Abstract
Abstract. A simple formulation of aggregation for two-moment bulk microphysical models is derived. The solution involves the evaluation of a double integral of the collection kernel weighted with the crystal size (or mass) distribution. This quantity is to be inserted into the differential equation for the crystal number concentration which has classical Smoluchowski form. The double integrals are evaluated numerically for log-normal size distributions over a large range of geometric mean masses. A polynomial fit of the results is given that yields good accuracy. Various tests of the new parameterisation are described: aggregation as stand-alone process, in a box-model, and in 2-D simulations of a cirrostratus cloud. These tests suggest that aggregation can become important for warm cirrus, leading even to higher and longer-lasting in-cloud supersaturation. Cold cirrus clouds are hardly affected by aggregation. The collection efficiency is taken from a parameterisation that assumes a dependence on temperature, a situation that might be improved when reliable measurements from cloud chambers suggests the necessary constraints for the choice of this parameter.
Highlights
Measurements by Nakaya and Matsumoto (1954) and Hosler and Hallgren (1960) indicate a Cirrus clouds, in particular at temperatures higher than −40◦C, often contain very large ice crystals with maximum dimensions exceeding 1 mm (Heymsfield and McFarquhar, 2002, Fig. 4.6). These large crystals generally have complex shapes (Field and Heymsfield, 2003, Fig. 3), and many of them seem to be aggregates of simpler crystals, one has to be careful in identifying irregular crystals with agtemperature dependence of the sticking ability, which could be explained by the liOquicdelaayner Sonctioepnocf ethe ice crystals
We have derived from the master-equation for coagulation a simple formulation of aggregation for two-moment bulk microphysical models
We developed the formulation for aggregation of crystals belonging to the same class only (the microphysics scheme of Spichtinger and Gierens (2009a) allows more than one class of ice)
Summary
In particular at temperatures higher than −40◦C, often contain very large ice crystals with maximum dimensions exceeding 1 mm (Heymsfield and McFarquhar, 2002, Fig. 4.6). The further evolution of the latter with time can be described by scaling transformations, that is, when the x (size) and y (number) axes are transformed with two simple functions of time (x (t) = x fx(t), y (t) = y fy(t)), the size distribution is represented by a constant curve in this changing coordinate system Such scaling behaviour in ice clouds has been demonstrated by several researchers and traced back to a dominance of aggregation processes Bulk models use only some low order moments of the a priori assumed size distribution and predict their temporal evolution subject to microphysical processes as nucleation, depositional or condensational growth (and evaporation or sublimation), sedimentation, and aggregation. The computation of the integrals for special choices of f (m) and the kernel is demonstrated
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