| dc.description.abstract | In the context of prediction science, the sources of uncertainty can be from the uncertainties of the experiments, modeling, model inputs, numerical analysis, etc. This study concentrates on quantifying the forecast uncertainty arising from the propagation of the uncertainties in the model inputs to the dynamical model. The uncertainties in the inputs include the randomness in (1) the initial conditions, (2) the forcing term (including both the external forcing and the boundary conditions), and (3) randomness in the parameters of the model. In order to quantify the uncertainties in the forecast, three uncertainty quantification (UQ) methods are studied, namely classical Monte Carlo (MC), polynomial chaos (PC) expansion and unscented transformation (UT). Using MC as the benchmark, two dynamical models are used in this study to examine the performance of PC expansion and UT. One is the low order (two components) spectral solution to the nonlinear advection equation, and the other one is the five-variable mixed-layer model which is used to describe the return flow event over the Gulf of Mexico during the cool season (between November and March) every year. The experimental results and the comparisons with MC have shown that both PC and UT can provide good estimates on the statistical information relating to the forecast, for example, the mean, variation (or standard deviation), covariance. The approach of UT utilizes a set of deterministically chosen sigma points to propagate the uncertainties contained in the inputs through the dynamical model. Only the first two moments of the forecast can be estimated by UT. Different from UT, the PC expansion represents the stochastic process in the form of a series expression (hence a surrogate approximation) in terms of the orthogonal polynomials whose type depends on the probability distribution of the random inputs. Ensemble forecast can be achieved by sampling the random variable used in the PC expansion. Furthermore, the histogram of the forecast can be constructed using the ensemble forecast, and then one can estimate the probability density function (PDF) of the forecast. What’s more, PC expansion can also give estimates on the statistics of higher order moments. The application of PC and UT in quantifying the forecast uncertainties in large scale system, the combination with data assimilation techniques and its real applications, and the ability to deal with nonGaussian distributions will be some of the topics for future study. | en_US |
