The recently published IPCC AR6 report presents a full and systematic evaluation of extreme weather events. It shows that severe precipitation increases 7% in intensity when the temperature increases 1°. Furthermore, the variability of torrential rainfall events is studied and seen well-related to global climate warming in the form of non-linear processes (IPCC, 2021; Zhang et al., 2021). Compared to regions at the same latitudes, Central Asia is more sensitive to global climate change for its complicated terrains and unevenly distributed hydrological sources (Yin et al., 2014; Li et al., 2015; Hu et al., 2016; Jiang et al., 2020). Featuring in scarce precipitation, Central Asia is experiencing an increase in the occurrence of extreme rainfall and has been vulnerable to extreme precipitation in recent years (Deng et al., 2014; Huang et al., 2014, 2015; Hu et al., 2014, 2017; Malsy et al., 2015; Zhao et al., 2016; Zhang et al., 2017). Increased extreme precipitation may help solve the limited water availability problem, but introduce floods and secondary disasters (Knapp and Coauthrs., 2008) at the same time. Severe droughts and floods threaten human lives and constructions of the Silk Road Economic Belt. Xinjiang province, the key area of the Silk Road Economic Belt, has suffered 45 local rainstorms and floods every year in average for the past 10 years (Wang and Wang, 2021). Apart from complicated terrains and soil types, dominant weather systems of different scales are also responsible for the sudden and extreme precipitations in both summer and winter (Ma et al., 2021). Anomalous precipitation is directly related to the moisture supply and can be represented by water vapor transport which is well studied and widely used globally or over East Asia (Ding, 1994; Trenberth et al., 1995; Zhou and Yu, 2005; Gao et al., 2017, 2021; Qin et al., 2021). Hu et al. (2021) studied the water vapor transport of the summer half-year from 1979 to 2018, the results showed that water vapor from the North Atlantic Ocean, Europe, and the Mediterranean Sea contributes to northern Xinjiang’s extreme precipitation, while water vapor from the Arabian Sea, the Arabian Peninsula, and the Indian Peninsula contribute to extreme precipitation over southern Xinjiang. By far, a detailed comprehension of the relationship between water vapor transport by different scales of motions and extreme precipitation over the Xinjiang province is deficient and should be an issue of considerable urgency.

Multi-scale flows coexist in the real atmosphere. In other words, real weather events can be seen as a combination of slow manifolds and fast ones from the perspective of phase space (Leith, 1980; Lorenz, 1980, 1986; Daley, 1991). Slow manifolds follow basic physical principles with high predictability, while fast ones contain randomness and thus are hard to forecast. However, the fast manifold motions and their interaction with slow ones are the direct reason for the initiation of most severe weather events. For climatic studies, the slow manifold covers systems of planetary scale and large-scale ones (Hasselmann, 1976). Most climate numerical models are constructed by eliminating fast manifolds which coexist as perturbations over the slow ones. For synoptic studies, the slow manifold serves as the background for the fast one which includes flows of sub-synoptic, mesoscale, and convective scales. There are three types of approaches to decompose slow and fast manifolds which are: the statistical method (Seager et al., 2010), synoptic analysis, and dynamic one. Barnes filter (Barnes, 1973) is a classical statistical method which has been broadly used in diagnosing typhoons, cyclones, and Meiyu fronts (Doswell, 1977; Gomis and Alonso, 1990; Xu et al., 2017; Xue et al., 2018; Zou et al., 2018; Ma et al., 2021), the mathematical procedure is direct and efficient, but the physical basis is not solid, especially for a specific case study. The synoptic analysis approach is based on the Helmholtz theorem by decomposing horizontal velocity into rotational and divergent flow components (Hawkins and Rosenthal, 1965; Dimego and Bosart, 1982; Ullah et al., 2020, 2021). The latter is the fast manifold which is directly linked to vertical motions and is responsible for severe weather. Applications of this physically solid method are wide in both atmospheric and oceanic motions. However, the accuracy and efficiency for mesoscale diagnosis in a limited domain limits this method in climatic or large-scale applications (Renfrew et al., 1997). Xu et al. (2011) designed an integral method with the adoption of Green’s function for limited areas of arbitrary shapes. The dynamic analysis approach approximates primitive equations to different extents and can be divided into geostrophic and balanced types (Allen, 1991; Xu, 1992). This is the most solid physical approach but at the same time is extremely complicated for numerical computations. High resolution dataset outputs from mesoscale models add difficulties to the applications of the dynamic analysis approach.

The intensity of the net water vapor advection or water vapor flux divergence in the lower troposphere is the core factor to judge the precipitation intensity, which is also the key factor in the analysis and forecast of large-scale rainstorm (Sun, 2017), therefore, water vapor flux divergence is critical in a rainstorm, and many case studies have confirmed the effectiveness of its decomposed components (Zhou and Zhang., 2016; Ma et al., 2022; Wu et al., 2022). Ma et al. (2022) analyzed the decomposition of water vapor flux divergence and its application to a Blizzard event over Ili Valley in Central Asia from 30 Nov to 1 Dec, 2018. Cao et al. (2022b) analyzed the decomposed components’ application to rainstorms caused by Typhoon Rumbia in 2018, and Wu et al. (2022) researched persistent extreme precipitation events in the post-flood season over Hainan Island from 16 to 18 Oct, 2020. The results of those cases showed that the decomposed water vapor flux divergence can better interpret which components play more important roles during extreme precipitation. This is useful for further applications in rainfall predictions. The main purpose of this study is to decompose water vapor flux divergence with the Barnes filter and synoptic methods in different precipitation events to see their performances when traditional analysis fails to identify the evolution of extreme precipitations over the Xinjiang province. Quantitative comparisons of these two methods in two severe precipitations distinct in synoptic and hydrological backgrounds, terrain heights ranging from 500 m to 4,000 m, and durations are performed with the hope to seize useful information for severe precipitation forecasts from decomposed manifolds. The traditional synoptic analysis and numerical configurations for the two real cases are presented in Section 2, followed with brief derivations of these two decomposition approaches. In Section 3, the decomposed slow manifolds by the Barnes filter and synoptic methods are analyzed compared to the original water vapor flux divergence and to each other. Further decomposition of the moisture parameter is carried out with the hope to seize the dominant signal for precipitations. Conclusions and short discussions are presented in Section 4.

Q^div shares similar quantities and evolving patterns with Q^all at all levels. However, neither of them presents divergent signals before the precipitation weakens. In winter snowstorms of short durations, the divergence regions at the middle levels seen in Q^all (Figure 3A) are blocked by large convergence at the middle and low levels (Figure 3B). In the summer case with persistent rainfall, divergent signals presented by Q^all (Figure 3E) show up after the precipitation reaches its maximum, and the divergence is weaker in Q^div (Figure 3F). Large convergent regions in Q^all and Q^div are also blocked at the middle levels as rainfall ends. Therefore, though occupying the largest magnitude in Q^all, Q^div fails to identify the weakening or ceasing of precipitation in both torrential events.

In both winter and summer events presented in Figure 3, Q^div (Figures 3B,F) shares the evolving patterns as Q^all (Figures 3A,E) at all levels with dominant quantities compared to the other two components. However, neither of them in both events discloses the divergent signals before precipitation weakens, as shown by the green curves. To be specific, the large divergent regions of Q^all (Figure 3A) after 20 UTC Nov. 30 above the middle levels are blocked by large convergent areas at lower levels which have resulted from negative values in Q^div (Figure 3B). Meanwhile, the convergent signals presented by Q^all (Figure 3E) and Q^div (Figure 3F) still occupy low and middle levels over the target domain for around 6 h after the precipitation reaches its maximum. Furthermore, as the rainfall ends, there is still large convergent Q^div transporting downward which contradicts with the precipitating characteristics. Therefore, though occupying the largest magnitude in Q^all, Q^div fails to identify the weakening or ceasing of precipitation in both torrential events.

Q_B ^S in both events (Figures 3C,G) present strong convergence as precipitation increases, and abruptly change to divergence before precipitation weakens. Q_H ^S (Figures 3D,H) performs slightly better compared to Q_B ^S (Figures 3C,G) in both the winter event with uniform divergence at lower levels since 20 UTC Nov. 30, and the summer event with small convergent areas before rainfall increases since 21 UTC June 15. As a short conclusion, the decomposed Q^S by both the Barnes filter and synoptic methods are useful for depicting the precipitating evolutions during the winter and summer events, while the latter performs better.

However, the accuracy between the reconstructed velocity and the initial one in winter is much lower than the summer case mainly due to the fact that the wind field is more complicated in the short duration snowstorm. The deviations of the reconstructed zonal and meridional wind component by the synoptic method and Barnes filter to their corresponding initial one over the target domain are investigated. In the winter, meridional differences by the synoptic method (Figure 4A) keep a uniform vertical distribution with a small magnitude of the same order as in the summer, while those by the Barnes filter (Figure 4B) are tremendously amplified with maximum centers after a snowstorm. Zonal differences by the synoptic method (Figure 4C) show a uniform distribution vertically, while those by the Barnes filter (Figure 4D) with the same magnitude but increase evidently as the rainfall intensifies in the summer. The power spectral density of the vertical velocity in the summer event (Figure 4F) is evidently less complicated than that in the winter (Figure 4E) event. Therefore, the capability for accurately reconstructing the complex flow field may be a reason for the better performance of the synoptic method over the Barnes filter in both summer and winter events.

Another possible reason for the worse situation by the Barnes filter in the winter event may due to the less abundance but more variable moisture. The moisture is thus decomposed by the Barnes filter with the same response function in Figure 1B to further decompose q into slow and fast manifold components as follows: q = q m + q ′ (4.1)

Substituting Eq. 4.1 into Eq. 3.3 leads to: Q B S = ( v S ⋅ ∇ q ) B =   Q B Sm + Q B Sd + Q B Fm Q B Sm = u S ∂ x q m | η + v S ∂ y q m | η − u S ( ∂ p q m ) ( ∂ x p ) | η − v S ( ∂ p q m ) ( ∂ y p ) | η Q B Sd = u S ∂ x q d | η + v S ∂ y q d | η − u S ( ∂ p q d ) ( ∂ x p ) | η − v S ( ∂ p q d ) ( ∂ y p ) | η Q B Fm = u F ∂ x q m | η + v F ∂ y q m | η − u F ( ∂ p q m ) ( ∂ x p ) | η − v F ( ∂ p q m ) ( ∂ y p ) | η Here, the subscript B denotes the Barnes filter, the superscript m denotes mean, and d denotes disturbance. Q_B ^S is the moisture convection term by non-divergent or slow manifold based on the Barnes filter, Q_B ^Sm is the mean component of the moisture convection term by non-divergent or slow manifold based on the Barnes filter, Q_B ^Sd is the disturbed component of the moisture convection term by non-divergent or slow manifold based on the Barnes filter, Q_B ^Fm is the mean component of the moisture convection term by divergent or fast manifold based on the Barnes filter.

Compared to the weak convergence in Q_B ^S (Figure 3C) when a snowstorm weakens, the decomposed mean component of Q_B ^Sm (Figure 5A) keeps uniform divergence as precipitation ceases. It can be seen from Q_B ^Sd (Figure 5B) that the false convergence signal is resulted from q’. This can be seen vividly in the distributions of q (Figure 5E) and its decomposed components (Figures 5F,G). However, both Q_B ^Sm and Q_B ^Sd in the summer event remain uniformly divergent as precipitation ceases and convergent as it increases, as shown in Figures 5C,D with q and its components keeping the same signals (Figs. omitted). This proves the necessity of further decomposing q especially for the winter event with complicated flow patterns.

In the research of extreme precipitation climate events, the method of decomposing the influence of water vapor flux divergence (Q^all) into climatic and large-scale systems has been mature. For extreme precipitation weather events, similar ideas are adopted to separate the influence of synoptic and sub-synoptic scale weather systems represented by slow and fast manifolds, respectively, in this study with the purpose to better forecast precipitation.

The statistical Barnes filter method and the synoptic decomposition approach are adopted by dividing Q^all under the terrain-following coordinate system into three components, i.e., Q^div, Q^S, and Q^F. These components represent flow divergence, moisture convection term by slow and fast manifolds. A blizzard process with a short duration and weak moisture and a persistent rainstorm event with abundant water vapor are investigated with both traditional synoptic analysis and decomposition methods. The main results are as follows:

(1) Q^div, which is directly related to the convergence and divergence of the large-scale velocity field, always occupies the biggest magnitude in Q^all. During the periods of intensification and weakening of extreme precipitation events, Q^all at the middle and lower levels converges which contradicts to the ceasing of the precipitation. Vertical distributions that show the divergent signals of mid-to-high-level Q^all are blocked at the middle and high levels.

The two decomposition methods can provide superior indicators for the prediction of extreme precipitation weather events, especially the decrease and termination of precipitation. However, the accuracy of the Barnes filter method is more related to the complexity of flow fields as well as the moisture conditions. In the future, this research will combine these two scale decomposition methods with high-resolution numerical models, and carry out research on other material transport and aggregation such as dust in other parts of the earth.