Moisture budget diagnostics
We applied the moisture budget diagnostics to investigate the physical processes driving the changes in precipitation variability. It has been widely used to diagnose changes in mean and extreme precipitation (6
). In a climate state, precipitation (P
) is balanced by evaporation (E
) and vertical (− < ω∂pq
>) and horizontal (− < V
· ∇ q
>) moisture advection that are related to low-level convergence and horizontal winds, respectively
is specific humidity, ω is vertical velocity, V
is horizontal wind vector, δ0
is the residual, and
denotes vertical integral throughout the troposphere. Such a balance also holds at a specific time scale
where the subscript f
denotes variation at a specific time scale derived from the filter.
Next, we applied simplifications to the full moisture budget to determine the moisture process that dominates the variation of precipitation and, based on which, to further understand the mechanisms for the projected changes.
First, among the moisture budget terms, the vertical moisture advection dominates precipitation variation at all time scales
It largely captures the phase and magnitude of precipitation variation, as supported by the high temporal correlation (or explained variance) and low root mean square deviation (RMSD) with precipitation (fig. S6). Therefore, the vertical moisture advection reasonably reproduces the climatological precipitation variability (fig. S5)
involves the vertical moisture gradient and the integration of vertical moisture advection throughout the troposphere. It can be simplified by a two-layer model, where the difference in moisture in the lower (ql
) and upper (qu
) troposphere is used to approximate the vertical gradient of moisture
represents the vertical motion at mid-troposphere, which is closely related to precipitation. As atmospheric moisture is concentrated in the lower troposphere, the right-hand side of Eq. 5
is dominated by its lower-level component. Hence, the variation in precipitation can be further approximated as that in the vertical advection of lower-level moisture
Here, ωm is represented by mid-tropospheric vertical velocity at 500 hPa and ql is represented by specific humidity at 925 hPa.
In terms of change, the vertical moisture advection reasonably reproduces changes in precipitation variability under global warming (comparing Figs. 4A
where σ denotes variability (estimated by standard deviation) and ∆ denotes the change between the baseline (1900–1959) and future (2040–2099), which are indicated by the subscripts 0 and 1, respectively.
We further separated the contributions from thermodynamics, dynamics, and nonlinear processes using idealized models. To estimate the thermodynamic (TH) contribution, which is related to changes in atmospheric moisture only, we change the specific humidity (ql
) to the future value and keep the circulation (ωm
) as in the baseline. The estimated changes in variability with this idealized model relative to the base period are regarded as the role of thermodynamics
Likewise, for the dynamic (DY) contribution, which is due to changes in circulation only, we change the vertical velocity (ωm
) to the future value and keep the humidity (ql
) as in the baseline. Hence, the DY contribution is estimated as the changes in variability with this configuration relative to the baseline
The nonlinear (NL) effect involves interactions between changes in humidity and circulation. It is estimated as the residual between the full changes in vertical moisture advection and the TH and DY contributions estimated from Eqs. 8
To provide a theoretical understanding of the thermodynamic and dynamic effects, we investigated the moisture budget in a further simplified framework. As the variability in vertical motion is far larger than that in humidity, the variation in vertical moisture advection is largely governed by that in vertical motion. Hence, by neglecting the variation in humidity and its interaction with circulation, Eq. 6
can be simplified as follows
is the climatological mean low-level humidity in a climate state. Thus, the variability in precipitation is proportional to that in vertical motion (σ[ − (ωm
Under this framework, the thermodynamic effect can be estimated as , which is determined by changes in atmospheric moisture and climatological circulation variability. The dynamic effect can be estimated as , which is determined by changes in circulation variability and climatological moisture availability.
The contributions of each term can be expressed as the percentage with respect to climatological precipitation variability, which then measures the direct contributions to the percentage precipitation variability change. The advantage is that the contributions of moisture and circulation changes are clearly separated between thermodynamics and dynamics
) and DY
) indicate the theoretical estimations of their contributions, respectively, and δ denotes a percentage change. To first order, the TH
effect acts to enhance precipitation variability by the rate of background moistening (Eq. 13
). The dynamic effect is associated with changes in the variability of vertical motion (Eq. 14
While the simplified model in Eq. 11
has limitations in neglecting the variation in humidity and its interaction with circulation, it provides a clear understanding of the thermodynamic and dynamic contributions, which are solely related to moisture and circulation changes, respectively, in a percentage sense. As all the moisture budget terms are normalized by climatological precipitation variability, the percentage contributions of the thermodynamic, dynamic, and nonlinear components add up to explain the percentage precipitation variability changes.
To test the validity of this framework, we compared the phase and magnitude of variation between precipitation and vertical moisture advection, which were indicated by temporal correlation (or explained variance) and RMSD between the filtered time series, respectively. Overall, the vertical moisture advection is a reasonable approximation of precipitation variation over climatologically wet regions, with an explained variance larger than 50% and RMSD less than 80% of the climatological precipitation variability (fig. S6). These regions correspond well to the climatologically wet regions with mean precipitation larger than 50% of the global average (see red contours in Fig. 6A
and fig. S6). In particular, the simplified framework can better capture precipitation variability in the tropics than in the mid to high latitudes, with higher explained variance and lower RMSD in the tropics (fig. S6) (22
). The high capability of the framework in the tropics has also been shown for annual-mean and seasonal-mean diagnosis (40
). In subtropical descending regions where convection is largely suppressed, the variation in precipitation is not well explained by that in vertical moisture advection. Thereby, the quantitative contributions of moisture budget processes are estimated for these wet regions only.
One limitation of the moisture budget framework is that it cannot distinguish the causality between precipitation and evaporation changes. Given the much weaker changes in evaporation variability (with a global mean magnitude approximately 10% that of precipitation variability change; figure not shown), its contribution to precipitation variability change is believed to be small. Despite the aforementioned limitations mainly occurring on regional scales, on the global scale and particularly in the tropics, the moisture budget framework works reasonably well and explains 82 to 93% of global mean precipitation variability changes across different time scales.