Mixtures of Gaussians for Uncertainty Description in Bivariate Latent Heat Flux Proxies

This paper proposes a new probabilistic approach for describing uncertainty in the ensembles of latent heat flux proxies. The proxies are obtained from hourly Bowen ratio and satellite-derived measurements, respectively, at several locations in the southern Great Plains region in the United States. The novelty of the presented approach is that the proxies are not considered separately, but as bivariate samples from an underlying probability density function. To describe the latter, the use of Gaussian mixture density models—a class of nonparametric, data-adaptive probability density functions—is proposed. In this way any subjective assumptions (e.g., Gaussianity) on the form of bivariate latent heat flux ensembles are avoided. This makes the estimated mixtures potentially useful in nonlinear interpolation and nonlinear probabilistic data assimilation of noisy latent heat flux measurements. The results in this study show that both of these applications are feasible through regionalization of estimated mixture densities. The regionalization scheme investigated here utilizes land cover and vegetation fraction as discriminatory variables.