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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. 

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. 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.