The LASSO LES framework systematically integrates routine ARM observations in a standardized, case-based structure designed to support process studies and model evaluation (Gustafson et al., 2017a). LASSO provides ensembles of high-resolution simulations based on the Weather Research and Forecasting (WRF) model, constrained by ARM-derived large-scale forcing over domains centered on the SGP site. The LASSO framework has been used to investigate the sensitivity of shallow convection to large-scale forcings (Shin et al., 2021), assess cloud–land coupling in LES ensembles (Zhang et al., 2024), and examine sampling strategies for cloud radars (Oue et al., 2016), the latter being particularly relevant to the sampling-strategy focus of this study. In this study, we analyze simulations from two LASSO releases, Alpha2 and Version 1, using the framework described by Gustafson et al. (2020). A consistent WRF–Thompson (Thompson et al., 2008; Thompson and Eidhammer, 2014) configuration is adopted for all analyzed cases to ensure comparability across releases.

This study employs the AAFMERGED dataset (Mei and Gaustad, 2024), which integrates measurements from multiple instruments operated by the AAF aboard the G-1 research aircraft. The merged dataset provides time-synchronized information on cloud microphysical properties, aerosol characteristics, thermodynamic variables, radiative quantities, and aircraft state information. However, only the aircraft latitude and longitude coordinates are used in this study. These position data are used to characterize the horizontal geometry of the HI-SCALE flight tracks. As the aircraft tracks extend beyond the LASSO model domains, the horizontal patterns are spatially scaled to the corresponding domain dimensions while retaining their characteristic geometry. The resulting trajectories are subsequently used to sample the LASSO model fields and evaluate the representativeness of different aircraft sampling strategies.

CWC is used as a proxy in this study; it is a fundamental variable for characterizing cloud microphysical structure and its interaction with radiation and precipitation processes. It is defined as the mass concentration of condensed liquid water within cloudy air and is calculated as CWC =ρqc, where qc is the cloud water mixing ratio and ρ is the air density. CWC was converted to g m⁻³ for the subsequent analyses presented here. The separately represented rainwater mixing ratio (qr) is not included in the CWC analyzed here. In this study, qc represents the cloud-water category of the Thompson microphysics scheme. The CWC vertical profile and its vertical integral can be used to characterize the vertical distribution and total liquid water content of clouds, respectively.

Figure 1 shows the HI-SCALE flight tracks and the representative horizontal sampling patterns used in this study. A total of 38 research flights were conducted during HI-SCALE (Fig. 1a), of which 32 provided flight-track geometries for deriving the representative horizontal sampling patterns. Because the observed HI-SCALE tracks extend over a substantially larger horizontal area compared with the LASSO domains, the latitude–longitude patterns used in the sampling analysis were spatially scaled to the corresponding model-domain dimensions while preserving the characteristic horizontal geometries. The doubly periodic model boundaries were not used to extend the trajectories through repeated passes across the domain. In the sampling analysis, these horizontal patterns are combined with the prescribed vertical sampling strategies to construct the 3-D sampling trajectories through the LASSO domain.

The 32 flights were manually sorted into four groups based on their horizontal geometries. The circle pattern (Fig. 1b) comprises six flights that circle the SGP site (red dot). The diagonal pattern (Fig 1c) comprises 10 flights that cross the site diagonally, while the straight pattern (Fig 1d) includes six flights with north–south tracks. The remaining 10 flights were classified as the combo pattern (Fig 1e), which incorporates multiple horizontal flight geometries around the SGP station. Figure 1f shows the idealized zigzag pattern. Unlike the other four patterns derived from HI-SCALE flight tracks, the zigzag is a prescribed sampling geometry (Wendisch and Brenguier, 2013; Stevens et al., 2019).

The CWC sampling resulting from the four HI-SCALE-derived horizontal patterns and the idealized zigzag pattern is shown in Fig 2. During the sampling process, the horizontal patterns are applied to instantaneous outputs from the LASSO simulation for each time separately. This sampling framework retains the horizontal trajectory geometry derived from field campaign latitude–longitude information but is not intended to fully reproduce real-world flight conditions. Surface topography is not represented in the LASSO simulations, which employ a horizontally uniform lower boundary without terrain variations. The sampled data are then averaged over all time steps and across 226 vertical layers. Horizontal sampling is performed separately for different LES domain sizes. The domain size is 25 × 25 km for cases from 2017 to 2019 and 14.4 × 14.4 km for cases from 2015 to 2016. The distributions for the 2017 to 2019 cases are more even than those for 2015–2016, likely due to the larger number of available cases.

The vertical sampling strategies were designed using three canonical flight patterns including level-leg, sine wave, and staircase, which have been widely adopted in cloud observational studies to characterize vertical cloud structure and variability (Gerber et al., 2005, 2013; Brenguier et al., 2013). These patterns are considered complementary as horizontal legs at fixed altitudes provide robust statistics at specific cloud levels, while vertically varying profiles capture gradients in thermodynamic and microphysical properties within clouds (Wang and Sassen, 2001; Gerber et al., 2005; Wendisch and Brenguier, 2013). The use of multiple vertical sampling modes is a long-standing observational practice in field campaigns, including ARM and DOE-supported aircraft missions, to balance vertical coverage, temporal continuity, and statistical representativeness of in-cloud measurements. In this study, the vertical sampling profiles were constructed using cloud-base and cloud-top information diagnosed from the LASSO simulations. The specific implementation differs among the sampling strategies, as described below.

Previous studies have shown that measurements obtained near cloud boundaries often differ from interior-cloud values due to entrainment and enhanced variability in microphysical properties (Passer et al., 2025; Gryspeerdt et al., 2022). To reduce sampling directly at cloud boundaries, 100 m offsets from the diagnosed cloud base and cloud top were applied where the cloud depth exceeded 200 m. For shallower cloud layers, these offsets were not applied.

For the level-leg profile, three fixed sampling altitudes were defined for each LASSO case based on the mean diagnosed cloud-base, mid-cloud, and cloud-top heights over the 6 h analysis period. The lower and upper legs were set 100 m above the diagnosed cloud base and 100 m below the diagnosed cloud top, respectively, and the middle level was defined as the midpoint between the diagnosed cloud-base and cloud-top heights. The trajectory progressed successively from the lower to the middle and upper sampling levels. Transitions between adjacent levels were represented by linear changes in altitude over 10 min, while the trajectory continued to advance horizontally. The sine wave profile was constructed using a continuous sine waveform, with wave crests corresponding to 100 m below cloud top and troughs to 100 m above cloud base, enabling repeated sampling across the cloud depth within a single transect. The staircase profile was constructed similarly but used three discrete altitude levels, with the aircraft flying successively near the cloud top, mid-cloud, and cloud base for approximately 10 min at each level, again applying the same altitude offsets. These three profiles provide complementary perspectives on cloud vertical heterogeneity: the level-leg pattern emphasizes quasi-horizontal variability, the sine wave track resolves continuous vertical gradients, and the staircase profile combines vertical sampling with temporally stable measurements, a balance commonly employed in aircraft-based cloud process studies (Gerber et al., 2005).

In addition to the separable horizontal–vertical sampling combinations described above, a zigzag trajectory was constructed as a distinct 3-D flight configuration. Unlike the level-leg, sine wave, and staircase profiles, which prescribe vertical variation independently of horizontal pattern type, the zigzag design integrates horizontal tracks and cloud-relative vertical transitions into a single structured pathway. Similar zigzag flight patterns have been widely employed in aircraft cloud-process studies to repeatedly sample cloud layers and resolve vertical variability (Gerber et al., 2013; Savelyev et al., 2018; Dorff et al., 2025). As illustrated in Fig. 3d, the aircraft performs successive horizontal legs across the LES domain while alternating among cloud base (+100 m), mid-cloud, and cloud top (-100 m) levels. Vertical transitions occur at the turning points between horizontal legs, forming a repeating stacked sequence of cloud-relative sampling levels. The altitude of each leg is diagnosed locally along the trajectory based on instantaneous cloud properties, consistent with the vertical profile construction described above, so that cloud base and cloud top heights vary spatially and temporally according to the evolving model state.

The idealized flight patterns were further interpreted in terms of characteristic aircraft operating speeds. Research aircraft were grouped into three categories according to their typical true airspeed during the atmospheric field sampling. Low-speed aircraft (approximately 30–100 m s⁻¹), such as the de Havilland Twin Otter (DHC-6), are capable of stable flight and fine-scale vertical maneuvering, making them well suited for detailed boundary layer and cloud-scale sampling. Moderate-speed aircraft (approximately 100–170 m s⁻¹) include the ARM G-1 aircraft (Schmid et al., 2014), which was used during the HI-SCALE campaign, the C-130/LC-130, Beechcraft 200 (King Air), and British Aerospace 146 (BAe-146; Sánchez-Marroquín et al., 2019). These platforms provide a balance between spatial coverage and sampling resolution and are commonly employed for mesoscale process studies. High-speed platforms (approximately 200–250 m s⁻¹), such as the NASA Douglas DC-8 and NASA WB-57, are typically used for missions requiring rapid regional coverage or sampling of the upper troposphere and lower stratosphere. Based on these characteristic speed regimes, nominal speeds of approximately 33, 100, and 200 m s⁻¹ were prescribed for the slow, moderate, and fast trajectories, respectively. The moderate speed was based on the characteristic G-1 research speed of approximately 100 m s⁻¹ (Schmid et al., 2014), while the slow and fast trajectories correspond to approximately one-third and twice the reference speed, respectively. Framing the sampling trajectories in terms of these speed regimes clarifies how the prescribed horizontal-vertical profile combinations relate to realistic aircraft operations and facilitates interpretation of sampling representativeness across different classes of airborne observations.

The prescribed aircraft speeds also determine the horizontal distance traveled between consecutive 1 s sampling positions. For the 100 m horizontal grid spacing used in the LASSO simulations, a speed of 100 m s⁻¹ corresponds approximately one grid spacing per 1 s sampling interval, whereas slower or faster aircraft traverse less or more than one grid spacing between consecutive samples. This does not require a one-to-one correspondence between aircraft samples and model grid cells. Rather, it determines the spatial separation between consecutive trajectory positions and the extent of the model domain traversed during a fixed sampling period.

The aircraft-like sampling strategy combines horizontal patterns derived from HI-SCALE observations with prescribed vertical profiles and characteristic aircraft speed categories. Although the Alpha2 and Version 1 simulations differ in horizontal domain size, the same vertical-profile design is applied to both datasets. The low-, moderate-, and high-speed categories provide a practical framework for examining how trajectory geometry influences the representativeness of aircraft-like measurements within the LES domain.

Figure 4 shows the simulated CF for 9 June 2015, together with the prescribed sampling trajectory. CF is used here to visualize the 3-D cloud structure and spatial distribution within the LES domain. The horizontal flight pattern is prescribed independently of the simulated CF distribution, whereas the vertical sampling levels are based on diagnosed cloud-base and cloud-top heights. As a result, the trajectory may intersect regions with different CF according to the spatial heterogeneity of the simulated cloud field. As the prescribed trajectory moves horizontally and vertically through the domain, it samples both cloud and less-cloudy regions and may cross cloud boundaries. Figure 4 therefore illustrates how the aircraft-like sampling trajectory intersects the simulated cloud field in 3-D for this example case.

To assess the representativeness of aircraft-like sampling relative to the model domain, trajectory-averaged CWC is compared with the corresponding in-cloud domain mean computed over the vertical layers intersected by the flight path. For consistency, both trajectory and domain averages are calculated from in-cloud CWC values only, excluding cloud-free trajectory positions and model grid points. Only positive CWC values are retained for averaging, while a threshold of 0.2 g m⁻³ is used to identify cloud boundaries. Aircraft observations provide spatially limited samples of heterogeneous cloud fields. Their representativeness can depend on the sampling strategy and the spatial scales over which the observations are interpreted (Field and Furtado, 2016; Schutgens et al., 2017). Restricting the domain average to the sampled layers ensures a consistent spatial reference as the trajectory-derived and domain-mean CWC represent the same vertical portion of the simulated cloud field. The domain mean is therefore used here as a domain-scale reference for quantifying sampling representativeness rather than an observational reference.

Figure 5 shows an example of the sampled CWC values. Scatterplots for all trajectory configurations and speed categories are provided in the Supplement (Fig. S1). For each trajectory configuration, paired sampled and domain-mean CWC values are calculated separately for each 10 min model-output interval within the 6 h analysis period. The regression is calculated across all cases, with the selected ensemble member for each case. The color distribution indicates that the relationship between CWC and sampling height is not uniform across the sampled trajectories. Although the Spearman's rank correlation between domain-mean CWC and sampling height is moderately positive (r=0.609), the corresponding trajectory-averaged CWC shows substantially weaker and more variable relationships across sampling strategies and aircraft speeds. This difference suggests that the vertical variation in the domain-scale CWC is not consistently represented by individual aircraft-like trajectories, which are also affected by horizontal cloud heterogeneity and the spatial sampling imposed by the flight path.

Linear regression slopes between trajectory-averaged and domain-mean CWC are calculated for each combination of horizontal pattern, vertical profile, and speed category (Fig. 5). The statistics summarized below are calculated across the analyzed cases from both LASSO domain configurations. A separate comparison for the moderate-speed zigzag configuration did not indicate reduced sampling representativeness for the larger domain (Table S3), although the effects of domain size cannot be isolated from differences among simulation years and LASSO releases. Figure 6 summarizes the resulting slope values across configurations, providing an integrated assessment of sampling representativeness under varying trajectory geometries and flight speeds.

For the level-leg, sine wave, and staircase vertical patterns, representativeness generally improves with increasing flight speed. Within the present sampling framework, higher prescribed speed increases the spatial extent traversed by the trajectory during each fixed model-output interval, reducing sensitivity to localized cloud variability and generally improving agreement with the domain-scale field. Among these vertical patterns, the staircase profile exhibits the most consistent agreement, with regression slope values exceeding 0.85 across all horizontal patterns and speed categories. For the staircase profile combined with the circle horizontal pattern, the slope increases from 0.94 at slow speed to 0.97 at moderate speed and approaches unity under the fast speed category. In contrast, the level-leg profile shows the largest deviation, ranging from approximately 0.78 to 0.89. The sine wave profile yields slopes ranging from approximately 0.81 to 0.98.

The statistical metrics summarized in Table 1 provide a quantitative assessment of sampling representativeness. The sample and domain means are calculated separately from their respective original CWC matrices, whereas nBias and nRMSE are calculated using valid paired values after excluding NaN values in either dataset. Correlation coefficients (r) for the level-leg, sine wave, and staircase profiles generally range from about 0.57 to 0.83 across the trajectory patterns and speed categories, indicating moderate to strong agreement between sampled and domain-mean CWC. Among these profiles, the staircase profile shows relatively consistent performance, with r values ranging from 0.60 to 0.83 across the horizontal patterns and speed categories. The highest correlation among these profiles is 0.83 for the staircase pattern under the fast-speed category, while the lowest is 0.57 for the level-leg profile with the diagonal pattern at slow speed. Normalized RMSE (nRMSE) values range from approximately 0.45 to 0.66 for level-leg, sine wave, and staircase profiles, while normalized bias (nBias) remains small, ranging from -0.17 to -0.01, indicating limited systematic deviation between sampled and domain averages. In contrast, the zigzag pattern shows greater variability across speed categories, with r ranging from 0.37 to 0.74, nRMSE from 0.76 to 1.27, and nBias from -0.13 to 0.20.

Overall, the statistical metrics show that agreement with the domain mean generally improved with increased flight speed for the level-leg, sine wave, and staircase profiles within the present sampling framework, while geometrically constrained patterns such as zigzag exhibit less consistent behavior.

The zigzag vertical pattern shows a distinct behavior in which slope values do not systematically increase with flight speed. The number of valid CWC samples retained for the zigzag analysis ranges from 19 410 at slow speed to 27 617 at fast speed, pooled across all cases. Despite the larger number of valid samples at higher speeds, the zigzag pattern shows a close coupling between horizontal position and cloud-relative height. Each horizontal track corresponds to a prescribed cloud-base, mid-cloud, or cloud-top level, forming a stacked sampling loop. Increasing aircraft speed therefore increases the distance travelled along the same geometric patterns without changing the underlying vertical–horizontal structure. As a result, the trajectory continues to sample similar cloud-relative levels. In contrast, the level-leg, sine wave, and staircase patterns decouple horizontal position from sampled cloud-relative height, allowing increased speed to provide broader spatial sampling of the cloud field.

Overall, the sampling representativeness depends on both flight speed and trajectory geometry. While increased speed generally improves agreement for most vertical patterns through increasing spatial coverage, the constrained geometry of the zigzag configuration results in a less consistent response to increasing speed.

The cloud-top and cloud-base conditions along the trajectory paths are further evaluated in Fig. 7, which presents box plots of the differences between sampled and domain-mean cloud-top and cloud-base for all horizontal patterns and speed categories. The sampled cloud-base and cloud-top heights are calculated from the cloudy columns intersected by the aircraft-like trajectories, while the corresponding domain-mean values are obtained by averaging cloud-base and cloud-top heights across all cloudy columns within the model domain; clear columns are excluded from both calculations. Across the horizontal configurations, sampled cloud-top heights exhibit systematic negative differences, indicating that the cloud tops along the aircraft-like trajectories are generally lower than those over the full model domain. In contrast, cloud-base heights show substantially smaller differences relative to the domain mean, showing stronger agreement across configurations. This asymmetry is consistent with the cloud-field statistics summarized in the Supplement (Table S1), which indicate greater variability in cloud-top height than in cloud-base height, as reflected by the larger standard deviation. These results suggest that the designed flight paths are more effective in capturing the lower cloud boundary, whereas the more heterogeneous cloud-top structure is less fully represented along the trajectories and therefore more susceptible to sampling variability. The performance of the zigzag pattern is consistent with other horizontal configurations in terms of the negative tendencies for cloud-top height and relatively improved agreement for cloud base. This indicates that the zigzag geometry does not introduce a distinct systematic bias in boundary height itself. Rather, its effect is more apparent in the CWC sampling comparisons shown in Fig. 6.

Differences among horizontal sampling patterns are comparatively secondary to the influence of flight speed. Across all patterns, discrepancies in both cloud-top and cloud-base heights decrease with increasing speed, with the fast-speed category exhibiting the smallest differences relative to the domain mean. At higher prescribed speeds, the trajectory covers a larger portion of each 10 min model field, reducing sensitivity to localized cloud gaps and cloud-edge variability. This greater spatial coverage improves agreement with the domain-mean cloud-boundary structure within the present sampling framework. Because the model field is held fixed within each 10 min interval, the observed speed dependence primarily reflects differences in spatial coverage rather than temporal sampling frequency or sample count. Horizontal sampling geometry has a comparatively smaller influence on boundary-height estimates.

The vertical profiles of sampled CWC obtained from designed aircraft trajectories using the level-leg, sine wave, staircase, and zigzag vertical sampling patterns under three speed categories are shown in Fig. 8. For the level-leg, sine wave, and staircase profiles, results are averaged across all horizontal sampling patterns to isolate the effects of vertical sampling and flight speed, while the zigzag configuration is evaluated separately. Across all vertical patterns, the sampled profiles capture the primary structural characteristics of the domain-mean CWC, including the altitude and magnitude of the main cloud layer.

The correlation coefficients calculated over the full sampled altitude range differ among the vertical sampling patterns. The level-leg profile yields correlations of 0.57, 0.62, and 0.65 for the slow, moderate, and fast speed categories, respectively. The sine wave profile shows higher correlations of 0.68, 0.76, and 0.82, while the staircase profile yields 0.69, 0.76, and 0.78. The zigzag configuration shows similarly high correlations of 0.82, 0.70, and 0.79. Because the level-leg pattern does not extend into the upper cloud layers, the statistical comparison was restricted to the common altitude range of approximately 0 to 6000 m. Within this shared layer, the correlations for the other three profiles increased substantially. Specifically, the sine wave correlations are 0.84, 0.82, and 0.91 for the slow, moderate, and fast speed categories, respectively. The staircase correlations are 0.73, 0.80, and 0.91, while the zigzag configuration yields correlations of 0.87, 0.93, and 0.90. The nBias values range from -0.38 to -0.34 for the level-leg profile, -0.27 to -0.16 for the sine wave, -0.33 to -0.21 for the staircase, and -0.23 to -0.12 for the zigzag. The nRMSE values range from 0.56 to 0.58, 0.28 to 0.42, 0.32 to 0.49, and 0.23 to 0.37, respectively. The negative nBias values across all profiles indicate the tendency for sampled CWC to be lower than the corresponding domain-mean CWC.

Across the vertical sampling strategies, the sine wave, staircase, and zigzag profiles generally show higher correlations and smaller errors than the level-leg profile over the common altitude range. Increasing flight speed generally improves agreement for most profiles, although the response is not uniform across all profiles. This suggests that greater spatial coverage can reduce sensitivity to localized variability, while vertical trajectory geometry remains a primary control on the representativeness of the domain-mean CWC profile. When the profiles are evaluated over their full vertical extent, variability in upper cloud layers may also contribute to the differences in agreement.

To examine whether sampling performance varies with cloud amount, the cases were grouped into four CF categories (0 %–25 %, 25 %–50 %, 50 %–75 %, and 75 %–100 %) based on the maximum CF among the 10 min model outputs within each simulated period. The four categories contain 39, 42, 7, and 3 cases, respectively. The correlation coefficients and regression slopes vary among the CF categories and sampling configurations (Table S2), but do not show a consistent monotonic change with increasing CF. For example, for the level-leg profile combined with the circle horizontal pattern, r ranges from 0.76 to 0.86, 0.43 to 0.68, 0.38 to 0.74, and 0.61 to 0.82 across the four CF categories, respectively, depending on flight speed. The corresponding regression slopes likewise vary among CF categories rather than changing systematically with increasing CF. The relatively small number of cases in the two highest-CF categories may reduce the stability of the corresponding statistics. Detailed results across sampling configurations are provided in Fig. S2.