| An honest declaration of the error in a mass, momentum or energy balance,
ε, simply raises the question of its acceptability: "At what value of
ε is the attempted balance to be rejected?" Answering this question
requires a reference quantity against which to compare ε. This quantity must
be a mathematical function of all the data used in making the balance. To deliver this
function, a theory grounded in a workable definition of acceptability is essential. A
distinction must be drawn between a retrospective balance and a prospective budget in
relation to any natural space-filling body. Balances look to the past; budgets look to
the future. The theory is built on the application of classical sampling theory to the
measurement and closure of a prospective budget. It satisfies R.A. Fisher's "vital
requirement that the actual and physical conduct of experiments should govern the
statistical procedure of their interpretation". It provides a test, which rejects,
or fails to reject, the hypothesis that the closing error on the budget, when realised,
was due to sampling error only. By increasing the number of measurements, the
discrimination of the test can be improved, controlling both the precision and accuracy
of the budget and its components. The cost-effective design of such measurement campaigns
is discussed briefly. This analysis may also show when campaigns to close a budget on
a particular space-filling body are not worth the effort for either scientific or economic
reasons. Other approaches, such as those based on stochastic processes, lack this
finality, because they fail to distinguish between different types of error in the
mismatch between a set of realisations of the process and the measured data.
Keywords: balance, budget, sampling, hypothesis test, closing error, Earth System |