A typical assumption is that ensemble data at each spatial location follows a
Gaussian distribution. We investigate the consequences of that assumption
when distributions are non-Gaussian. A sufficiently acceptable interpolation
scheme needs to be addressed for the interpolation of non-Gaussian
distributions. We present two methods to calculate interpolations between two
arbitrary distributions and compare them against two baseline methods. The
first method uses a Gaussian Mixture Model (GMM) to represent distributions.
The second method is a non-parametric approach that interpolates between
quantiles in the cumulative distribution functions. The baseline methods for
comparison purposes are: (a) using a Gaussian representation and
interpolating the means and standard deviations, and (b) forming a new
distribution based on the interpolation of individual realizations of the
ensemble. We show that the two proposed non-Gaussian interpolation methods
have the following behavior: the interpolated distributions do not decompose
to more constituent Gaussian distributions than the highest modality of those
being interpolated, and do not have variances less than the smallest variance
from the grid points being interpolated. Finally,we compare these four
interpolation methods when used in the analysis of scalar and vector fields
of ensemble data sets, particularly in areas where the distribution is
non-Gaussian.