The Measurement Error Proxy System Model: MEPSM v0.2

Abstract. Proxy system models (PSMs) are an essential component of paleoclimate data assimilation and for testing climate field reconstruction methods. Generally, current statistical PSMs consider the noise in the output (proxy) variable only and ignore the noise in the input (environmental) variables. This problem is exacerbated when there are several input variables. Here we develop a new PSM, the Measurement Error Proxy System Model (MEPSM), which includes noise in all variables, including noise auto- and cross-correlation. The MEPSM is calibrated using a quasi-Bayesian solution, which leverages Gaussian conjugacy to produce a fast solution. Another advantage of MEPSM is that the prior can be used to stabilize the solution between an informative prior (e.g., with a non-zero mean) and the maximum likelihood solution. MEPSM is illustrated by calibrating a proxy model for δ18Ocoral with multiple inputs (marine temperature and salinity), including noise in all variables. MEPSM is applicable to many different climate proxies and will improve our understanding of the effects of predictor noise on PSMs, data assimilation, and climate reconstruction.