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<br />12 <br /> <br />All ice-liquid collisions are assumed to result in a new ice particle having a <br /> <br />mass equal to the sum of the masses of the colliding particles. The riming process <br /> <br />is only allowed to operate if the liquid drop involved is supercooled. Ice-iice <br /> <br />collisions are assumed to have a coalescence efficiency of zero. The stochastic <br /> <br />riming process can then be represented as: <br /> <br />Xl x" CO <br />D(x) = J I f(x')g(xl)t(X',X")j9(X1, x",x) dx"dx' - J g(x)f(xl)f(X,x') dx' (eq. 11) <br />000 <br /> <br />where <br /> <br />f(x) = the density function of number at liquid mass x <br /> <br />g(x) = the density function of number at ice mass x <br /> <br />D(x) = the gain (or loss) of number at ice mass x <br /> <br />f(x' ,x") = the liquid-liquid collection kernel as modified by <br />the ice-liquid particle differential fall speed, the <br />efficiency being assumed to be the same as that <br />for the liquid-liquid collision <br /> <br />All other values take the same meaning as presented in the coalescence-breakup <br /> <br />equation. The factor of one-half is missing here in the double integral due to the <br /> <br />lack of symmetry in the f(x')g(x") and g(x')f(xll) collisions. <br /> <br />Due to problems in the Eulerian representation of mixed phase particles, all <br /> <br />liquid-ice collisions above the freezing level are assumed to freeze to solid spherical <br /> <br />ice particles at a density of 0.9 gm/cm 3. No riming growth is allowed at temperatures <br /> <br />o <br />warmer than 0 C . <br />