Field experiments were performed at the Mid-Collins (CLN) snow study plot in Alta, Utah, USA (40°34^′33.66^′′ N, 111°38^′19.93^′′ W, elevation 2945 m) during the 2020–2021 winter season. The site averages 1300 cm of snowfall annually and has 17.4 d with at least 25 cm of snow per winter . The Alta study plot is located in a clearing surrounded by an ≈10 m tall tree canopy surrounded by complex mountainous terrain. This site was chosen in-part to avoid the additional measurement of windblown snow that is typically lifted from exposed terrain features.

The instrumentation deployed for this work was collocated with existing operation instruments operated by Alta Ski Area as well as manual snow measurements conducted twice daily. Data collection at Alta consisted of one CSAT3 Campbell Scientific, Inc. sonic anemometer-thermometer that was maintained at ≈1.5 m above the snow surface that measured all three components of the wind and sonic temperature. These data were logged at 20 Hz to capture high frequency measurements of the along-wind component of the wind velocity ux, the transverse component uy, and the vertical velocity component uz. One high-precision slow-response Vaisala HMP 155 thermometer/hygrometer was located at approximately 1.5 m above ground and sampled at 1 Hz. The CSAT3 and HMP 155 data were logged using a Campbell Scientific CR1000. A Differential Emissivity Imaging Disdrometer (DEID) was maintained at the same height as the sonic anemometer to measure individual snowflake mass, density, and geometric characteristics. Collocated with the DEID was a particle tracking system for measuring individual snowflake positions and velocities. A photograph of the main tower is presented in Fig.  (Fig.  was adapted from with the permission of AIP Publishing. © 2023 AIP Publishing.). Detailed descriptions of the DEID and particle tracking system are given below.

In addition to the instruments on the main tower, a Multi-Angle Snowflake Camera (MASC) was deployed at ≈1 m above the snow surface on a mast located within 10 m of the main tower. The MASC captures high-resolution photographs of individual snowflakes; however, its data were not used in the present analysis. We have also used temperature data from Alta Ski Area's high-elevation Mt. Baldy observation station located at an elevation of 3373 m (40°34^′3.72^′′ N, 111°38^′14.64^′′ W)

Intensive Observation Periods (IOPs) were performed during most nighttime snowfall events throughout the 2020–2021 season and comprised millions of snowflake settling velocities and physical properties measurements. This paper focuses on four cases conducted during snow-event IOPs on 12 December 2020 (Case 1), 4 January 2021 (Case 2), 16 March 2021 (Case 3), and 26 March 2021 (Case 4). Details about the meteorology condition, observation time intervals, and microphysical parameters are provided in Table .

The motions of settling individual snowflakes were imaged using a particle tracking system consisting of a laser sheet with a sampling volume (or region of interest, ROI) of 24.6cm×13.8cm×6.5cm oriented normal to the viewing angle of a Nikon D850 SLR camera with a single focal length Nikon AF-S VR Micro – Nikkor 105 mm f/2.8G IF-ED lens. The SLR camera recorded 3840pixel×2160pixel images with a spatial resolution of ≈64 µmpixel-1 at 30 fps within a vertical laser sheet created using three 10 W, 520 nm diode lasers and a collimator lens. The collimator lens creates a spread angle of ≈6.8°, which yielded a laser light sheet with a nearly constant thickness of ≈6.5 cm throughout the ROI. The camera arrangement and settings ensured that all particle images captured within the thickness of the laser sheet were well-focused (see Fig. ). Recordings were performed at night so that only well-focused snowflake motions within the thickness of the light sheet were captured.

Snowflake tracking was performed using the Particle Streak Velocimetry (PSV) technique to measure Lagrangian velocities of individual particles Vp in the laser sheet for concentrations up to 3400 m-3. Here, Vp is the vertical component, which is positive when falling toward the ground. Typically, PSV is used for speed measurements, but we used the PSV technique to measure fall velocity using the fall angle and streamwise particle speed; details of the calculations are given in Appendix .

Observed snowflakes moved both downward and upward depending on turbulence levels and the characteristic sizes of turbulent eddies (see Fig. ). Positive downward and negative upward values of Vp are determined by segmenting the analysis into periods where the bulk particle motion or streamwise air flow is exclusively from left to right or vice-versa in the images as discussed in detail in Appendix .

Hydrometeors that exit the bottom of the laser viewing plane of the SLR camera are then captured by the hotplate surface of the DEID situated directed below. The DEID consists of an infrared camera pointed at a low-emissivity heated metal plate as described in detail in and . The DEID makes use of the contrasting thermal emissivities of water (ε>0.95) and aluminum (ε<0.1) at the same temperature. A piece of Kapton tape (ε>0.95) is maintained on one side of the hotplate to provide a reference length scale as to provide the temperature of the plate. Images from the thermal camera were recorded with a resolution of 531pixels×362pixels and a sampling rate of 15 Hz. Hydrometeors are imaged within a 9cm×6cm section of the hotplate located at its center appearing to the thermal camera due to the contrasting emissivity of water and metal imagery as bright images on a dark background. The hotplate is powered by a 120 V, 5 A supply and uses a digital proportional integral derivative (PID) feedback control mechanism to maintain a constant plate temperature. Binarized images were used to determine the contact area of each individual hydrometeor by counting the white pixels. The contact area of each snowflake was obtained from its melted imprint on the aluminum hotplate. As demonstrated by , the difference between pre- and post-melting equivalent diameters is approximately 5 %, indicating that the melt footprint reliably preserves the original two-dimensional geometry owing to the plate's near-90° contact angle.

The DEID provides accurate measurements of the mass of individual hydrometeors (m), along with the density (ρp), the circumscribed ellipse area (A), and the actual contact areas (Ae) as described in and illustrated in Fig. 3. Detailed calculations of A and Ae, along with the complexity, are provided in the following paragraph and in Appendix A, following the approach of . The circumscribed ellipse area (A) is obtained from an ellipse constructed using the bounding-box width and height, representing the smallest ellipse that fully encloses the projected shape of the hydrometeor.

From these parameters, individual snowflake-equivalent still-air terminal velocities can be estimated using an aerodynamic formula namely, Vt=f(m,Ae,A). Details of the calculation are provided in . The estimated Vt using is ≈15 % smaller than that calculated using . Note that we estimated Vt using in this analysis, following the method described therein, with detailed calculation steps provided in Appendix B.. Also, size distributions are expressed here in terms of the effective diameter, Deff, which is the diameter of the equivalent circle of area Ae given by Deff=4/πAe.

The density of individual snowflakes is determined based a new method that exploits the rate of heat transfer during the melting of a hydrometeor on the hotplate . Combining microphysical measurements of the snowflakes with turbulence parameters of the surrounding air allows for the computation of frozen-particle Stokes numbers using the timescale ratio St=τp/τη. The turbulence Kolmogorov (micro)timescale, τη, is given by τη=(ν/ϵ)1/2 where ν is the kinematic viscosity of air and ϵ is the dissipation rate of turbulent kinetic energy. Here, η is the Kolmogorov micro(length)scale, which is the characteristic length scale of the smallest turbulent eddies in the flow . τη is the timescale associated with these small-scale eddies and is calculated from 30 min of turbulence data, and individual particle response times are given by τp=Vt/g. The density ratio parameter β is calculated for each snowflake as, 1β=3ρfρf+2ρp. A value of β=0 corresponds to heavy particles that are perceived as having infinite inertia and β=1 implies particles that match the surrounding fluid density and behave as idealized fluid tracers. A density of air at approximately 2945 ma.s.l. of ρf=0.9 kgm-3 is used here.

The combination of snowflake shape and density is characterized here with two newly introduced non-dimensional parameters we term the complexity and the shape-density index (SDI). Hydrometeor complexity is defined as the ratio of the area of a circumscribed ellipse, constructed using the bounding-box width and height, to the actual cross-sectional area (Ae) measured on the DEID hotplate. The corresponding ellipse area is given by A=πab, where a and b are the semi-axes derived from the bounding-box dimensions using MATLAB's Regionprops function, consistent with the definition used previously.

The complexity is then given by: 2Complexity=πabAe, where a and b are the semi-major and semi-minor axes of the ellipse, respectively. A perfectly circular particle has a complexity of unity, with higher values indicating increasingly irregular or elongated shapes.

The SDI accounts for the shape of the snowflake relative to a spherical water droplet, defined as 3SDI=AeAmel. where Amel is the projected area of the equivalent spherical water droplet formed once the snowflake has melted, as given by 4Amel=1.2(m/ρw)2/3, where ρw is the density of liquid water and 1.2 is a dimensionless geometric constant. An SDI value of unity corresponds to a liquid water sphere. Large, aggregate-type snowflakes with low densities have high SDI. As illustrated in Fig. , small, dense snowflakes such as graupel have lower values of SDI . Note that SDI is a dimensionless version of the specific surface area (SSA) per unit mass, which is widely used in the snow science literature .

High-frequency wind velocity data were collected using a sonic anemometer situated at the same height and 1 m adjacent to the location of the DEID and SLR region of interest (ROI). To analyze the velocity data, the raw velocity signals are decomposed into a time averaged component (e.g. Ux and a fluctuating component ux′). Specifically, ux=Ux+ux′, uy=Uy+uy′, and uz=Uz+uz′ for the along-wind, transverse, and vertical velocity components of the wind velocity. To ensure that the anemometer is rotated into the streamwise coordinate system, two rotations are applied to each 30 min averaging period. This procedure follows methods outlined by where the first rotation aligns the x and y axis about the z axis so that Uy = 0, aligning with the horizontal component of the flow. Calculation of turbulence parameters using sonic anemometer data is outlined in Appendix . The integral time scale (τL) and the integral length scale (L) are calculated using the temporal autocorrelation function of the horizontal-wind fluctuation. The turbulent Reynolds number Rλ=u′λ/ν, where u′ is the root mean square (r.m.s.) of along-wind velocity fluctuation and λ is the Taylor microscale length scale of turbulence. We compute the commonly used non-dimensional turbulence intensity TI from the sonic anemometry data as 5TI=12(σux2+σuy2+σuz2)1/2Ux=TKE1/2Ux. TKE is used in place of the streamwise velocity fluctuations ux′ to account for the chaotic multi-directional turbulence observed at the CLN field site.

Figure  shows a time series, using a 10 s moving average of the vertical wind velocity (uz) and streamwise velocity (ux), that highlights differences in the mean and fluctuating velocity components during periods of relatively high turbulence and low turbulence associated with Cases 1 and 3, respectively. Turbulence statistics for each 30 min case are summarized in Table  and are used to identify and segment cases into periods of high and low turbulence. For all cases, the winds are generally light (less than about 1 ms-1), however, clear differences can be seen between the turbulence characteristics of Cases 1 and 2 (high turbulence) vs. Cases 3 and 4 (low turbulence).

Snowflake characteristics such as complexity and density are determinants of hydrometeor drag and hence the terminal fall speed . Thus, we expect that understanding the microphysical characteristics of snowflakes is important for determining actual fall speeds. Figure  shows probability density functions or PDFs of effective diameter, mass, complexity, density, terminal fall speed, Stokes number, density ratio, SDI, and SSA obtained from DEID measurements of 86 086 individual snowflakes for a low-turbulence situation, Case 3. Datasets like these are unique and illustrate the wide range of values that microphysical variables take on during a single storm leading to large variability in fall speeds. The following are median values with corresponding lower and upper quartiles for the measured parameters: Deff=1.4[1.1,1.8] mm; Mass =0.06[0.03,0.15] mg; Complexity =1.3[1.1,1.5]; ρ=54[41,72] kgm-3; Vt=0.6[0.4,0.8] ms-1; St=0.18[0.12,0.26]; β=0.02[0.02,0.03]; SDI =8.5[6,12]; SSA =0.03[0.01,0.04]. Furthermore, we also found that the mass distribution of the snowflakes follows a power-law function, as shown in Fig. b, departing from the more familiar negative exponential distribution observed for Deff . This discrepancy arises because our measurements directly capture particle mass, whereas previous studies inferred it from mass–diameter relations in which the exponent varies between 1–3 , leading to deviations from a pure power-law distribution.

Table  presents relationships that are also not typically available in the analysis of complex snow-storm events but are extremely useful for modeling. In particular, mass-diameter, density-diameter, and terminal settling speed-diameter parameterizations are shown for all four cases studied. While some of the parameterizations characterize the snowflakes well, most do not. This emphasizes the complexity of the distributions. Specifically, these distributions include different types of snowflakes which are expected to have their own relationships .

The distributions of snowflake effective diameters (Deff) and particle densities (ρp) under high and low turbulence conditions are shown in Fig. . High-turbulence cases (Case 1 and Case 2) exhibit broader Deff and ρp PDFs with slightly larger densities and almost identical mean sizes. These trends underscore the influence of turbulence on snowflake size and density variability. This may be a result of increased snowflake collisions that occur during higher turbulence . These observations highlight the significant role of turbulence intensity in modulating snowflake microphysical properties.

The distributions of snowflake effective diameters (Deff) and particle densities (ρp) under high and low turbulence conditions are shown in Fig. . High-turbulence cases (Case 1 and Case 2) exhibit broader Deff and ρp PDFs with slightly larger densities and nearly identical mean sizes. This indicates that turbulence primarily affects the spread rather than the mean value of Deff. Increased turbulent fluctuations enhance relative motion, orientation variability, and collision or fragmentation frequency, leading to broader distributions even when the mean remains unchanged .

Direct measurements of individual snowflake settling velocities, obtained using PSV, and their terminal velocities Vt obtained from the DEID are presented in this section. Snowflake fall speeds, Vp, are compared to concurrent measurements of the snowflakes' terminal velocities Vt to identify settling reduction and enhancement periods and to understand the mechanisms governing the behavior.

Table  shows how fall-speed enhancement and reduction correlate with Stokes number for 30 min averages. An enhancement in settling speed is noted when St<1, while a reduction is observed when St>1. Evidently, higher St values are associated with reductions in the average fall speeds Vp as snowflake trajectories become more horizontal. This is a rather surprising result that was discussed in and . It is important to note that in this case, the elevated St=τp/τη results from increased turbulence intensity, which reduces τη, rather than from greater particle inertia or increased τp. As illustrated in Fig. , individual particles with Stokes numbers less than 1 also tend to exhibit enhancement, while those with St>1 show a reduction, similar to the 30 min averages shown in Table . The extent of both effects is closely linked to the SDI. Figure a, representing a low-turbulence case, shows that particles with low St exhibit enhanced settling, with enhancement factors reaching up to 6 for particles with high SDI and values close to unity for particles with low SDI. Figure  also shows an inverse relationship between SDI and St.

By looking at individual snowflakes and analyzing their orientation dynamics during free fall under varying turbulence conditions, our observations reveal that orientation is not fixed but evolves continuously as the particle descends . Interestingly, the rate of change in orientation exhibits distinct statistical behaviors depending on the turbulence intensity. These orientation dynamics have direct implications for drag force estimation and terminal velocity prediction. Since drag is strongly dependent on the projected area normal to the direction of motion, variations in particle orientation lead to corresponding fluctuations in the instantaneous Vt. Specifically, we observe that terminal velocity estimates can vary significantly depending on whether the minimum or maximum projected area is used in the drag calculation. The maximum terminal velocity corresponds to the configuration with the smallest frontal area, while the minimum terminal velocity is associated with the largest area given with respect to the gravitational vector. Analysis of millions of individual snowflake measurements reveals that the ratio of maximum to minimum terminal velocity can be as large as 1.5. This result underscores the importance of accounting for orientation-induced drag variability when modeling particle settling, particularly for irregular, anisotropic particles such as snowflakes.

Figure , shows fall speeds as a function of particle density across a broad range of turbulence intensities. Both intuitively and formally (see Eq.  for the terminal velocity), we expect frozen hydrometeors with larger masses to fall at higher speeds in quiescent conditions. Within all 30 min datasets, even for the minimum observed Reynolds number condition (Reλ = 416), we see that turbulence effects are always present and this is in part why we see a decreasing Vp as density increases. Under high-turbulence conditions (Cases 1 and 2), settling velocities are significantly reduced, leading to longer atmospheric residence times. Notably, we also observed an increase in snowflake density under these conditions similar to the processes occurring within clouds, suggesting that prolonged suspension in turbulent flow may facilitate the formation of denser snowflakes (i.e. snowflakes with low SDI). These results are observational and emphasize the statistical relationships among turbulence intensity, particle density, and fall speed. A complete physical interpretation would require concurrent measurements of the local flow field and particle-scale forces, which are beyond the scope of this study.

Figure  shows the relationship between the Vp/Vt and TKE for all cases. Each data point represents a one-minute average collected over a 120 min observational period. The data exhibit a clear inverse relationship, showing that increased turbulence intensity tends to reduce the fall speed of snowflakes. The observed suppression of fall speed at high TKE suggests that turbulent updrafts and eddies play a significant role in delaying particle settling. This is surprising since both experimentally and numerically, loitering is not expected, except in constrained channels. The observed inverse relationship between turbulence intensity and fall speed is unexpected since previous studies, generally at lower Reλ, reported sweeping rather than loitering behavior . Our results extend into higher Reλ regimes and show that this inverse trend persists even in open, fully developed turbulence, indicating that settling dynamics depend on the turbulent scale and may not be fully captured by existing low-Reλ models. Furthermore, our measured loitering and sweeping is an order of magnitude larger than the results of . Note that the scatter about the best fit line is largely due to variations in SDI.

Figure  shows PDFs of observed hydrometeor fall speeds Vp and terminal velocities Vt determined using DEID measurements and Eq. (). During the high-turbulence intensity Case 1 and Case 2 events, many particle streaks had upward trajectories, 33.5% and 8.9%, respectively, representing a clear reduction in Vp compared to the terminal fall speed. A mean settling speed reduction of 57.1% was measured relative to the mean terminal velocity during a 30 min high-turbulence event (Case 1) with Reλ=13187±923; a mean reduction of 28.3% was observed during another high-turbulence event (Case 2) with Reλ=10163±711 (Table  and Fig. a and b). Conversely, during periods of lower turbulence (Case 3 and Case 4) with Reλ=467±32 and Reλ=416±29, respectively, an enhancement in settling speed of 19.4% and 155.2% was observed (see Fig. c and d).

The results from these cases point to a reduction in fall speed for the case of high turbulence and an enhancement for lower turbulence. Similar numerical and experimental studies primarily find enhancements in settling speed for small inertial particles as turbulence increases Vp by way of preferential sweeping mechanisms. What distinguishes the measurements presented here is the availability of the DEID to directly measure hydrometeor microphysical snowflake properties for computation of Vt and a more precise evaluation of the degree of settling reduction or enhancement.

Reductions in Vp during high-turbulence events are associated with broadening of the settling distribution with an increasing fraction of snow particles that move near horizontally or upwards. The lowest turbulence event with Reλ = 416 and TI=0.27 observed in Case 4 has a much narrower distribution than the other cases. Interestingly, the two-dimensional speed (in the plane of the laser sheet, see Vv in Appendix ) of the snowflakes is however comparatively similar among each of the four datasets.

Also notable in Fig.  is that, for all events, the fall-speed distributions have long tails implying high fall speeds occur more often than expected from calculated values of Vt. Secondly, fall-speed distributions during lower-turbulence events are bimodal with peaks near zero fall speed and at higher speeds. High-turbulence cases are unimodal with peaks near zero settling speed. Note that distributions of density and effective diameter during this period do not show any bimodal behavior (Fig. ).

By combining the critical variables collected by all components of the experimental setup (i.e. DEID, PSV, and sonic anemometer), we have shown that snowflake fall speed is a function of snowflake density, snowflake shape, and turbulence intensity. Expressed in terms of non-dimensional parameters, we hypothesize this functional form to be Vp/Vt=f(SDI,TI), with the specific form of the equation given by the following power-law 6VpVt=A0SDIaTIb.

Figure  shows this power-law along with data points from all of the cases studied, where the constants A0=0.013, a=1.65, and b=-0.32 were determined by multiple linear regression. The resulting R2 for the fit is 0.75. The data-point markers in Fig.  are colored by SDI and sized by TI. In these results, TI governs both the enhancement and reduction of Vp/Vt, consistent with the findings in Sects. 3.2 and 3.3. Figure  illustrates the inherent coupling that is observed between TI and SDI (i.e. snowflake microphysical characteristics). That is, storms with high levels of turbulence are typically associated with low SDI values, while storms with low-turbulence levels are associated with high SDI values. Thus, we expect to see light, fluffy snowflakes during periods of light winds and low turbulence.