cycle have to be adequately represented. Physical processes characterizing the interactions between local circulation and the thermodynamic environment of convection, especially those that remain under-resolved by global storm-resolving models-including boundary layer turbulence and thermodynamics, local circulation patterns at mountain-valley scales, as well as microphysics-are critical. Orographically-locked precipitation, in addition to being an important phenomenon on its own, can provide a natural laboratory for studying convection where the updrafts and precipitation tend to occur frequently in a particular location. This can facilitate both modeling and potentially the design of field campaigns to examine the inflow of environmental air into the region of active deep convection.

Taiwan, a tropical island with complex topography, is an optimal region to study diurnal convection over complex topography. During summertime, when synoptic-scale weather systems are inactive, rainfall is dominantly produced by diurnal convection (Wang & Chen, 2008). Diurnal convection frequently occurs over specific hotspots on the terrain of Taiwan (Huang et al., 2016;Kuo & Wu, 2019;Lin et al., 2011) when the environmental conditions favor the development of local circulation (land-sea-mountain-valley breeze). Figure 1 displays the conditional probability of summertime diurnal rainfall under weak southwesterly or weak synoptic events classified by the Taiwan Atmospheric Events Database (S.-H. Su et al., 2018). Notable clusters of hotspots can be identified over the northern tip of the Central Mountain Range (magenta box in Figure 1; denoted NCMR hereafter) and the Alishan Mountain Range (southwestern mountains in Taiwan). This prominent feature provides an opportunity to investigate the primary physical processes for the evolution of boundary layer and local circulation associated with orographically-locked diurnal convection over complex topography.

The supply of moisture and energy from the lower troposphere is crucial to the occurrence and maintenance of deep convection (Holloway & Neelin, 2009;Schiro et al., 2016;Tian et al., 2021;Zhang & Klein, 2010). Recent observations identified a typical updraft mass flux structure-for both organized and isolated deep convectionthat indicates substantial entrainment of environmental air into the updraft throughout a deep lower-tropospheric layer (Savazzi et al., 2021;Schiro et al., 2018). Such a "deep-inflow" structure implies that the lower-tropospheric layers approximately contributed equally to the estimated conditional instability, consistent with the weighting profile inferred from the observed precipitation-buoyancy relation (Ahmed & Neelin, 2018). The entrainment of environmental air can occur via a coherent inflow or small-scale turbulent mixing (Schiro et al., 2018). The coherent inflow contribution to the dynamical entrainment can be induced by the secondary circulation of organized mesoscale convective systems (Nowotarski et al., 2020) or the local circulation along with boundary layer development (land-sea-mountain-valley breeze).

In regions with complex topography, the path of the inflow associated with diurnally driven convection is often constrained (Barry, 2008;Houze, 2012). Here we hypothesize that the local circulation upon the terrain-constrained inflow path can further augment convection development, strengthening convective activity. This study aims to quantify the importance of the coherent inflow-layer contribution to the convective updraft for orographically-locked diurnal convection in Taiwan. To identify key physical processes, we conduct an ensemble of large-eddy simulations (LESs) implemented with realistic, high-resolution topography of Taiwan, subject to weak synoptic conditions favorable for the development of diurnal local circulation. This manuscript is organized as follows. Section 2 reveals the simulation configuration details and how the deep-inflow features are identified and analyzed. The analysis for diurnal convection over complex topography is presented in Section 3, including the convective updraft structure and the circulation pattern of moist static energy (MSE) transport. Section 4 discusses the preliminary observational results of the deep-inflow layer from the initial field measurements guided by the analysis of the LESs. The discussion and summary are in Section 5.

For this study, we used the vector vorticity equation cloud-resolving model (VVM; Jung & Arakawa, 2008) with high-resolution Taiwan topography and land-use types, named TaiwanVVM (Wu et al., 2019). The horizontal resolution is 500 m and the domain size is 512 km × 512 km. The length of the simulations is 24 hr, starting from 00:00 (i.e., midnight) through 24:00, which is tied to the local insolation cycle. Since the land-atmosphere coupling is noted to be an essential component for convective development in TaiwanVVM, the Noah land surface model (Noah LSM; F. Chen & Dudhia, 2001;F. Chen et al., 1996) version 3.4.1 is coupled to the model; The top soil layers for all land grids are initialized using the daily average soil moisture over the island of Taiwan from the Global Land Data Assimilation System (GLDAS; Rodell et al., 2004) version 2.0. In the VVM formulation the pressure gradient force is eliminated, and the vorticity field-driven by horizontal buoyancy gradient-directly responds to surface fluxes. This makes TaiwanVVM advantageous to simulate local circulation driven by differential surface heating over complex, steep topography; aerosol effect on diurnal convection (Chang et al., 2021); and air pollutant transport affected by lee vortex and boundary layer development (Hsieh et al., 2022;Hsu et al., 2023).

The TaiwanVVM LES ensemble analyzed here has been documented in Chang et al. (2021). The ensemble consists of 30 cases selected to cover the environmental variability of the summertime weak synoptic weather regime that favors local circulation development. The observed soundings are simplified as the uniform initial condition over the entire domain, commonly used in LESs (e.g., Grabowski et al., 2006), to emphasize the decisive environmental factors that modulate the development of convection, while the ensemble members represent the variability of these environmental factors. In such a "semi-realistic" approach, the evolution of local circulation and convection is dominated by interactions among physical processes.

The magenta box in Figure 1 is selected to focus on precipitation hotspots. We impose criteria on the rain rate and vertical velocity to ensure the sampling of deep convective columns over precipitation hotspots. Each ensemble Figure 1. The topography of Taiwan (gray shading) and conditional probability (colored dots) of summertime diurnal rainfall under the weak synoptic or weak southwesterly events. To find the days with a prominent diurnal precipitation cycle, only the days with precipitation in the afternoon greater than that in the morning and with the peak rainfall occurring in the afternoon are selected. The threshold of the hourly accumulated rainfall is at least 0.5 mm. The precipitation is from the Central Weather Bureau hourly rain gauge data from 1993 through 2020 (Data Bank for Atmospheric and Hydrologic Research, 2023). For visual clarity, the area of colored dots is proportional to the probability. The magenta box marks the northern end of the Central Mountain Range area (NCMR) on which subsequent analyses are focused. member's 99th percentile of the rain rate in the NCMR area is defined as the critical rain rate of that simulation. The largest contiguous grids that once experienced rainfall greater than the critical rain rate of its simulation would be determined as the precipitation hotspot. Inside the precipitation hotspot, atmospheric columns with a mean vertical velocity between 3 and 10 km greater than 1 m s -1 are further identified as deep convective columns. This criterion upon vertical velocity is less strict than those in Schiro et al. (2018), so the precipitating columns with mild low-level downdraft can still be included, preserving the simultaneous existence of precipitation and upward motion in general. In all 30 semi-realistic ensemble members, 25 simulations have wide enough deep convective columns in the NCMR area, whose critical rain rates range from 15.16 to 74.99 mm.

Aside from identifying deep convective columns through rain rate and vertical velocity, distinguishing the surroundings of deep convective columns further helps us to conceptualize the deep-inflow mixing of deep convective columns over complex topography. To diagnose the buoyancy characteristics of deep convective columns, we define the environment of the precipitation hotspot. It is a square area centered at the centroid of the precipitation hotspot, whose side length is six-fold the effective radius of the precipitation hotspot. Furthermore, we determine the cross-section profile of the deep-inflow by the upstream vector to explore the circulation patterns of deep convective columns and their deep-inflow. The upstream vector is defined as the mean integrated vapor transport in the environment of the precipitation hotspot below 2 km and within 2 hr before rain initiation.

The buoyancy of deep convective columns can contribute to the tendency of vertical velocity. It is calculated from

, where g is the gravitational acceleration, θ v is the virtual potential temperature of deep convective columns, and θ v,env is the mean virtual potential temperature of the environment. The convective mass flux of deep convective columns can be translated from vertical velocity, representing the upward transport of air mass. It is calculated from m = ρσw, where ρ is the mean air density of deep convective columns, σ is the fraction of deep convective columns covered by updrafts, and w is the mean vertical velocity of deep convective columns.

In this section, we examine orographically-locked diurnal convection using the deep-inflow mixing framework following Schiro et al. (2018). The convective updraft mass flux profile provides evidence for deep-inflow mixing. Thus, the analyses of convective structures are displayed. Since diurnal convection is orographically-locked, the deep-inflow can be analyzed in the physical space relative to a specific deep-inflow path. The concept of deep-inflow mixing is further extended to characterize the upstream MSE transport via local circulation. Schiro et al. (2018) depicted an increasing convective mass flux with height in the lower troposphere, indicating the characteristic of deep-inflow mixing. The buoyancy, vertical velocity, and convective mass flux profiles of deep convective columns in all simulations are illustrated in Figures 2a-2c (black lines), representing the convective structures. The profiles of these deep convective columns have a common shape with substantial variability in updraft intensity. The mean buoyancy of deep convective columns is positive between 0.45 and 10.73 km, reaching its peak of 2.62 × 10 -2 m s -2 at 5.22 km. Since buoyancy represents the tendency of vertical motion, we suppose an accelerated updraft with height inside deep convective columns, and the peak of the mean vertical velocity appears at a higher altitude than the mean buoyancy. As expected, the mean vertical velocity of deep convective columns increases with height, reaching its peak of 3.80 m s -1 at 6.23 km. The convective mass flux, which is related to the mean vertical velocity and the updraft fraction in deep convective columns, also shows an increase with height in the lower troposphere. The mean convective mass flux of deep convective columns reaches the peak of 1.95 × 10 2 g m -2 s -1 at 5.53 km. Since deep convective columns usually occur over topography higher than 1.6 km, the vertical structure at low levels could be influenced by the terrain, showing values of approximately zero. The increasing convective mass flux with height in the lower troposphere, providing positive buoyancy, indicates a deep layer of environmental air flows into the updraft of deep convective columns.

The deep-inflow mixing reveals the influence of the environment on convection. Thus, the influence function is utilized to quantify the contribution from different layers. The formulation of the influence function can be approximated by 𝐴𝐴 𝐴𝐴(𝑧𝑧𝐵𝐵, 𝑧𝑧) = 1 𝑚𝑚(𝑧𝑧 𝐵𝐵 )

𝜕𝜕𝑧𝑧 (Schiro et al., 2018), which is the vertical rate of change for convective mass flux normalized by the convective mass flux of the reference level (z B ). This approximation is valid only for 𝐴𝐴 𝜕𝜕𝜕𝜕(𝑧𝑧) 𝜕𝜕𝑧𝑧 > 0 , provided there is no detrainment. For the height of the maximum convective mass flux (z B = 5.53 km) used as the reference, the influence function has variation in height and peaks around 3.65 km (Figure 2e). For a theoretical linear dependence of convective mass flux with height, an approximation of a constant influence function 𝐴𝐴 𝐴𝐴 = 𝑧𝑧 -1 𝐵𝐵 ≃ 0.18 km -1 can be made. This theoretical convective mass flux is displayed by the red line in Figure 2c, with the initial level (z i ) being the lowest level of continuous increase in buoyancy with height (1.95 km). The theoretical convective mass flux corresponds well with the mean convective mass flux of deep convective columns, indicating that the approximation is reasonable. 𝑧𝑧 𝐵𝐵 ∫ 𝑧𝑧 𝑖𝑖 MSEenv𝐼𝐼(𝑧𝑧𝐵𝐵, 𝑧𝑧)𝑑𝑑𝑧𝑧 , representing the contribution of upstream MSE transport of each layer from the deep-inflow. The theoretical MSE has little difference compared with the mean MSE of deep convective columns, indicating that the contribution from the pre-existing local MSE in the deep convective columns is limited. Nevertheless, the feature of upstream MSE transport provides sufficient evidence of deep-inflow mixing via local circulation in TaiwanVVM simulations.

For diurnal convection developed randomly over great plains (e.g., the Amazon), the inflow can come from all directions, making it challenging to clarify the direction of the inflow and illustrate the circulation patterns. Since diurnal convection over complex topography is orographically-locked, we can demonstrate the deep-inflow mixing features by not only the convective structures but also the circulation patterns of the deep-inflow. Figures 3a-3d show the circulation pattern of the deep-inflow of an ensemble member as an example case. In Figure 3a, the blue area is the precipitation hotspot of this example case, and the red cross-section line, determined by the upstream vector defined in Section 2.2, passes through the centroid of the precipitation hotspot, portraying the deep-inflow path. Figures 3c and 3d illustrate the composite profile of the cross-section line during the developing stage and the mature stage of the example case. The developing stage (green shading period in Figure 3b) is within 2 hr before the mean rain rate in the NCMR area surpasses 0.5 mm hr -1 , while the mature stage (red shading period in Figure 3b) is when deep convective columns appear. During the developing stage, an inflow layer below 2.0 km depth transports MSE from the plain toward the mountains. The averaged upstream MSE flux below 2 km is 5.44 × 10 5 J m -2 s -1 . The surface heating and the turbulent mixing in the boundary layer result in the development and thickening of the inflow layer. During the mature stage, diurnal convection develops near the center of the precipitation hotspot. The depth of the inflow layer is about 2.6 km, accompanied by the averaged upstream MSE flux below 2 km of 7.71 × 10 5 J m -2 s -1 .

The high MSE transport is the prominent feature of the deep-inflow mixing from the perspective of circulation patterns. Figures 3c and 3d reveal that the MSE transport during the developing stage can contribute to the growth of diurnal convection, which is further supported by the statistics in Figure 3e. As the upstream integrated MSE transport during the developing stage rises from below 6 × 10 8 J m -1 s -1 to exceeding 7 × 10 8 J m -1 s -1 , the mean rain rate in the precipitation hotspot during the mature stage increases from 14.25 to 19.38 mm hr -1 . That is, enhanced upstream integrated MSE transport during the developing stage leads to a 36% increment in the mean rain rate in the precipitation hotspots during the mature stage. The results highlight the importance of non-local dynamical entrainment of the deep-inflow, transporting MSE via local circulation to supply the growth of orographically-locked diurnal convection.

The circulation pattern of the deep-inflow mixing and the accompanied upstream MSE transport can be identified in the TaiwanVVM simulations. Furthermore, the statistics from the TaiwanVVM semi-realistic LES ensembles provide helpful guidance for deploying boundary layer observations. Figure 3f shows the frequency of the deep-inflow. Two frequent paths, simplified by the yellow arrows in Figure 4a, are located over the two river valleys. At Sunsing (the magenta star in Figure 4a), a location over the foothill with a high frequency of the deep-inflow path, we released the Storm Tracker (ST) mini-radiosondes to observe the evolution of the deep-inflow. The ST mini-radiosonde is a compact, light-weight, economical, and well-calibrated sensor (Hwang et al., 2020), and it has been utilized in the Yilan Experiment of Severe Rainfall (YESR2020) field campaign (S.-H. Su et al., 2022). An observation was conducted on 26 August 2022. This afternoon, Taipingshan Station (CWB station number 01U560) in the NCMR area recorded 59.0 mm in 2 hr (Figure 4a). Figure 4b displays the evolution of MSE and horizontal wind observed by the ST mini-radiosondes. The depth of the low-level northeasterly increased from 09:00 to 15:00 Taiwan Standard Time (TST, UTC+8), revealing the evolution of the inflow layer. The MSE in the inflow layer also increased with time, reaching its maximum at 14:00 TST, just before the maximum rainfall occurred at Taipingshan Station. The observational evidence demonstrated the high MSE transport by the deep-inflow toward the precipitation hotspot.

This study focuses on regions with high occurrence of strong convection, that is, precipitation hotspots, over mountains under weak synoptic weather regime during summertime in Taiwan. Such a weather regime favors the development of local land-sea-mountain-valley-breeze circulation driven by differential surface heating over steep topography. A TaiwanVVM LES ensemble is simulated with the realistic, complex topography of Taiwan and initiated using a set of radiosonde observations to span the variability of the background environment. In this ensemble, through mass continuity, a deep layer of inflow can be inferred from the common mass flux structure of strong updrafts-the mass flux increasing gradually with height throughout the lower troposphereidentified during heavy precipitation over the hotspots. Furthermore, a deep layer (including the boundary layer) of coherent inflow air can be directly identified in the simulations with elevated MSE transport along its path. The orographically-locked diurnal convection over the hotspot is enhanced by the high upstream MSE transport, leading to an averaged 36% increase in rain rate.

The presence of orographically-locked convection provides a unique opportunity for studying convective updrafts and precipitation-because the typical location of the updraft is geographically constrained, field measurements can be more easily placed to sample the environment likely to influence the convection. A field campaign on 26 August 2022, guided by the simulations, released the ST mini-radiosondes (Hwang et al., 2020) to quantify the upstream environment of the most common deep-inflow path. The initial analysis supports the existence of high MSE transport within the inflow layer when organized convection occurs over the region of precipitation hotspot. While aspects of this flow may be specific to the orographic conditions, the presence of the deep inflow layer is consistent with and reinforces other lines of evidence (Ahmed & Neelin, 2018;Derbyshire et al., 2004;Holloway & Neelin, 2009;Houze, 2004Houze, , 2018;;Nicolas & Boos, 2022;Nowotarski et al., 2020;Schiro et al., 2018) that the other properties of deep convection may also be examined in the upcoming field observations motivated by the analyses in the present study.