By I G Enting
An outline of the mathematical concepts used to interpret greenhouse fuel assets and sinks.
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Extra resources for Inverse Problems in Atmospheric Constituent Transport
Sample text
1 lists some of the components of the dry atmosphere. The main constituents, those in the upper group in the table, are distributed virtually uniformly in space and time, although it has recently become possible to measure the very small changes in oxygen content and use them to interpret aspects of the carbon cycle. 1. The composition of the dry atmosphere in terms of molar proportions. Values in the upper group are from the US Standard Atmosphere [340], apart from the rate of change in concentration of oxygen.
In this book, one of the most important applications of toy models is to illustrate the differences between forward and inverse modelling with various types of model. In addition, toy models may often give useful estimates of uncertainty. For illconditioned inverse problems, estimates of the form xˆ = a j c j will frequently involve cancellations and so accurate estimates require accurate values of the ‘inversemodel’ coefficients, a j . In contrast, for independent data, errors of the form var xˆ = |a j |2 var c j involve sums without cancellations and so are much less sensitive to errors and approximations in the model.
Additional characteristic time-scales exist, such as the Madden–Julian oscillation (MJO) in the tropical troposphere and the quasi-biennial oscillation (QBO) in the stratosphere. 2 represent such wave-like phenomena. An important part of the study of atmospheric dynamics addresses the issues of conditions under which various types of wave can grow. Longer time-scale effects such as El Ni˜no (or the southern oscillation) [6] and longer-term interdecadal variability reflect chaotic behaviour of the combined atmosphere–ocean system.