Assimilation of ocean colour data into a biochemical model of the North Atlantic - Part 2. Statistical analysis

摘要

In a companion paper [J. Mar. Syst. 40/41 (2003)], hereafter referred to as Part 1, we investigated an advanced data assimilation technique, the ensemble Kalman filter, for sequentially updating the biochemical state of a three-dimensional coupled physical-biochemical model of the North Atlantic. Within the methodology, an ensemble of model states is integrated forward to a measurement time, where an estimate based on information from both the model and the observations is calculated. The ensemble of states can provide estimates of any statistical moment, although moments of order three and higher are discarded in the analysis. In the Part 1 paper, we presented a simple demonstration experiment for the months April and May 1998, with some additional sensitivity tests at the first measurement time. The simulation included the early part of the spring bloom, which is characterized by strong nonlinear biochemical activity. It was concluded that the ensemble Kalman filter was able to provide an updated state consistent with the observations, and it was seen that the ensemble variance of the different biochemical components decreased during the analysis. In this paper, we make some important remarks about linear versus nonlinear systems, emphasizing the fact that a data assimilation problem may become extremely complicated for strongly nonlinear problems. Statistical moments of any order may develop from Gaussian initial conditions during nonlinear evolution, and important information may be discarded by calculating an estimate based on only the Gaussian part of the full probability distribution. We demonstrate that a Monte Carlo approach can provide information about the system under consideration.. For example, an ensemble of states, which is a representative of the true probability density function, can be visualized in one, two or three dimensions. Also, one can find estimates for the degree of nonnormality of the ensemble, which may act as indicators of the validity of performing a data assimilation based on the Gaussian part of the full probability distribution. (C) 2003 Elsevier Science B.V All rights reserved. [References: 10]