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Register a new userUniversality in snowflake aggregation
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Added by
Christopher David Westbrook
Publication date
2003
fields
Physics
and research's language is
English
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Aggregation of ice crystals is a key process governing precipitation. Individual ice crystals exhibit considerable diversity of shape, and a wide range of physical processes could influence their aggregation; despite this we show that a simple computer model captures key features of aggregate shape and size distribution reported recently from Cirrus clouds. The results prompt a new way to plot the experimental size distributions leading to remarkably good dynamical scaling. That scaling independently confirms that there is a single dominant aggregation mechanism at play, albeit our model (based on undeflected trajectories to contact) does not capture its form exactly.
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Convective self-aggregation refers to a phenomenon that random convection can self-organize into large-scale clusters over an ocean surface with uniform temperature in cloud-resolving models. Understanding its physics provides insights into the development of tropical cyclones and the Madden-Julian Oscillation. Here we present a vertically resolved moist static energy (VR-MSE) framework to study convective self-aggregation. We find that the development of self-aggregation is associated with an increase of MSE variance in the boundary layer (BL). We further show that radiation dominates the generation of MSE variance, which is further enhanced by atmospheric circulations. Surface fluxes, on the other side, consume MSE variance and then inhibits self-aggregation. These results support that the BL plays a key role in the development of self-aggregation, which agrees with recent numerical simulation results and the available potential energy analyses. Moreover, we find that the adiabatic production of MSE variance due to circulation mainly comes from the near-surface layer rather than the low-level circulation emphasized by previous literature. This new analysis framework complements the previous MSE framework that does not resolve the vertical dimension.
This study investigated an approach to improve the accuracy of computationally lightweight surrogate models by updating forecasts based on historical accuracy relative to sparse observation data. Using a lightweight, ocean-wave forecasting model, we created a large number of model ensembles, with perturbed inputs, for a two-year study period. Forecasts were aggregated using a machine-learning algorithm that combined forecasts from multiple, independent models into a single best-estimate prediction of the true state. The framework was applied to a case-study site in Monterey Bay, California. A~learning-aggregation technique used historical observations and model forecasts to calculate a weight for each ensemble member. Weighted ensemble predictions were compared to measured wave conditions to evaluate performance against present state-of-the-art. Finally, we discussed how this framework, which integrates ensemble aggregations and surrogate models, can be used to improve forecasting systems and further enable scientific process studies.
Snowflake growth provides us with a fascinating example of spontaneous pattern formation in nature. Attempts to understand this phenomenon have led to important insights in non-equilibrium dynamics observed in various active scientific fields, ranging from pattern formation in physical and chemical systems, to self-assembly problems in biology. Yet, very few models currently succeed in reproducing the diversity of snowflake forms in three dimensions, and the link between model parameters and thermodynamic quantities is not established. Here, we report a modified phase field model that describes the subtlety of the ice vapour phase transition, through anisotropic water molecules attachment and condensation, surface diffusion, and strong anisotropic surface tension, that guarantee the anisotropy, faceting and dendritic growth of snowflakes. We demonstrate that this model reproduces the growth dynamics of the most challenging morphologies of snowflakes from the Nakaya diagram. We find that the growth dynamics of snow crystals matches the selection theory, consistently with previous experimental observations.
We explore the possibility to identify areas of intense patch formation from floating items due to systematic convergence of surface velocity fields by means of a visual comparison of Lagrangian Coherent Structures (LCS) and estimates of areas prone to patch formation using the concept of Finite-Time Compressibility (FTC, a generalisation of the notion of time series of divergence). The LCSs are evaluated using the Finite Time Lyapunov Exponent (FTLE) method. The test area is the Gulf of Finland (GoF) in the Baltic Sea. A basin-wide spatial average of backward FTLE is calculated for the GoF for the first time. This measure of the mixing strength displays a clear seasonal pattern. The evaluated backward FTLE features are linked with potential patch formation regions with high FTC levels. It is shown that areas hosting frequent upwelling or downwelling have consistently stronger than average mixing intensity. The combination of both methods, FTC and LCS, has the potential of being a powerful tool to identify the formation of patches of pollution at the sea surface.
We compute $d$-dimensional scalar six-point conformal blocks in the two possible topologies allowed by the operator product expansion. Our computation is a simple application of the embedding space operator product expansion formalism developed recently. Scalar six-point conformal blocks in the comb channel have been determined not long ago, and we present here the first explicit computation of the scalar six-point conformal blocks in the remaining inequivalent topology. For obvious reason, we dub the other topology the snowflake channel. The scalar conformal blocks, with scalar external and exchange operators, are presented as a power series expansion in the conformal cross-ratios, where the coefficients of the power series are given as a double sum of the hypergeometric type. In the comb channel, the double sum is expressible as a product of two ${}_3F_2$-hypergeometric functions. In the snowflake channel, the double sum is expressible as a Kampe de Feriet function where both sums are intertwined and cannot be factorized. We check our results by verifying their consistency under symmetries and by taking several limits reducing to known results, mostly to scalar five-point conformal blocks in arbitrary spacetime dimensions.
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