Assimilation and Network Design

Abstract

Information on the carbon cycle comes from a variety of sources. The methods described in this chapter provide a formalism for combining this information. Without such a formalism we are left making ad hoc choices about how to improve our understanding in the light of disagreements among various streams of information. The introduction of such methods into carbon cycle research, principally via the atmospheric studies of Enting et al. (1993, 1995), revolutionised the field and laid the groundwork for most of the subsequent investigations. The methods in question are fundamentally statistical. They hence provide estimates of the confidence we should have in quantitative statements about the carbon cycle. These statements are usually couched as spreads of probability distributions or as confidence intervals. We refer to them generally as posterior uncertainties. These posterior uncertainties depend on the prior uncertainties of the various data streams that feed the estimation process, the method for combining these data streams (usually some kind of model) and the particular state of the system. Of course, an important aim of measurements is to reduce the posterior uncertainty. The present chapter is concerned with quantitative network design, by which we understand the optimisation of a measurement strategy via minimisation of this posterior uncertainty for target quantities of particular interest. Examples of such target quantities are the long-term global mean terrestrial flux to the atmosphere over a period in the past or in the future. The computational tool that transforms the information provided by an observational network of the carbon cycle into an estimate of posterior uncertainty is a Carbon Cycle Data Assimilation System (CCDAS). Hence, network design is closely linked to assimilation both conceptually and computationally. Much of the work reviewed in this chapter lies in a small subset of possible network design applications for the carbon cycle. In particular, it uses a limited set of types of observations. This is not an inherent limitation of the approach but rather a limitation in modelling approaches that can combine many streams of measurements. This is changing now. Hence, much of the chapter looks forward to applications that combine different measurement approaches. It is useful, therefore, to describe the problem in general even if most cited examples are from simpler cases.