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Abstract. The deterministic motions of clouds and turbulence, despite their chaotic nature, have nonetheless been shown to follow simple statistical power-law scalings: a fractal dimension D relates individual cloud perimeters p to a measurement resolution, and turbulent fluctuations scale with the air parcel separation distance through the Hurst exponent, ℋ. However, it remains uncertain whether atmospheric turbulence is best characterized by a split isotropy that is three-dimensional (3D) with H=1/3 at small scales and two-dimensional (2D) with ℋ=1 at large scales or by a wide-range anisotropic scaling with an intermediate value of ℋ. Here, we introduce an “ensemble fractal dimension” De – analogous to D – that relates the total cloud perimeter per domain area 𝒫 as seen from space to the measurement resolution, and we show theoretically how turbulent dimensionality and cloud edge geometry can be linked through H=De-1. Observationally and numerically, we find the scaling De∼5/3 or H∼2/3, spanning 5 orders of magnitude of scale. Remarkably, the same scaling relationship links two “limiting case” estimates of 𝒫 evaluated at resolutions corresponding to the planetary scale and the Kolmogorov microscale, which span 10 orders of magnitude. Our results are nearly consistent with a previously proposed “23/9D” anisotropic turbulent scaling and suggest that the geometric characteristics of clouds and turbulence in the atmosphere can be easily tied to well-known planetary physical parameters. 

A significant uncertainty in assessments of the role of clouds in climate is the characterization of the full distribution of their sizes. Order-of-magnitude disagreements exist among observations of key distribution parameters, particularly power law exponents and the range over which they apply. A study by Savre and Craig (2023) suggested that the discrepancies are due in large part to inaccurate fitting methods: they recommended the use of a maximum likelihood estimation technique rather than a linear regression to a logarithmically transformed histogram of cloud sizes. Here, we counter that linear regression is both simpler and equally accurate, provided the simple precaution is followed that bins containing fewer than ∼ 24 counts are omitted from the regression. A much more significant and underappreciated source of error is how to treat clouds that are truncated by the edges of unavoidably finite measurement domains. We offer a simple computational procedure to identify and correct for domain size effects, with potential application to any geometric size distribution of objects, whether physical, ecological, social or mathematical. 

Abstract. It is a challenge to obtain accurate measurements of the microphysical properties of delicate, structurally complex, frozen, and semi-frozen hydrometeors. We present a new technique for the real-time measurement of the density of freshly fallen individual snowflakes. A new thermal-imaging instrument, the Differential Emissivity Imaging Disdrometer (DEID), has been shown through laboratory and field experiments to be capable of providing accurate estimates of individual snowflake and bulk snow hydrometeor density (which can be interpreted as the snow-to-liquid ratio or SLR). The method exploits the rate of heat transfer during the melting of a hydrometeor on a heated metal plate, which is a function of the temperature difference between the hotplate surface and the top of the hydrometeor. The product of the melting speed and melting time yields an effective particle thickness normal to the hotplate surface, which can then be used in combination with the particle mass and area on the plate to determine a particle density. Uncertainties in estimates of particle density are approximately 4 % based on calibrations with laboratory-produced particles made from water and frozen solutions of salt and water and field comparisons with both high-resolution imagery of falling snow and traditional snowpack density measurements obtained at 12 h intervals. For 17 storms, individual particle densities vary from 19 to 495 kg m−3, and storm mean snow densities vary from 40 to 100 kg m−3. We observe probability distribution functions for hydrometeor density that are nearly Gaussian with kurtosis of ≈ 3 and skewness of ≈ 0.01. 

We use a novel experimental setup to obtain the vertical velocity and acceleration statistics of snowflakes settling in atmospheric surface-layer turbulence, for Taylor microscale Reynolds numbers (Reλ) between 400 and 67 000, Stokes numbers (St) between 0.12 and 3.50, and a broad range of snowflake habits. Despite the complexity of snowflake structures and the non-uniform nature of the turbulence, we find that mean snowflake acceleration distributions can be uniquely determined from the value of St. Ensemble-averaged snowflake root mean square (rms) accelerations scale nearly linearly with St. Normalized by the rms value, the acceleration distribution is nearly exponential, with a scaling factor for the (exponent) of −3/2 that is independent of Reλ and St; kurtosis scales with Reλ, albeit weakly compared to fluid tracers in turbulence; gravitational drift with sweeping is observed for St < 1. Surprisingly, the same exponential distribution describes a pseudo-acceleration calculated from fluctuations of snowflake terminal fall speed in still air. This equivalence suggests an underlying connection between how turbulence determines the trajectories of particles and the microphysics determining the evolution of their shapes and sizes. 

Abstract. Cloud area distributions are a defining feature of Earth's radiative exchanges with outer space. Cloud perimeter distributions n(p) are also interesting because the shared interface between clouds and clear sky determines exchanges of buoyant energy and air. Here, we test using detailed model output and a wide range of satellite datasets a first-principles prediction that perimeter distributions follow a scale-invariant power law n(p) ∝ p-(1+β), where the exponent β = 1 is evaluated for perimeters within moist isentropic atmospheric layers. In model analyses, the value of β is closely reproduced. In satellite data, β is remarkably robust to latitude, season, and land–ocean contrasts, which suggests that, at least statistically speaking, cloud perimeter distributions are determined more by atmospheric stability than Coriolis forces, surface temperature, or contrasts in aerosol loading between continental and marine environments. However, the satellite-measured value of β is found to be 1.26 ± 0.06 rather than β = 1. The reason for the discrepancy is unclear, but comparison with a model reproduction of the satellite perspective suggests that it may owe to cloud overlap. Satellite observations also show that scale invariance governs cloud areas for a range at least as large as ∼ 3 to ∼ 3 × 105 km2, and notably with a corresponding power law exponent close to unity. Many prior studies observed a much smaller range for power law behavior, and we argue this difference is due to inappropriate treatments of the statistics of clouds that are truncated by the edge of the measurement domain. 

Abstract. Due to the discretized nature of rain, the measurement of a continuous precipitation rate by disdrometers is subject to statistical sampling errors. Here, Monte Carlo simulations are employed to obtain the precision of rain detection and rate as a function of disdrometer collection area and compared with World Meteorological Organization guidelines for a 1 min sample interval and 95 % probability. To meet these requirements, simulations suggest that measurements of light rain with rain rates R ≤ 0.50 mm h−1 require a collection area of at least 6 cm × 6 cm, and for R = 1 mm h−1, the minimum collection area is 13 cm × 13 cm. For R = 0.01 mm h−1, a collection area of 2 cm × 2 cm is sufficient to detect a single drop. Simulations are compared with field measurements using a new hotplate device, the Differential Emissivity Imaging Disdrometer. The field results suggest an even larger plate may be required to meet the stated accuracy, likely in part due to non-Poissonian hydrometeor clustering. 

Abstract. Ground-based measurements of frozen precipitation are heavily influenced by interactions of surface winds with gauge-shield geometry. The Multi-Angle Snowflake Camera (MASC), which photographs hydrometeors in free-fall from three different angles while simultaneously measuring their fall speed, has been used in the field at multiple midlatitude and polar locations both with and without wind shielding. Here, we present an analysis of Arctic field observations – with and without a Belfort double Alter shield – and compare the results to computational fluid dynamics (CFD) simulations of the airflow and corresponding particle trajectories around the unshielded MASC. MASC-measured fall speeds compare well with Ka-band Atmospheric Radiation Measurement (ARM) Zenith Radar (KAZR) mean Doppler velocities only when winds are light (≤5ms-1) and the MASC is shielded. MASC-measured fall speeds that do not match KAZR-measured velocities tend to fall below a threshold value that increases approximately linearly with wind speed but is generally <0.5ms-1. For those events with wind speeds ≤1.5ms-1, hydrometeors fall with an orientation angle mode of 12∘ from the horizontal plane, and large, low-density aggregates are as much as 5 times more likely to be observed. Simulations in the absence of a wind shield show a separation of flow at the upstream side of the instrument, with an upward velocity component just above the aperture, which decreases the mean particle fall speed by 55 % (74 %) for a wind speed of 5 m s−1 (10 m s−1). We conclude that accurate MASC observations of the microphysical, orientation, and fall speed characteristics of snow particles require shielding by a double wind fence and restriction of analysis to events where winds are light (≤5ms-1). Hydrometeors do not generally fall in still air, so adjustments to these properties' distributions within natural turbulence remain to be determined. 

The inertial response of a particle to turbulent flows is a problem of relevance to a wide range of environmental and engineering problems. The equation most often used to describe the force balance is the Maxey-Riley equation, which includes in addition to buoyancy and steady drag forces, an unsteady Basset drag force related to past particle acceleration. Here we provide a historical review of how the Maxey-Riley equation was developed and how it is only suited for studies where the Reynolds number is less than unity. Revisiting the innovative mathematical methods employed by Basset (1888), we introduce an alternative formulation for the unsteady drag for application to a broader range of particle motions. While the Basset unsteady drag is negligible at higher Reynolds numbers, the revised unsteady drag is not. 

Abstract. The Differential Emissivity Imaging Disdrometer (DEID) is a new evaporation-based optical and thermal instrument designed to measure the mass, size, density and type of individual hydrometeors as well as their bulk properties. Hydrometeor spatial dimensions are measured on a heated metal plate using an infrared camera by exploiting the much higher thermal emissivity of water compared with metal. As a melted hydrometeor evaporates, its mass can be directly related to the loss of heat from the hotplate assuming energy conservation across the hydrometeor. The heat loss required to evaporate a hydrometeor is found to be independent of environmental conditions including ambient wind velocity, moisture level and temperature. The difference in heat loss for snow vs. rain for a given mass offers a method for discriminating precipitation phase. The DEID measures hydrometeors at sampling frequencies of up to 1 Hz with masses and effective diameters greater than 1 µg and 200 µm, respectively, determined by the size of the hotplate and the thermal camera specifications. Measurable snow water equivalent (SWE) precipitation rates range from 0.001 to 200 mm h−1, as validated against a standard weighing bucket. Preliminary field experiment measurements of snow and rain from the winters of 2019 and 2020 provided continuous automated measurements of precipitation rate, snow density and visibility. Measured hydrometeor size distributions agree well with canonical results described in the literature. 

Abstract. A new precipitation sensor, the Differential Emissivity Imaging Disdrometer (DEID), is used to provide the first continuous measurements of the mass, diameter, and density of individual hydrometeors. The DEID consists of an infrared camera pointed at a heated aluminum plate. It exploits the contrasting thermal emissivity of water and metal to determine individual particle mass by assuming that energy is conserved during the transfer of heat from the plate to the particle during evaporation. Particle density is determined from a combination of particle mass and morphology. A Multi-Angle Snowflake Camera (MASC) was deployed alongside the DEID to provide refined imagery of particle size and shape. Broad consistency is found between derived mass–diameter and density–diameter relationships and those obtained in prior studies. However, DEID measurements show a generally weaker dependence with size for hydrometeor density and a stronger dependence for aggregate snowflake mass.