Constrained probabilistic collocation method for uncertainty quantification of geophysical models

The traditional probabilistic collocation method (PCM) uses either polynomial chaos expansion (PCE) or Lagrange polynomials to represent the model output response. Since the PCM relies on the regularity of the response, it may generate nonphysical realizations or inaccurate estimations of the statistical properties under strongly nonlinear/unsmooth conditions. In this study, we develop a new constrained PCM (CPCM) to quantify the uncertainty of geophysical models accurately and efficiently, where the PCE coefficients are solved via inequality constrained optimization considering the physical constraints of model response, different from that in the traditional PCM where the PCE coefficients are solved using spectral projection or least-square regression. Through solute transport and multiphase flow tests in porous media, we show that the CPCM achieves higher accuracy for statistical moments as well as probability density functions, and produces more reasonable realizations than does the PCM, while the computational effort is greatly reduced compared to the Monte Carlo approach.