This study focuses on the local warm season (May–September) when thermodynamically driven convection is most prevalent and land surface feedback plays an important role in determining precipitation (Myoung and Nielsen-Gammon, 2010). Unless stated otherwise, all measurements are taken at the DOE ARM SGP central facility (CF) in northern–central Oklahoma (36.60° N, 97.48° W) and the region within a 50 km radius of the CF for 2001–2018. Below are the specific details about the datasets used in this study.

Previous research on local land–atmosphere interaction mainly focused on the influences of surface flux and moisture in the PBL on convection initiation and precipitation, such as those related to HCF and mixing diagram metrics. The CTP / HILow metric considers the effect of lapse rate 100–300 hPa (or about 2–4 km) above ground level (a.g.l.) on vertically integrated buoyancy in the LT (i.e., CTP) and humidity of the PBL (i.e., HILow), but it does not account for the impact of LT moisture.

Isolating the local influence from other factors in observations presents a significant challenge. Understanding the relationship between near-surface and upper-level information could be crucial for addressing this. In this study, we first examine the correlation between the q profile in the LT and the mixed-layer humidity (qm), defined as the average q in the 0–1 km a.g.l. mixed layer, to assess the potential influence of land surface on LT moisture (Fig. 1). We choose mixed-layer humidity over humidity directly above the surface to represent the land surface moisture condition because (1) radiosonde measurements near the surface are often more susceptible to errors and local disturbances, which could skew the representation of actual surface moisture conditions; (2) at noon, the 0–1 km mixed layer offers a more representative snapshot of the land surface moisture by capturing the integrated effect of surface evaporation and convective mixing processes; (3) we observe strong correlations, exceeding 0.95 (p<0.05), between the q near the surface and qm. However, this correlation diminishes with increasing height above the PBL. Notably, the LT humidity above 2 km maintains a significant correlation with qm, suggesting a potential influence from the surface. To isolate the effect of the land surface on LT humidity, we establish a “land-coupled LT humidity profile qLC” for 2–4 km a.g.l., which is linked to land surface moisture conditions. This profile is derived using a linear regression between the q(h,t) profile within this layer (2 km ≤h≤ 4 km) and qm(t). In our regression model, represented by the equation y=a×x+b, y is the q at a given height and time q(h,t) and x is qm(t), with a(h) and b(h) being the linear coefficients at each height level. By solving a(h) and b(h) for each height level in the LT, we can then calculate the land-coupled LT humidity as the fitted LT humidity, i.e., qLC(h,t)=q^(h,t)=a(h)*qm(t)+b(h).

To quantify the direct influence of LT moisture on convective buoyancy, we adopt an entraining parcel model used in Zhuang et al. (2018). In this model, the air parcel is lifted with the initial condition of an average value within the mixed layer. The ascending air parcel then goes through three processes at each vertical level: a dry adiabatic process (the parcel ascends without interacting with the environment, entropy conservation), an entrainment process (which interacts with ambient air, enthalpy conservation), and a precipitation process (which releases condensate, temperature conservation). We apply the deep-inflow-A entrainment (DIA) scheme which has been shown to more realistically represent the buoyancy profile required for deep convection compared to the other assumptions of the lateral entrainment rates such as the constant fractional entrainment rate scheme (e.g., Holloway and Neelin, 2009; Schiro et al., 2016; Siebesma et al., 2007). The DIA scheme uses an entrainment rate inversely proportional to the altitude (αz-1) for simplicity. All condensates formed from the previous two processes are set to fall out in the precipitation process (pseudo-adiabatic process). Finally, buoyancy is calculated by b=gTpv-TevTev, where Tpv and Tev are the virtual temperatures of the parcel and the environment, respectively. Details of this model are provided in Zhuang et al. (2018).

To quantify the influence of LT humidity on the lateral entrainment of the convection and, consequently, the buoyancy of the convective air parcel, we consider two q profiles for the lateral entrainment process: (1) the observed humidity profile (qR) and (2) the land-coupled humidity profile (qLC). The qLC below 2 km a.g.l. equals the observed q, and qLC between 2 and 4 km a.g.l. is a coupled LT humidity profile constructed from the regression between q and the averaged q in the mixed layer. Since the effect of entrainment accumulates continuously after the parcel is lifted, we calculate the buoyancy profile with qR as the humidity profile (bR) and that with qLC as the humidity profile (bLC), and then we use the vertical integral of their difference in the LT (2–4 km a.g.l.), BLT=∫2kma.g.l.4kma.g.l.bR-bLCdz, to quantify the additional effect of LT moisture variation on the parcel buoyancy that is not coupled with the PBL. We also calculate the integral of buoyancy based on qLC, i.e., BLC=∫2kma.g.l.4kma.g.l.bLCdz, to assess the land-coupled effect on convection. To make the results comparable, we apply a normal percentile transform (Wilks, 2011) to obtain standardized scores of the BLT, which we use for further analysis.

The CTP / HILow framework developed by Findell and Eltahir (2003a) is commonly used to identify the atmospheric preference of an LAC state. CTP is calculated by integrating the difference between moist adiabat temperature and the ambient temperature profile from 100 to 300 hPa a.g.l. It is a measure of the energy available for convection, and the 100–300 hPa a.g.l. is a critical level for the development of the daytime boundary layer. HILow, on the other hand, indicates the pre-existing moisture of the very lower atmosphere and is defined as HILow=T-Td150hPaa.g.l.+T-Td50hPaa.g.l.. In this framework, a wet soil advantage regime occurs when the atmospheric state is closer to the wet adiabatic lapse rate, resulting in a low CTP and large latent heat flux (small HILow). Conversely, a dry soil advantage regime occurs when the temperature profile is close to the dry adiabatic lapse rate with weak thermal stability (high CTP) and the soil provides less water vapor but more heat. This condition favors convection lifted by the boundary layer growth due to high sensible heat fluxes at the surface (Ek and Holtslag, 2004; Huang and Margulis, 2011; Gentine et al., 2013).

We adopt a modified CTP / HILow framework proposed by Wakefield et al. (2019) using the standardized score of CTP / HILow. We first calculate CTP and HILow using sounding data at 11:30 LST and the average FWI during 06:00–12:00 LST. Then, dry-coupling cases are defined as days with an anomalously high CTP (higher than the climatological CTP for our analysis period) over dry soil (FWI < 0.4), which is similar to the dry soil advantage regime in Findell and Eltahir (2003a, b); wet-coupling cases, on the other hand, are characterized by an anomalously low HILow over wet soil (FWI > 0.7), which corresponds to a moisture-abundant, energy-limited regime where the atmospheric profile is likely near-moist-adiabatic (Findell and Eltahir, 2003a, b). The wet soil condition is expected to promote precipitation recycling through the addition of moist static energy via evapotranspiration and provides a continuous supply of low-level moisture.

Since LAC would mostly affect the thermodynamically driven afternoon convection, we focus on the morning (06:00–13:00 LST), afternoon (14:00–20:00 LST), and evening (21:00–24:00 LST) precipitation events in our analysis. Afternoon precipitation events (APEs) are identified as daily samples that meet the following two criteria: (1) daily precipitation peaks during the afternoon hours defined above, and (2) the afternoon precipitation is at least twice as large as the morning precipitation and also greater than the evening precipitation (filter out organized precipitation). The cases not categorized as APEs are referred to as non-APEs afterward. We obtain a total of 368 APEs from the 2172 soundings. We further select APEs associated with either dry-coupling or wet-coupling conditions, resulting in 94 dry-coupling APEs and 79 wet-coupling APEs. These account for 24.2 % of the total of 388 dry-coupling cases and 20.3 % of the total of 389 wet-coupling cases, respectively. The comparable number of APEs for both dry- and wet-coupling conditions aligns with the finding of Findell and Eltahir (2003b) that the SGP is in the transitional region where negative and positive feedback days occurred with a similar frequency. In addition, our analysis also shows that (Fig. S1 in the Supplement), within all 368 APEs, 16 instances exhibit a HILow lower than 5 °C – a threshold established in Findell and Eltahir (2003a, b). Among these, eight are wet-coupling APEs and have a significantly higher FWI compared to the other groups. This suggests that the low HILow values observed before noon in these cases are likely influenced by soil moisture evaporation rather than purely controlled by atmospheric factors. Furthermore, one of these cases is categorized as a dry-coupling APE and seven as “other APEs”, which are APEs not categorized as either dry-coupling or wet-coupling APEs. These cases likely represent “atmospherically controlled days”, as per the CTP–HILow framework, and only account for a small fraction (∼ 2.2 %) of all the APEs we identified.

To identify favorable atmospheric conditions for coupling APEs, we evaluate the differences in temperature (T), specific humidity (q), and relative humidity (RH) at 11:30 LST between averaged local coupling APEs and non-APE cases in the warm seasons (May to September), as shown in Fig. 2. Regardless of soil moisture conditions and coupling regimes, APEs are always associated with a wetter lower troposphere (0–4 km) than non-APEs. For dry-coupling regimes, the increases in q and RH in the PBL and the LT associated with APEs are also stronger than those with the non-APEs, especially between 0.5 and 3.5 km a.g.l., and the contrast between APEs and non-APEs in dry-coupling regimes is larger than that for wet-coupling regimes. These humidity differences are expected, as more humid preconditions favor the occurrence of APEs. Note that the greatest contrast between the RH of APEs and that of non-APEs occurs between 1 and 3.5 km a.g.l. (above the PBL), which is the combined result of high q and decreasing T over this layer, highlighting the possible strong influence of LT humidity on deep convection.

In contrast, the sign of the temperature difference between APEs and non-APEs below 1.7 km a.g.l. varies between the dry-coupling and wet-coupling regimes. For the dry-coupling regimes, the average temperature of APEs is lower than that of non-APEs. This is presumably due to the stronger surface sensible flux and less stable atmosphere (a steep lapse rate or a faster decrease in temperature with height) associated with APEs than non-APEs under the dry-coupling regime. For the wet-coupling regime, the average temperature of the APEs is warmer than that of the non-APEs below 1.7 km a.g.l. This is consistent with a weaker lapse rate associated with a more humid environment, presumably due to vertical mixing of shallow convection, in the APEs than in the non-APEs. Above 1.7 km a.g.l., the temperature of the APEs is lower than that of the non-APEs for both the dry- and wet-coupling regimes, as expected from less stable thermodynamic conditions in the APEs than in the non-APEs.

To investigate the differences in atmospheric conditions that favor APEs under the dry- versus wet-coupling regimes, we compare the composite differential profiles of RH, q, and T between the dry- and wet-coupling APEs, as shown in Fig. 3. In general, T is higher for APEs under dry-coupling regimes than under wet-coupling regimes (Fig. 3a), especially in the PBL (below 2 km). This can be attributed to stronger sensible heat flux and temperature mixing over a dry surface. Notably, there is a significant difference in LT specific humidity between dry- and wet-coupling regimes (Fig. 3b), with the q associated with APEs slightly lower below 1 km a.g.l. under dry-coupling regimes than under wet-coupling regimes but higher above 1 km, especially between 2 and 3 km a.g.l. This suggests that APEs require entrainment of higher LT moisture under dry-coupling regimes than under wet-coupling regimes. Both Figs. 2b and 3b suggest that higher LT specific humidity is needed for APEs under dry-coupling regimes than under wet-coupling regimes. Moreover, RH associated with dry-coupling regimes is less than that of wet-coupling regimes in the PBL (Fig. 3c), as expected from a drier PBL over a dry surface. However, such an RH difference becomes smaller and eventually disappears in the LT (2–4 km). This is because the lower RH in the dry-coupling regimes is mainly due to a warmer T below 2 km a.g.l. (Fig. 3b), whereas, above 2 km a.g.l., the higher q and slightly warmer T in the dry-coupling regimes balance each other out and lead to a similar RH to the wet-coupling regimes.

Recent studies on the SM–P relationship have highlighted the greater impact of soil moisture anomalies on boundary layer stability and precipitation formation than on the ambient moisture (e.g., Seneviratne et al., 2010; Santanello et al., 2018). To investigate how humidity affects the preconditioning of the convective environment and how it impacts instability in the dry- and wet-coupling regimes, we use an entraining parcel model to calculate buoyancy profiles for bR and bLC, respectively, with parcels originating in the mixed layer. We then compute differences in the integral buoyancy between the bR and bLC profiles for the 2–4 km a.g.l. range to explore the influence of LT humidity-related convective thermodynamic instability.

To evaluate the atmospheric thermodynamic structure associated with the BLT, we evaluate the composite average sounding profiles based on three terciles of the BLT in the warm season as shown in Fig. 4. The BLT values for the three terciles range from -55.8 to -8.8, from -8.8 to 10.2, and from 10.0 to 72.8 J kg-1, respectively. It is noteworthy that the temperature and dew point are similar among these three terciles of the BLT near the surface (below 900 hPa) but clearly different from above 900 hPa up to at least 400 hPa a.g.l., which indicates the importance of LT humidity.

For the lower tercile (0 %–33 %) of the BLT, dew point values are substantially lower than those for the middle and upper terciles of the BLT. The sharp decrease in dew point values with height, the near-constant temperature, and the large gap between the temperature and dew point profiles at 700–900 hPa suggest strong dry shallow convection. For the middle tercile, dew point and temperature decrease gradually with a height between 900 and 700 hPa, and the gap between the dew point and temperature profiles is smaller than those for the lower tercile of the BLT. These features suggest a mixture of dry and moist shallow convection. For the upper tercile of the BLT (67 %–100 %), dew point values are nearly constant from the surface to 700 hPa, and the humidity of the free troposphere, as indicated by the gap between the temperature and dew point profiles, is substantially wetter (implying a higher RH) than for the middle and lower terciles of the BLT. These features suggest that moist shallow convection dominates LT. Higher dew point values between 700 and 500 hPa also suggest a more humid middle troposphere associated with the upper BLT tercile than with the middle and lower BLT terciles. Thus, Fig. 4 suggests that BLT variations are strongly influenced by the humidity in the lower and middle troposphere.

To investigate the effect of the LT humidity versus land surface air humidity on APEs, we evaluate the probability distribution of APEs as a function of the BLT and BLC for dry- and wet-coupling APEs, respectively, in Fig. 5. BLC is usually more negative over dry soil (Fig. 5b) than over wet soil (Fig. 5a) and therefore usually more negative over a dry PBL than over a wet PBL. Figure 5b shows that dry-coupling APEs occur more frequently with a negative BLC (69 %) and a positive BLT (77 %), indicating that the influence of a more humid LT can override the influence of surface air aridity. For the land surface, favoring local precipitation (BLC>0), dry-coupling APEs occur more frequently with a positive BLT (26 %) than with a negative BLT (5 %). For the wet-coupling conditions, 57 % of APEs occur with a positive BLT, while 31 % occur with a humid PBL precondition (Fig. 5a). Overall, for dry-coupling cases, more APEs are associated with a humid LT (positive BLT) than with humid surface air (positive BLC), but this trend is not evident for wet-coupling cases.

To evaluate the influence of LT humidity on LAC in the CTP / HILow framework, we compare the joint distribution of all APEs, wet-coupling APEs, and dry-coupling APEs, respectively, as a function of BLT scores and HILow scores (Fig. 6) using a normal percentile transform (Wilks, 2011). Larger-than-normal BLT (humid LT) values were associated with 61 % of all the APEs, regardless of the PBL humidity. Smaller-than-normal HILow (humid PBL) occurred in 63 % of all the APEs, regardless of the LT humidity. About 40 % of all the APEs occur under both humid PBL and humid LT. Thus, the probabilities of APEs occurring under either a humid PBL or a humid LT are similar, with a preference for APEs to occur under both humid PBL and humid LT conditions. For dry-coupling conditions, 76 % of the APEs occur under a humid LT versus 59 % under a humid PBL. Therefore, APEs appear to prefer a humid LT more than a humid PBL under dry-coupling conditions, but this preference is not found under wet-coupling conditions. This result is consistent with the findings in Fig. 5.

To further investigate how the LT humidity or BLT can affect the probability of APEs under the dry-coupling and wet-coupling regimes, respectively, we present three statistical measures of APEs as a function of the BLT in Fig. 7. Figure 7a shows that, for the dry-coupling cases, the fractional occurrence of APEs (defined as the proportion of APEs relative to all dry-coupling cases) in each BLT bin increases with BLT up to its 70th percentile, with a significant correlation (R=0.65, p<0.05). For the wet-coupling cases, the fractional occurrence of the APEs peaks when BLT is between the 30th and 70th percentiles. Thus, APEs appear to prefer higher LT humidity under dry coupling than under wet coupling.

Next, we explore how BLT affects the partition of dry-coupling and wet-coupling APEs. Figure 7b shows that the proportion of the dry-coupling APEs relative to all the APEs increases with BLT, with a strong correlation (R=0.89, p<0.05). The proportion ranges from 0.04 at the bottom 10 % to 0.47 at the top 10 % of the BLT. However, the proportion of wet-coupling APEs per BLT bin peaks at lower- to medium-BLT percentiles (30 %–50 %) and decreases almost monotonically with an increasing BLT from 50 % to 100 %.

We also investigate how BLT affects rain rates associated with dry-coupling and wet-coupling APEs, respectively. Figure 7c shows a clear increase in the rain rate with BLT for the dry-coupling APEs, except for the 90th to 100th percentiles of the BLT, where there are few APE samples. In contrast, we find no clear dependence of the rain rate on BLT for the wet-coupling APEs. Thus, our findings suggest that a high BLT tends to increase the frequency and intensity of the dry-coupling APEs as well as the relative frequency of dry-coupling APEs compared to wet-coupling APEs.

In addition, we evaluate the variations of deep convection (cloud top height (CTH) > 8 km), shallow convection (CTH < 3 km), and convective congestus (CTH between 3 and 8 km) associated with APEs based on hourly precipitation and cloud fraction following Zhuang et al. (2017). In general, APEs associated with all three convective types increase with BLT under dry-coupling conditions (Fig. S2). Under wet-coupling conditions, APEs associated with deep convection do not exhibit a clear dependence on BLT. However, APEs associated with shallow convection decrease with increasing BLT, while those associated with congestus increase with increasing BLT. These results imply that the increase in BLT can lead to a deepening of shallow convection into congestus due to reduced buoyancy dilution caused by entraining wetter LT air for wet-coupling convection.