1 Introduction

Atmospheric moisture transport occurs across many different temporal and spatial scales and is associated with various weather systems ranging from atmospheric rivers and low-level jets to tropical and extratropical cyclones, fronts, monsoon lows, and organized convective systems (Gimeno et al. 2016). While large-scale advection of water vapor from oceans to land is mainly carried out by the mean circulation, the moisture transport over land is also characterized by many small-scale features and turbulent transport (Newman et al. 2012). Deviations from the mean flow, so-called transient eddies, are particularly important in the mid-latitudes because eddies are responsible for carrying water vapor and energy from the tropics to the higher latitudes. Identifying the temporal scales and weather systems that make up the climatological mean moisture transport is important because variations in these components determine the seasonal water supply in particular regions. In addition, moisture transport is a primary factor for convective storms that produce heavy precipitation since these require sufficient moisture at storm initiation and replenishment of moisture from the surrounding region as they grow upscale (Trenberth et al. 2003). Understanding how atmospheric variability acts upon moisture transport is therefore important to understand variations in convective organization that can potentially lead to extreme events and flooding.

Downwind regions of major mountain ranges are often highlighted as centers for cyclogenesis (Barry 1992; Pierrehumbert 1986) and convective organization (Laing and Michael Fritsch 1997; Feng et al. 2021). In the mid-latitudes, such leeside storm formation is among other factors conditioned by moisture availability which can be provided by local surface evaporation or by low-level jets and monsoon-like wind circulations that advect water vapor from remote maritime regions (Stensrud 1996). For example, Rasmussen and Houze Jr (2016) showed that convective initiation and the occurrence of intense storms east of the Andes are associated with a strengthening of the South American low-level jet. Similarly, the occurrence of summer mesoscale convective systems (MCSs) east of the Rocky Mountains is favored by the transport of warm and humid air through the Great Plains low-level jet (Feng et al. 2019).

In this study, we focus on the downwind region of the Tibetan Plateau (TP) where the formation of MCSs is favored by southerly moisture transport through the Indian summer monsoon (Kukulies et al. 2021, 2023) and in some cases by mesoscale vortices that form over the plateau (Kukulies et al. 2023). Being located in the transition zone between mid-latitudes and tropics (ca. 28 \(^\circ \)N-43 \(^\circ \)N), the region is affected by large-scale moisture transport from the tropics and by the interaction between the large-scale atmospheric circulation and the high mountain barrier. With an average elevation of about 4000 m and an area of about 2.5 million km\(^2\), the TP is the highest and largest plateau on the planet. Due to the mechanical and thermodynamic effects of this giant topographic barrier on the atmosphere, the TP itself shapes the weather and climate in its downwind regions and over continental East Asia (Wu et al. 2015). It is, for instance, vital for the evolution and northward extension of the South Asian summer monsoon (Hahn and Manabe 1975; Webster and Yang 1992; Yanai et al. 1992) because it represents a large-scale elevated heat source that modifies and warms the middle and upper troposphere through upward motion and latent heat release (Hahn and Manabe 1975; Duan and Wu 2005). This heat source helps in maintaining the continental-scale low-pressure system associated with the Asian summer monsoon and produces a strong pressure gradient that has been suggested to enable the low-level southerly moisture transport to reach farther northward (Hahn and Manabe 1975). In addition, the topographic barrier of the TP also affects the extratropical westerly circulation owing to the impact of orographic gravity wave drag (Palmer et al. 1986).

The downwind region of the TP is frequently affected by MCSs (Kukulies et al. 2021; Feng et al. 2019; Li et al. 2020) and mesoscale vortex systems that originate over the mountains and propagate eastward (e.g., Li et al. 2017; Curio et al. 2019). It is debated whether such vortices mainly originate from the diabetic heating of the mountain surface (Zhang et al. 2019), but the impact of mountainous low-pressure systems on heavy precipitation in the downwind region has been widely reported (Curio et al. 2019; Kukulies et al. 2023, e.g.,). This study addresses the question of how different scales of moisture transport in the downwind region are linked to precipitation and MCSs.

While it is well known that the wet season in the TP downwind region is characterized by large-scale water vapor advection through the East Asian (Yihui and Chan 2005) and Indian summer monsoon systems (Goswami et al. 2006), it remains unclear which weather systems and temporal scales are most important for the transient moisture transport over land. It is challenging to disentangle the individual effects of large-scale and mesoscale atmospheric processes on moisture transport and convective organization and to date, not much research has focused on the role of eddy transport around the TP. In particular, it is an open question of how variations in the large-scale circulation affect both the mean and eddy components of atmospheric water vapor transport. Given that climate change is expected to modify many large-scale atmospheric circulation systems (Seager et al. 2010; Wang et al. 2020; Yang et al. 2022) and consequently their interactions with major mountain ranges like the TP, there is a need to understand the implications of such changes on both mean flow and eddy moisture transport. Decomposing the different components of moisture transport may also help to better understand the role of moisture transport through mesoscale weather systems and if these scales are sufficiently well represented in current climate models.

The aim of this study is therefore to analyze the importance of the mean flow and eddy moisture transport in the downwind region of the TP from an atmospheric moisture budget perspective. We explore the different temporal scales that make up the total eddy moisture transport and show how these are linked to other components of the atmospheric moisture budget and large-scale atmospheric circulation systems. In addition, we compare the components of moisture transport between the global reanalysis ERA5 and dynamically downscaled climate data based on the Weather and Research Forecast (WRF) Model (Skamarock et al. 2008).

The following research questions are the focus of this analysis:

  • What are the relative contributions of mean flow and eddy moisture transport and which temporal scales are most important for the total eddy transport?

  • How are the mean flow and eddy moisture transport linked to variations in the large-scale atmospheric circulation, evaporation, precipitation, and convection?

  • How do these components differ between reanalysis and dynamically downscaled climate data?

2 Data and methods

2.1 Reanalysis data

The presented analysis is based on hourly data from the ERA5 reanalysis (Hersbach et al. 2020) for all summer seasons in the historical period 1980–2019. The focus is on the summer months June to August because precipitation and convection over land peak during these three months ( e.g., Kukulies et al. 2021).

We used specific humidity and cloud condensates (both liquid and ice water) together with the horizontal wind fields from 37 pressure levels (1000 hPa to 1 hPa) to compute the vertically integrated moisture flux divergence and the vertically integrated total moisture transport as well as their mean flow and eddy flux components. We also used precipitation and evaporation from ERA5 to relate the moisture transport to the atmospheric moisture budget (see next section for more details). However, different global reanalyses show a much better agreement for moisture flux divergence than for precipitation or evaporation (Trenberth et al. 2011). Therefore, the focus of this analysis is on the role of different moisture transport components in reanalysis and downscaled climate data rather than on biases in precipitation and evaporation that are both strongly dependent on physical parameterization schemes.

2.2 WRF simulation

Because the horizontal spatial resolution of ERA5 (0.25\(^\circ \) x 0.25\(^\circ \)) may not be sufficient to resolve all relevant mesoscale processes that influence turbulent moisture transport, we compared the results of ERA5 to high-resolution regional climate model data. We hypothesize that the moisture transport carried out by eddies makes up a greater contribution in this dataset because the finer-scale surface features and mesoscale weather systems in the dynamically downscaled data allow for a more detailed representation of small-scale variations in the humidity and wind fields.

The regional climate model simulation was created through dynamical downscaling (Laprise et al. 2008) of the ERA5 reanalysis with the Weather and Research Forecast (WRF) model version 3.7.1. (Skamarock et al. 2005) for the same 40-year period over the domain shown in Fig. 1. The model simulation (hereafter: WRF\(_{9km}\)) was conducted at a horizontal grid resolution of 9 km and without cumulus parameterization in a non-hydrostatic configuration (Ou et al. 2020). The simulation was evaluated in Ou et al. (2020) and Ou et al. (2023) and sensitivity tests with and without cumulus parameterization showed that the timing and frequency of short-duration precipitation as well as the seasonal mean precipitation were better captured in the simulations without cumulus parameterization at this resolution (Ou et al. 2020). It should be noted that a horizontal resolution of 9 km is regarded as the upper boundary of the gray zone of turbulence wherein turbulent kinetic energy is only partially resolved (Wyngaard 2004). This means that only the larger-scale, well-organized storm systems are represented in this data and it remains unclear to which extent the simulation lacks important contributions from small-scale convection to precipitation. While this leads to some uncertainty in the simulated regional precipitation patterns, we have more confidence in the simulated moisture transport as mesoscale circulations likely have a larger effect on regional-scale moisture transport than the feedback of small-scale convection on moisture transport.

Spectral nudging was used as a technique to constrain the large-scale circulation within the WRF model domain such that it does not depart too much from the large-scale circulation of the driving reanalysis. This means that WRF\(_{9km}\) inherits the large-scale forcing from ERA5 not only at the lateral boundaries but also in the inner model domain at synoptic-scale wavelengths. In theory, the simulated large-scale atmospheric fields in the model should thus show the same variations as in the driving reanalysis. More details about the nudging parameters, the model configuration, and the used parametrization schemes can be found in Ou et al. (2020).

Fig. 1
figure 1

WRF domain and model elevation at 9 km grid spacing. The gray box (28 \(^\circ \)N-43 \(^\circ \)N and 100 \(^\circ \)E-120 \(^\circ \)E) shows the focus region in the downwind of the Tibetan Plateau that was chosen to include most parts over land in the latitudinal range that is likely be affected by mountainous weather systems

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2.3 The atmospheric moisture budget

To investigate the role of atmospheric moisture transport on the downwind side of the TP, we start our analysis by examining components of the atmospheric moisture budget. On monthly to seasonal time scales, precipitation at a given location is balanced by the sum of surface evaporation and the local net influx of water vapor which can be quantified by the horizontal moisture flux convergence (Peixoto et al. 1992). Mathematically, the atmospheric moisture budget can be described as:

$$\begin{aligned} \overline{P} - \overline{E} \approx \underbrace{- \overline{ \nabla \int _{p_s}^{p_t} (q \overrightarrow{V}) dp} }_{\text {horizontal moisture flux convergence}} \end{aligned}$$
(1)

where \(\overline{P}\) is the temporal mean of precipitation and \(\overline{E}\) the temporal mean of evaporation (Peixoto et al. 1992). The right-hand side of the equation describes the negative divergence (hence: convergence) of the vertically integrated horizontal moisture fluxes with q referring to specific humidity [kg kg\(^{-1}\)] and \(\overrightarrow{V}\) referring to the horizontal wind vector [m s\(^{-1}\)]. Because this is a steady-state moisture budget averaged over a longer period, the local change rate of water vapor and the vertical moisture flux divergence become negligible (Peixoto et al. 1992).

We computed the horizontal moisture flux divergence from hourly specific humidity (including cloud water) and wind fields at all pressure levels for ERA5 and WRF\(_{9km}\) and integrated the resulting divergent moisture fluxes from the surface pressure (\(p_s\)) to the top of the atmosphere (\(p_t\); 1 hPa for ERA5 and 10 hPa for WRF) using the trapezoidal rule. For ERA5 data, this requires that the u and v components of the horizontal moisture fluxes at pressure levels below the surface pressure are set to 0 and that near-surface humidity is approximated by interpolating q between the surface pressure and the lowermost pressure level above the surface pressure. Note also that the different grid configurations in ERA5 and WRF\(_{9km}\) (i.e. regular lat/lon grid vs. equal distance grid spacing) need to be considered in the computation of the divergence term.

2.4 Decomposition of moisture transport

Like any other atmospheric motion, moisture transport occurs on a continuous spectrum of spatial and temporal scales. To disentangle the relatively steady, large-scale flow from smaller-scale disturbances, one of our goals is to quantify the relative contributions of mean flow and the eddies to the climatological mean moisture transport. We first decomposed the total vertically integrated moisture transport into its monthly mean flow and eddies that are super-imposed on the mean flow:

$$\begin{aligned} \underbrace{\int _{p_s}^{p_t} (\overline{q\overrightarrow{V} } ) dp}_{\text {total mean moisture transport }} = \underbrace{\int _{p_s}^{p_t} (\overline{q}{\overline{\overrightarrow{V}}} ) dp }_{\text {mean flow}} + \underbrace{ \int _{p_s}^{p_t} (\overline{q^\prime {\overrightarrow{V}^\prime }}) dp }_{\text {eddy transport}} \end{aligned}$$
(2)

The bars denote the temporal mean (i.e. monthly) and the primes denote the deviation from that mean (e.g. deviation of hourly q and V from the monthly mean, but this can also be replaced by daily deviations from the monthly mean). This decomposition can be done for both the total moisture transport as derived from vertically integrated moisture fluxes as well as for the horizontal moisture flux divergence.

From equation 2, it can be inferred that the accuracy of the total mean transport on the left-hand side depends on the time scale on which the eddy transport (\(\overline{q^\prime {\overrightarrow{V}^\prime }})\)) is calculated. For example, if \(\overline{q\overrightarrow{V} }\) is computed from daily mean humidity and wind fields, the result is not as exact as if it was calculated from hourly values because it would not contain any information about the sub-daily variations. The most precise approximation to the total moisture transport can be thus obtained when the smallest temporal scale is considered. In theory, that would be the model timestep, but we are here limited to the model output which is at hourly timesteps.

The eddy component can be further decomposed into different bins of the time scale spectrum that together make up the total turbulent transport. Consider, for example, the difference between the total transport as calculated from hourly mean values (\(\overline{q_h\overrightarrow{V_h} }\)) and the total transport calculated from daily mean values ( \(\overline{q_d\overrightarrow{V_d} }\)), decomposed in the same way as in equation 2:

(3)

The gray terms drop out because they are identical, which leaves us with the difference between the hourly and daily primes as the missing term to describe the total eddy transport from hourly values which is the closest approximation to the true eddy transport based on the model and reanalysis output variables. Equation 3 shows that the total eddy transport can be decomposed into an arbitrary number of time scale bins between the hourly eddies and the mean flow component. The terms on the right-hand side can then be used to quantify how much the different time-scale bins contribute to the total eddy transport. The following equation gives an example of the total eddy transport decomposed into daily, 6-hourly, and hourly components:

$$\begin{aligned} \begin{aligned} \underbrace{ \int _{p_s}^{p_t} (\overline{q_h^\prime {\overrightarrow{V_h}^\prime }}) dp }_{\text {total eddy transport}}&= \underbrace{ \int _{p_s}^{p_t} (\overline{q_d^\prime {\overrightarrow{V_d}^\prime }}) dp }_{\text {daily eddies}} + \underbrace{ \int _{p_s}^{p_t} (\overline{q_{6h}^\prime {\overrightarrow{V_{6h}}^\prime }}) dp - \int _{p_s}^{p_t} (\overline{q_d^\prime {\overrightarrow{V_d}^\prime }}) dp }_{\text {6-hourly --daily eddies}} \\&+ \underbrace{ \int _{p_s}^{p_t} (\overline{q_{h}^\prime {\overrightarrow{V_{h}}^\prime }}) dp - \int _{p_s}^{p_t} (\overline{q_{6h}^\prime {\overrightarrow{V_{6h}}^\prime }}) dp }_{\text {hourly --6-hourly eddies}} \end{aligned} \end{aligned}$$
(4)

We computed the eddy transport for eight different time scales to cover a wide range of different bins of the time scale spectrum: 10-daily, 5-daily, 3-daily, daily, 12-hourly, 6-hourly, 3-hourly, and hourly. Among these scales, 10- to 5-daily eddies are associated with synoptic-scale systems (e.g. frontal systems, atmospheric rivers (Pan and Lu 2020) or break cycles in the monsoons (Randel and Park 2006)). Eddies associated with daily to 3-daily timescales could be related to mesoscale disturbances (e.g. TPVs and long-lived MCSs (Curio et al. 2019; Kukulies et al. 2021)). Finally, sub-daily eddies between 12 and one hour are associated with the smallest variations in moisture transport, e.g. associated with the diurnal cycle of wind systems, short-lived convection, and land-atmosphere interactions that influence local circulations and atmospheric moisture. We chose here to look at hourly, 3-hourly, 6-hourly, and 12-hourly separately to investigate to whether sub-daily variations occur at a particular scale or are similarly distributed.

2.5 Large-scale circulation indices

Table 1 Large-scale circulation indices used to quantify the impact of large-scale atmospheric circulation on moisture transport scales
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Since it has long been recognized that atmospheric moisture transport and precipitation in the downwind of the TP are influenced by the Asian summer monsoon (e.g., Turner and Annamalai 2012) and upper-level westerly jet (e.g., Schiemann et al. 2009), we used a collection of different large-scale circulation indices that primarily describe circulations associated with these two systems (Table 1). Variations in these large-scale indices were then correlated with the different components of the atmospheric moisture transport and the atmospheric moisture budget.

Four of these indices are linked to the upper-level westerly circulation: The jet intensity (a) in Table 1 describes the maximum daily wind speed between 100 hPa and 500 hPa (computed as in Schiemann et al. 2009, ). The jet latitude (b) refers to the latitudinal position of this maximum. We also compute the same intensity and latitude parameter (c, d) for the upper-level wind circulation above the TP, assuming that the effect of the mountains on the westerly flow plays a crucial role in forming upper-level troughs and ridges, thereby influencing the lower levels of the atmosphere in the downwind region. In addition to the westerly-related indices, we use three broad-scale monsoon indices, namely the Indian summer monsoon index (ISM), the Webster-Yang index (WYI) and the Wang index (e-g) to represent the southern component of the Asian summer monsoon (Goswami et al. 2006) and the West North Pacific Monsoon index (WNPM) to represent the eastern component of the Asian summer monsoon (Wang et al. 2020). Most of the monsoon indices are based on the horizontal wind shear of zonal winds at 850 hPa (Table 1). In contrast to that, the ISM is based on vertical wind shear of the meridional wind because it assumes that the monsoon circulation is primarily manifested through the Hadley cell and driven by large-scale contrasts in diabatic heating (Goswami et al. 2006). We calculated all indices based on the wind fields in ERA5 assuming that WRF\(_{9km}\) inherits the main large-scale features from ERA5, both through at the lateral boundaries and through the applied spectral nudging technique. A monthly time series representing both the interannual and intra-seasonal variability of the indices is presented in Appendix 19. It should also be noted that the different indices are not independent and their correlations are shown and briefly discussed in Appendix 20.

3 Results

3.1 Climatological atmospheric moisture budget

To set the context for the analysis of moisture transport around the TP, we start by examining the atmospheric moisture budget components for the climatological summer season in ERA5 and WRF\(_{9km}\) (Fig. 2). Over large regions, including the TP and the Indian subcontinent, precipitation and evaporation are lower in WRF\(_{9km}\), which causes a more pronounced west-to-east gradient over the TP compared to that in ERA5. This points towards a less active water cycle in WRF\(_{9km}\), which is consistent with the fact that regional WRF simulations tend to reduce the well-known wet bias of ERA5 over the TP (e.g., Prein et al. 2022; Ou et al. 2023).

WRF\(_{9km}\) exhibits more small-scale structures and therefore shows some regions with higher precipitation and evaporation in the downwind region east of the TP. The spatial patterns of precipitation and evaporation also reflect the better-resolved topography in WRF\(_{9km}\) compared to ERA5. For example, the spatial patterns of evaporation closely follow the elevational gradient around the Sichuan basin at the eastern edge of the TP (\(\sim \)102\(^\circ \)E -105\(^\circ \)E in Fig. 2, see also Fig. 1). Over the TP mountains and along the Himalayan foothills, the spatial patterns of precipitation, evaporation and P-E are much more heterogeneous in ERA5 compared to WRF\(_{9km}\) which could be linked to hampered moisture fluxes from the south through the mountain barrier in WRF\(_{9km}\)Lin et al. (2018).

In terms of convergence zones, WRF\(_{9km}\) and ERA5 show the same regions with positive P-E (which corresponds approximately to zones of moisture convergence; Eq. 1), but with considerably smaller values over the Bay of Bengal and the Indian subcontinent in WRF\(_{9km}\) (Fig. 2). This is mainly caused by the smaller amounts of precipitation in WRF\(_{9km}\) rather than by higher amounts of evaporation. The divergence zones (negative P-E) over the ocean west of India and in the drying northwest of the TP show similar spatial patterns and magnitudes in WRF\(_{9km}\) and ERA5.

Fig. 2
figure 2

Atmospheric moisture budget components for June–August 1980–2019 in ERA5 and WRF\(_{9km}\): Mean precipitation \(\overline{P}\), mean surface evaporation \(\overline{E}\) and water availability expressed as \(\overline{P}\) - \(\overline{E}\). Given that \(\overline{P}\) - \(\overline{E}\) corresponds approximately to the vertically integrated horizontal moisture flux convergence (\(\nabla \int {q \overrightarrow{V}}\)), the blue regions in the lower panels indicate regions of moisture convergence, whereas the red regions indicate regions of moisture divergence

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According to Eqs. 1 and 2, monthly or seasonal precipitation is inherently linked to surface evaporation and the mean flow and eddy components of horizontal moisture flux divergence. Figures 3 and 4 demonstrate to which extent each of these three components explains the month-to-month precipitation variability in ERA5 (upper panels; turquoise) and WRF\(_{9km}\) (lower panels; blue). Figure 3 shows scatter plots and correlation coefficients of monthly surface precipitation anomalies related to monthly anomalies in mean flow divergence, eddy divergence, and surface evaporation averaged over the entire domain. The anomalies in the mean flow of moisture flux divergence show a strong positive correlation with anomalies in monthly precipitation anomalies, indicating that the mean flow component of moisture transport is the dominating factor in precipitation variability in both WRF\(_{9km}\) and ERA5. Anomalies in surface evaporation are also positively correlated to precipitation. This means that more precipitation is associated with more evaporation in both datasets, but the correlation is only statistically significant for WRF\(_{9km}\) (Fig. 3). By contrast, anomalies in eddy divergence are negatively correlated with precipitation anomalies and this correlation is stronger in WRF\(_{9km}\). Notice that the negative correlation between precipitation and eddy divergence anomalies does not mean that higher monthly precipitation is generally associated with weaker turbulent transport. This is because the total eddy divergence averaged over the entire domain is negative in most summer months, which in turn reflects that the eddy transport is primarily responsible for the moisture transport outside of the domain or in other words from the tropics towards higher latitudes.

Figure 4 shows the same scatter plots as in Fig. 3 but averaged over the downwind region (see box in Fig. 1). The monthly anomalies of the mean flow moisture flux divergence still show a strong correlation to monthly precipitation anomalies in ERA5 on a regional scale. For WRF\(_{9km}\), this correlation is much weaker compared to ERA5 and compared to the correlation between precipitation and mean flow divergence anomalies for the entire domain (Figs. 4, 3). The correlation between eddy divergence and precipitation anomalies is statistically significant for ERA5 but only weak and not statistically significant for WRF\(_{9km}\) (Fig. 4). There is almost no correlation between surface evaporation and precipitation anomalies on the regional scale, highlighting again the importance of moisture transport rather than evaporation for precipitation variability in the downwind of the TP.

Fig. 3
figure 3

Scatter plots and Pearson correlation coefficients showing the relationship between precipitation, surface evaporation, mean flow divergence, and eddy divergence for ERA5 (turquoise) and WRF\(_{9km}\) (blue). The data points represent monthly anomalies with respect to the climatological value of the respective month (e.g. June\(_{2000}\) minus June\(_{1980-2019}\)) averaged over the entire model domain in WRF and over the corresponding region (\(\sim \) 10 \(^\circ \)N-50 \(^\circ \)N and \(\sim \) 60 \(^\circ \)E-130 \(^\circ \)E) in ERA5

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Fig. 4
figure 4

Same as in Fig. 4 but for the focus region in the downwind of the TP (28 \(^\circ \)N-43 \(^\circ \)N and 100 \(^\circ \)E-120 \(^\circ \)E)

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3.2 Mean flow and eddy moisture transport

3.2.1 Spatial patterns and relative importance

The preceding section showed that precipitation variability at a monthly scale is only weakly correlated with the eddy horizontal moisture flux divergence in the downwind of the TP (correlation coefficient R=0.3 for ERA5; Fig. 4). This reflects the negative net effect of eddies in the downwind of the TP due to the role of eddies in carrying moisture out of the region. It does, however, not imply the absence of eddy flux convergence nor that eddies do not play any significant role in mean moisture transport and precipitation anomalies. To further investigate the importance of eddy transport for the climatological mean moisture transport, we analyze the spatial patterns and the relative contributions of mean flow and eddy transport in this section.

Figure 5 shows maps of the total vertically integrated moisture transport (IVT= \(\sqrt{qu^2 + qv^2}\)) divided into its mean flow and eddy components at different temporal scales. This allows us to identify regions wherein turbulent transport is critical in addition to the regions of convergence and divergence that were shown in Fig. 2.

The mean flow transport over land is largest at latitudes below 30\(^\circ \) and gradually decreases towards the higher latitudes (Fig. 5). It primarily affects the study region through the moisture influx through the southern boundary which is approximately the boundary between the tropics and mid-latitudes. The eddy transport at multi-daily scales (here: between 10-daily and 5-daily) is less pronounced compared to daily and sub-daily time scales. An interesting feature is the dominant role of the eddy transport derived from hourly deviations (Eq.. 3; including the temporal scales from hourly to daily) along the eastern edge of the TP. Both the downwind region east of the TP and the southwest of the Himalayas exhibit larger magnitudes for eddy transport, suggesting that the TP barrier is an important factor in sub-daily transient transport near the TP. This could, for instance, be explained by the occurrence of mountainous weather systems such as TPVs (Curio et al. 2019), eastward propagating convective systems (Kukulies et al. 2021) or western disturbances (Hunt et al. 2018). However, since many processes can influence humidity, wind flow and the consequent precipitation in the downstream region of the TP, future studies are needed to connect the mean flow and eddy moisture components with specific weather systems.

The magnitude and general spatial patterns of both the mean flow and eddy transport in the downwind region are similar between ERA5 and WRF\(_{9km}\). The largest difference between the data sets is the lower total moisture transport over the central TP in WRF\(_{9km}\). This is most notable in both the mean flow and sub-daily to daily components of the moisture transport and suggests not only that WRF\(_{9km}\) has a generally lower moisture transport over the TP, but also that the spatial patterns of mean flow and eddy components are different. This can have many reasons since the wind and humidity fields in the high-resolution model can be affected by a variety of mesoscale processes. But even if the moisture transport outside of the TP would be similar, a possible reason for the lower moisture transport over the TP could be the reduced influx through the southern boundary due to a better-resolved topography in higher-resolution simulations, as has been discussed by (Lin et al. 2018). However, we also confirm that the mean flow and eddy moisture fluxes from the south to the downwind regions are lower WRF\(_{9km}\) than in ERA5 which shows that the reduced moisture transport is not only prevalent over the TP (Appendices 17, 18).

Fig. 5
figure 5

Maps of the vertically integrated moisture transport (IVT = \(\sqrt{qu^2 + qv^2}\)) computed based on monthly, 5-daily, daily and hourly values for humidity and wind fields. The upper panels represent the IVT mean flow component while the lower panels represent the eddy components for different time scale bins (see eq. 3) in ERA5 and WRF\(_{9km}\) for June-August 1980 – 2019. Notice that the color bar scales are different for mean flow and eddies due to the dominance of the mean flow that would mask spatial patterns of the eddy transport. The black box marks the study region (28 \(^{\circ }\)N-43 \(^{\circ }\) and 100 \(^{\circ }\)E-120 \(^{\circ }\)E).)

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Fig. 6
figure 6

Maps showing the relative contributions of mean flow (upper panels) and eddy (lower panels) components to the total vertically integrated moisture transport (IVT = \(\sqrt{qu^2 + qv^2}\)) for ERA5 and WRF\(_{9km}\). Notice that different color bar scales are used for mean flow and eddies to highlight the regions downwind of the TP that have eddy contributions up to 40% at certain locations of the total transport

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Figure 6 shows the relative contribution of the mean flow and total eddy transport to the climatological mean transport in different regions. Here, it can be seen that the eddy transport is not only most important in the east of the TP, but that it contributes up to 40 % to the total climatological mean transport in some locations. This is an important finding because it implies that variations in the underlying weather systems that are responsible for the eddy transport can significantly change the total moisture transport in a season. The same is true for the TP itself which exhibits higher relative contributions of eddies compared to its surroundings. Although the overall moisture transport over the TP is significantly lower compared to its downwind regions, this suggests that resolving mesoscale processes that are linked to the eddy transport over the high mountains is important for modeling the water cycle of the TP. Figure 6 also suggests that the mean flow component of moisture transport is least important over the central-eastern TP. This could mean that the high occurrence of smaller-scale convective systems (Kukulies et al. 2021) and local moisture sources such as soil moisture (Barton et al. 2021) and evapotranspiration in these regions play a more crucial role in the total moisture transport than what is controlled by the mean circulation. The analysis of eddy transport provides a complementary perspective of the role of local moisture recycling over the TP that has been addressed by others (e.g., Zhang et al. 2023; Tang et al. 2023).

The relative contributions of mean flow and eddy transport averaged over the entire study region and the temporal spectrum of eddy transport approximated by the chosen time scales are visualized in Fig. 7. The bars in the upper panel show that the mean flow transport contributes about 80 % to the total vertically integrated moisture transport (IVT), whereas the eddy transport contributes about 20 % to the latter (Fig. 7).

While the maps of mean flow and eddy transport showed a few more small-scale structures in WRF\(_{9km}\) in Fig. 5, the domain-averaged relative contributions to the total moisture transport and the month-to-month variability (indicated by the error bars) are similar between WRF\(_{9km}\) and ERA5 (Fig. 7). This disproves our hypothesis that the finer spatial resolution in WRF\(_{9km}\) could significantly change the magnitude and contributions of eddy moisture transport by resolving mesoscale processes and surface features that are not well represented in ERA5. A possible explanation for the small differences between WRF\(_{9km}\) and ERA5 is that the gray-zone resolution of 9 km in WRF is still not sufficient to resolve processes and feedbacks of convective systems that influence the moisture transport.

The lower panel in Fig. 7 depicts the absolute values (markers) and relative contributions (bars) of the different eddy time scales that together make up the total eddy moisture transport averaged over the study region. The markers correspond to the eddy component as derived from equation 2 with the primes being calculated at the denoted time scale. The total area-averaged eddy IVT (right y-axis) increases with decreasing temporal scales because the smallest temporal scale (here: hourly) is equal to the total eddy moisture transport and contains thus the information of turbulent transport at the other temporal scales superimposed onto the hourly scale. The difference between the temporal scales becomes smaller as the curve converges towards smaller scales, which means that not much information is added from e.g. 6-hourly to hourly scales. The bars, in contrast, reflect the differences between each time scale and correspond to the relative contribution of a certain time scale bin to the total eddy transport (see eq. 3). The relative contributions in % are consistent with the slopes of the absolute IVT values (see the line that connects the markers), where a steeper slope corresponds to a higher contribution of a certain time scale bin to the total eddy transport.

Figure 7 shows that the eddies calculated from 10-daily and daily averages contribute most to the total eddy moisture transport. Again, these time scales reflect bins of the time scale spectrum rather than discrete scales, which implies that the time scale ranges between monthly and 10-daily and between 3-daily and daily are the bins that dominate the eddy transport in the study region. On the sub-daily scales, the relative contributions become steadily smaller and the difference between 3-hourly and hourly contributions is almost negligible.

While the differences between the relative contributions of individual time scale bins can be partly explained by their different bin width (e.g., daily to 3-daily vs. hourly to 3-hourly), they also offer a few interesting insights about the time spectrum of eddy transport. First, there is a rather abrupt increase in relative and absolute eddy transport from 3-daily to daily which suggests that different atmospheric processes occur at these two time scales. A potential weather system that often prevails for multiple days is the TPV (Curio et al. 2019) which can trigger but is different from convective organization east of the TP which is more short-lived (Kukulies et al. 2023). The highest relative contributions (> 20%) are from 10-daily and daily time scales which separate synoptic (e.g. fronts, baroclinic waves) from mesoscale atmospheric processes (convective organization, diurnal variations) that affect the eddy transport. Considering multiple time scales together, it is noticeable that the multi-daily (10-daily to 3-daily) scales contribute about 50 % to the total eddy transport, whereas the other 50 % can solely be explained by the daily to sub-daily scales. This highlights the importance of both daily to sub-daily scales as well as more synoptic scales as major components that influence the total eddy transport.

Fig. 7
figure 7

Upper panel: Relative contributions of mean and eddy components of the time-and area-averaged vertically integrated moisture transport (\(\widehat{IVT}\) = \(\widehat{\sqrt{qu^2 + qv^2}}\)) in ERA5 and WRF\(_{9km}\). Lower panel: Absolute and relative contributions of eddy moisture transport at different time scales, where the plotted line and markers indicate the absolute values of the vertically integrated eddy moisture transport (\(\widehat{IVT}\) eddy) as calculated from the respective time scale (left y-axis). The bars show the relative contributions of the different time scales to the total eddy transport (right y-axis). The error bars denote the inter-annual and intra-seasonal monthly variability. )

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3.2.2 Sub-seasonal variability

The error bars in Fig. 7 suggest that the mean flow and eddy transport contributions can vary by about 20 % between individual months or years. Therefore, we briefly discuss the sub-seasonal variability of the mean flow and eddy transport in this section. Figures 8, 10, 9 show the anomalies of individual summer months (June, July, August) with respect to the summer mean flow and eddy transport. The strongest eddy transport in the study region occurs in June (Fig. 8), whereas the strongest mean flow transport occurs in July (Fig. 9). In June, the mean flow through the southern boundary and the eddy transport across the entire region are enhanced as the South Asian summer monsoon begins to extend to the north. The mean flow transport in the northern parts of the downwind area shows negative anomalies with respect to the entire summer season, and the moisture transport out of the area is consequently small (Fig. 8). In July, this pattern is flipped, and the eddy transport across the area shows a negative anomaly, whereas the mean flow transport is now enhanced across the entire region as opposed to just the southern boundary (Fig. 9). In August, the mean flow and the eddy transport show negative anomalies across the downwind region, indicating that the moisture transport associated with the monsoon systems dissipates again (Fig. 10).

Fig. 8
figure 8

Anomalies of mean flow and eddy moisture transport for June with respect to the summer climatology (Jun–Aug 1980 – 2019). Blue regions indicate a positive anomaly (greater moisture transport ) for June, while the red regions indicate a negative anomaly (less moisture transport ). The line plots to the left of the maps indicate the climatological zonal moisture transport (solid line) compared to the zonal moisture transport in June (dashed line) for the respective data set and time scale

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Fig. 9
figure 9

Similar as in Fig. 9, but for July

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Fig. 10
figure 10

Similar as in Fig. 10, but for August

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3.2.3 Linkage to large-scale circulation

The previous section showed that there is sub-seasonal variability in both the mean flow and eddy transport components. In this section, we explore to which extent the variability of the eddy transport might be related to the strength of the mean flow component and prevailing large-scale systems. Using the large-scale circulation indices presented in Table 1, we aim to understand the correlations between the components of the climatological mean moisture transport and different large-scale atmospheric circulation systems. The correlation matrices in Figs. 11 and 12 show the Pearson correlation coefficients (and their significance at the 95 % level indicated by the asterisk) for the time series of summer mean flow and eddy transport components correlated with the summer mean large-scale circulation indices and moisture budget components (precipitation and evaporation) for each year. The correlation analysis was performed for the entire summer season rather than individual months because both the moisture transport and most of the large-scale circulation indices follow a pronounced sub-seasonal cycle (see the previous section and Appendix 19) which would dominate the correlation signal.

Mesoscale convective systems (MCSs) could be one of the weather systems at sub-daily to daily scales that influence eddy moisture transport. Therefore, we also show the relationship of the moisture transport components to the average occurrence frequency of MCSs from a satellite-derived tracking database described in Kukulies et al. (2021). The upper panels in Figs. 11 and 12 show the mean flow and eddy components of the southerly moisture influx to the study region, and the lower panels refer to the spatially integrated total moisture flux convergence. The southern boundary is located at latitude 28\(^{\circ }\)N and represents thus the water vapor from the tropics to the higher latitudes. The focus on the southern boundary in this analysis is motivated by the fact that it is the most active boundary for moisture inflow both for the mean flow and eddy transport (Fig. 5). In fact, it is the only boundary that shows positive eddy moisture influxes, whereas all other boundaries are dominated by the outflow of eddy moisture transport during summer (see Figs. 17 and 18 in the Appendix for the climatological moisture fluxes through the boundaries).

Fig. 11
figure 11

Correlation heat map for mean flow and eddy components of total southerly moisture influx (upper panel) and spatially integrated total moisture flux convergence (lower panel; MFC) in ERA5 related to large-scale circulation indices, precipitation, evaporation, and MCS frequency. The asterisks indicate correlations with p-values < 0.05 (meaning that these are statistically significant at the 95 % level)

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Fig. 12
figure 12

Same as in Fig. 11, but for WRF\(_{9km}\)

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Figure 11 reveals that the WNPMI, representing the East Asian summer monsoon component (Table 1), shows the highest correlation to the mean southerly influx and mean moisture flux convergence among all large-scale circulation indices. The correlation between the WNMPI and the mean flow is negative, implying a higher mean flow for a weaker East Asian monsoon circulation. The indices representing the South Asian monsoon (WYI, Wang, and ISM) show considerably smaller correlations to the mean flow but are instead positively correlated with the southerly mean inflow. These results indicate the concurrent effects of the South and East Asian monsoon components on the moisture supply in the downwind of the TP. A question that arises from this finding is how these concurrent effects will change in a warmer climate. It has, for instance, been suggested that there will be an increased variability of the West North Pacific subtropical high (Yang et al. 2022). We show here that this change could imply an increased variability in the mean flow transport and consequently precipitation and convection as both the mean flow moisture transport from the south and the mean moisture flux convergence are positively correlated to mean precipitation and mean MCS frequency (Fig. 11).

The cross-TP jet latitude, WYI, and Wang (Table 1) are negatively correlated to the eddy southerly inflow at daily to sub-daily time scales, which suggests that these large-scale systems influence weather systems associated with turbulent transport rather than multi-daily synoptic systems. The correlation between the cross-TP jet latitude and the eddy moisture influx is particularly interesting because it indicates that more moisture is transported towards the study region when the maximum of the upper-level zonal winds over the TP is located closer to the equator (Fig. 11). This finding is consistent with Kukulies et al. (2023) who demonstrated that a strong positive anomaly of southerly moisture influx that was associated with a flood-producing MCS case was influenced by the jet dynamics and a mesoscale disturbance over the TP. Since it is well-known that TPVs are transported and modulated by the westerly jet (e.g., Curio et al. 2019), the findings of this paper together with Kukulies et al. (2023) suggest that interactions between the mesoscale disturbances transported by the westerly jet could be an important determining factor for how far north moisture provided by the monsoon systems is transported in the downwind of the TP. Variations in the interactions between the westerly circulation and monsoon need to be further studied to understand their impact on variations in continental moisture supply and distribution of convective systems. While earlier generations of CMIP models have partly projected strengthening of the South Asian summer monsoon Turner and Annamalai (2012), a large portion of the more recent CMIP5 and CMIP6 simulations project a weakening of the Asian summer monsoon (Sooraj et al. 2015; He et al. 2023) together with a northward shift in the extratropical westerly circulation (Lee et al. 2021). In the context of climate change, our analysis suggests that such changes will not only modulate the mean flow moisture transport but also the eddy transport that in turn might be more important for precipitation extremes.

The correlations between large-scale indices and the moisture transport and moisture budget components in WRF\(_{9km}\) are generally much smaller than ERA5. Although the WRF simulation is driven by and nudged to ERA5, this shows that the feedback of mesoscale processes in the higher-resolution simulations significantly affects the moisture transport and budget components. This should be considered in future simulations that serve the purpose of studying the effect of the large-scale circulation on moisture transport at different scales.

A caveat of this study is that we focus on linear relationships between the large-scale atmospheric circulation and the moisture transport components. The eddy moisture transport may be linked to large-scale atmospheric features through non-linear relationships, e.g. when the large-scale atmospheric circulation modifies moisture availability and atmospheric stability or when eddy moisture transport is associated with convection over land that modifies the large-scale atmospheric circulation through latent heating or cloud radiative effects. To disentangle such processes, it is a crucial step for the future to investigate the role of eddy moisture transport in convective organization over land.

4 Implications for convection and precipitation

While our results confirm that the position of the jet over the TP is linked to daily and sub-daily eddy transport from the south, the eddy inflow exhibits a negative correlation to MCS frequency and no significant correlation to precipitation or evaporation (Fig. 11). In contrast to the eddy inflow, the mean inflow through the southern boundary is positively correlated to MCS frequencies (Fig. 11). Moreover, a higher MCS frequency is also associated with a stronger eddy moisture flux divergence across the downwind region (Fig. 11).

Given that the mean flow transport dominates the total climatological mean transport (Fig. 7) and precipitation anomalies (Fig. 4), the relationship between eddy transport and MCSs and precipitation might thus be masked when the eddy transport itself is also influenced by the magnitude of the mean flow transport. The scatter plots in Fig. 13 show the relationship between the ERA5 mean flow and eddy components of moisture transport, precipitation, and MCS frequency. It can be seen that in addition to the positive correlation between mean flow and precipitation and MCSs, the magnitude of the mean flow and eddy components of both southerly moisture influx and divergence depend on each other such that the eddy inflow is stronger for a weaker mean flow (Fig. 4a,c). In addition, more moisture diverges from the region through eddies when the mean flux convergence is higher (Fig. 4b,d). However, there are also several months with high precipitation amounts (> 8 mm hr\(^{-1}\)) with moderate mean inflow but higher eddy inflow (Fig. 4a). This suggests that eddy transport can still play a significant role in regional precipitation, not only for single events but also for the monthly mean.

Fig. 13
figure 13

Scatter plots of the monthly mean flow and eddy components of southerly moisture influx (a, c) and total moisture flux convergence (b, d) in the lee of the Tibetan Plateau. The shading shows the monthly mean precipitation and MCS frequency over the same region, where MCS frequency refers to the total number of large and deep cloud areas detected in hourly satellite data of that month (i.e. clouds that persist for multiple timesteps are counted for each timestep)

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5 Summary and conclusions

In this study, we investigated mean flow and eddy components of moisture transport in the downwind region of the Tibetan Plateau using 40 years of ERA5 reanalysis and a dynamically downscaled climate simulation with WRF. We further decomposed eddies into different temporal scales to investigate the role of more multi-daily, more synoptic systems vs. sub-daily smaller-scale systems. We also related the moisture transport components to large-scale circulation indices, the atmospheric moisture budget, and MCS activity.

Turning back to the research questions posed at the beginning of this paper, the main conclusions from the presented analysis can be summarized as follows:

  1. 1.

    Mean flow and eddy moisture transport: Monthly precipitation anomalies in the study region are primarily associated with anomalies in the mean flow rather than anomalies in evaporation or eddy transport. This is true for both ERA5 and WRF\(_{9km}\), but ERA5 shows a higher correlation between evaporation and precipitation than WRF\(_{9km}\). Mean flow moisture transport contributes about 80 % to the total vertically integrated moisture transport in the study region, whereas eddy transport stands for the remaining 20 %. This is consistent in both ERA5 and WRF\(_{9km}\), with WRF\(_{9km}\) showing a slightly higher month-to-month variability in these components. Eddy moisture transport can contribute with up to 40% to the climatological mean transport in certain locations downwind of the TP. This suggests that the moisture transport in this region is to a higher degree influenced by synoptic to mesoscale disturbances than its surroundings. Multi-daily scales contribute 50 % to the eddy transport, and daily to sub-daily scales contribute \(\sim \) 50 % to the total eddy transport. Eddy transport between 3-daily and daily scales makes up the largest contribution to the total eddy transport among the studied time scale bins.

  2. 2.

    Linkage to large-scale circulation and moisture budget components: The West North Pacific Monsoon Index (WNMPI) showed the strongest correlation to the mean flow moisture transport from the south to the study region, with a larger mean inflow being associated with a weaker WNMP circulation. In addition, the latitude of the jet maximum over the TP and the South Asian summer monsoon is negatively correlated with downwind eddy divergence and moisture inflow from the south at daily and sub-daily scales. This implies an enhanced southerly eddy inflow, but a weaker eddy divergence when the jet is located closer to the equator and when the South Asian monsoon circulation is less strong. Conversely, a stronger eddy flux divergence and weaker eddy inflow through the southern boundary are associated with a more northern jet latitude. An enhanced mean flow through the southern boundary is positively correlated with mean precipitation and higher MCS frequencies in the study region, whereas an enhanced eddy inflow through the southern boundary is associated with the opposite. The absent effect of enhanced eddy moisture influx on regional precipitation and convection could be related to the dominance of the mean flow transport and the associated weaker eddy moisture influx when the mean flow component is stronger.

  3. 3.

    ERA5 vs. WRF \(_{9km}\): The spatial patterns, magnitude, and relative contributions of both the mean flow and eddy transport are similar between ERA5 and WRF\(_{9km}\). This suggests that downscaling the ERA5 data from \(\sim \)30 km to 9 km does not significantly change the components of the moisture transport although the WRF simulation exhibits more small-scale features. The differences are larger over the TP, which suggests that the effect of topography on moisture transport plays a role for the moisture transport into the TP rather than for the moisture transport on the downwind side. WRF\(_{9km}\) showed in general much weaker correlations between the moisture transport and large-scale circulation indices which highlights the feedback of mesoscale processes in the high-resolution model that decouples regional moisture transport from the large-scale forcing.