The means and variances of the normal–lognormal mixture model are provided by CLUBB in the macroscale equations. Two-dimensional tensor product integration with (a) a = −∞ and (b) a = 1 in (42).Įxact (a) autoconversion and (b) accretion rates for different altitudes at t = 72 h in the RICO experiment within CLUBB. (left to right), (top to bottom) Two-dimensional tensor product quadrature rules using Hermite–Hermite, Hermite–Legendre, and Hermite–Laguerre in the x and y directions, respectively. The Laguerre quadrature levels out due to double precision limits. The Legendre quadrature levels out due to error and, respectively. (right) Convergence of quadrature rules for over the region [1, ∞). (left) Convergence of quadrature rules for over the truncated region [1, ∞). This time, the discontinuity is present only in the derivative so convergence is slightly better. (c) Convergence for Hermite quadrature with, where we integrate over the entire domain. (b) Hermite quadrature exhibits very poor performance when we add a single jump discontinuity at a = 1 where. (a) Hermite quadrature easily outperforms both Monte Carlo and Latin hypercube sampling approaches.
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