component's increase concentrated on the first day. The increase in the dynamic component's influence, without an extended impact period, is attributed to same-day moisture removal. Increased moisture supply via the thermodynamic and HA in a warmer climate may extend precipitation periods. Probability densities show increased spread as climate warms, indicating a higher likelihood of extreme precipitation events. The increase in spread is largest for the dynamic component, especially in the tropics and storm track regions. The dynamic component's impact on same-day precipitation has the largest increase in spread, while the thermodynamic and HA have smaller increases. Light rainfall events are less probable in the future. Geographical distribution of impacts shows increased spread of dynamic components in the tropics and storm tracks, and decreased impact in the subtropics, defying the stationary upward motion assumption of the WGWDGD paradigm. The thermodynamic component's impact is less localized, emphasizing the tropics and storm tracks. Horizontal advection emphasizes moisture advection to extratropics. Interactions among components show that increased dynamic processes reduce moisture content the following day, reducing horizontal advection. Increased thermodynamic component enhances the dynamic component, leading to more precipitation in warmer climates. The interactions are consistent over land and ocean, with minor differences. The impact of thermodynamics on dynamics is greater over the ocean.

The findings verify the importance of atmospheric vertical motion to heavy precipitation, consistent with other studies. The dynamic process dominates rainfall anomalies associated with the Asian monsoon, while the thermodynamic process is important in East Asia. The dynamic effect extends to winter extratropics, although the thermodynamic influence can be significant there. Discrepancies with other studies may be due to the temporally varying methods or differing model outputs. The study's statistical model clarifies the interactions and temporal variations among moisture budget components. The dynamic process's contribution is amplified in warmer climates. The thermodynamic influence increases for a longer period in warmer climates but remains smaller than the dynamic contribution. The contrast between time-averaged and instantaneous contributions explains the disparities in previous research regarding the roles of dynamic and thermodynamic processes.

This study demonstrates the increasing dominance of atmospheric vertical motion in heavy precipitation events as the climate warms. The dynamically interactive model reveals the complex interplay between dynamic and thermodynamic processes, highlighting the limitations of time-averaged analyses. Future research should focus on investigating the model's findings with observed data, examining sub-daily variability, and exploring the influence of micro-processes and local factors on moisture budget component interplay.

The study utilizes daily average rainfall, potentially hiding sub-daily scale processes. While the SVAR model can handle sub-daily variations, the use of convective parameterizations in models limits precise calculations of the dynamic process at that scale. The influence of micro-processes and local factors (soil moisture, cloud cover, topography) on the interplay of moisture budget components warrants further investigation. The choice of RCP4.5 scenario may influence the results compared to other scenarios like RCP8.5.