Atmospheric Data Assimilation and Quality Control
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stantially less accurate. Computationally feasible methods for integrating this
knowledge more effectively into the assimilation, treating it as a single four-dimensional problem, are the subject of current research.
5.4 Products and U ses of Assimilation
Assimilation produces a convenient, comprehensive, high resolution, representation of the atmosphere. It has been clearly demonstrated that the use of a computer model is usually better (i.e. leads to better forecasts) than the subjective
human approach. The main practical use ofthese assimilated "analyses" is for initialising numerical weather prediction forecasts. They are also useful for climate
and general circulation studies, for instance in the calculations of fluxes, which
make use oftheir high resolution and comprehensive coverage. However it must be
remembered that the blend of observed and modelled information will vary according to the accuracy and coverage of the observations. So they must be used with
great care for model validation, and climate change detection.
Very useful secondary products of a data assimilation system are the statistics on
the (mis-)fit of observations to model. These can be more directly used for model
(in-)validation, and for the monitoring of observing systems.
5.5 The Optimal Combination of Information
The history of this goes back to Gauss (1809, 1823), who in his study of the
motion ofthe planets developed methods for the weighted combination of observations with errors. We will approach it from a Bayesian standpoint, following
Lorenc (1986) and Lorenc and Hammon (1988). The resulting equations are equivalent to Gauss's minimum variance approach, for observations with a Gaussian
error distribution.
5.5.1 Bayes' Theorem for Discrete Events
The Bayesian approach is to use probabilities to describe the accuracy of our
knowledge about past events. We then have a formalism for modifYing the probabilities in the light of new knowledge; exactly what we need to do in sequential
data assimilation. We introduce this with a discrete example for events A and B.
P(A) is the probability of A occurring (this is the usual use of probabilities), or a
measure of our certainty that A occurred in the past (this is the Bayesian use of
probabilities). Then P(AnB) is the probability that A and B both occurred, and
P(A I B) is the conditional probability of A given B has occurred. We have two
ways of expressing P(AnB):
75
stantially less accurate. Computationally feasible methods for integrating this
knowledge more effectively into the assimilation, treating it as a single four-dimensional problem, are the subject of current research.
5.4 Products and U ses of Assimilation
Assimilation produces a convenient, comprehensive, high resolution, representation of the atmosphere. It has been clearly demonstrated that the use of a computer model is usually better (i.e. leads to better forecasts) than the subjective
human approach. The main practical use ofthese assimilated "analyses" is for initialising numerical weather prediction forecasts. They are also useful for climate
and general circulation studies, for instance in the calculations of fluxes, which
make use oftheir high resolution and comprehensive coverage. However it must be
remembered that the blend of observed and modelled information will vary according to the accuracy and coverage of the observations. So they must be used with
great care for model validation, and climate change detection.
Very useful secondary products of a data assimilation system are the statistics on
the (mis-)fit of observations to model. These can be more directly used for model
(in-)validation, and for the monitoring of observing systems.
5.5 The Optimal Combination of Information
The history of this goes back to Gauss (1809, 1823), who in his study of the
motion ofthe planets developed methods for the weighted combination of observations with errors. We will approach it from a Bayesian standpoint, following
Lorenc (1986) and Lorenc and Hammon (1988). The resulting equations are equivalent to Gauss's minimum variance approach, for observations with a Gaussian
error distribution.
5.5.1 Bayes' Theorem for Discrete Events
The Bayesian approach is to use probabilities to describe the accuracy of our
knowledge about past events. We then have a formalism for modifYing the probabilities in the light of new knowledge; exactly what we need to do in sequential
data assimilation. We introduce this with a discrete example for events A and B.
P(A) is the probability of A occurring (this is the usual use of probabilities), or a
measure of our certainty that A occurred in the past (this is the Bayesian use of
probabilities). Then P(AnB) is the probability that A and B both occurred, and
P(A I B) is the conditional probability of A given B has occurred. We have two
ways of expressing P(AnB):