Global uncertainty assessments by high dimensional model representations (HDMR)

A general set of quantitative model assessment and analysis tools, termed high-dimensional model representations (HDMR), have been introduced recently for high dimensional input-output systems. HDMR are a particular family of representations where each term in the representation reflects the independent and cooperative contributions of the inputs upon the output. When data are randomly sampled, a RS(random sampling)-HDMR can be constructed, which is an efficient tool to provide a fully global statistical analysis of a model. The individual RS-HDMR component functions have a direct statistical correlation interpretation. This relation permits the model output variance σ² to be decomposed into its input contributions σ² = Σ_iσ²_i + Σ_i<j σ²_ij +. due to the independent variable action σ²_i, the pair correlation action σ²_ij, etc. The information gained from this decomposition can be valuable for attaining a physical understanding of the origins of output uncertainty as well as suggesting additional laboratory/field studies or model refinements to best improve the quality of the model. To reduce sampling effort, the RS-HDMR component functions are approximately represented by orthonormal polynomials. Only one randomly sampled set of input-output data is needed to determine all σ_i, σ_ij, etc. and a few hundred samples may give reliable results. This paper presents its methodology and applications on an atmospheric photochemistry model and a trace metal bioremediation model.