5 Atmospheric Data Assimilation and
Quality Control
ANDREW c. LORENC
The Met. Office, Bracknell, England
5.1 Introduction
In this paper we discuss the basic physics of the atmospheric data assimilation
problem, in order to understand the important factors to be considered in its mathematical solution. The key mathematical technique, the optimal combination of
information, is also approached from its Bayesian basics. Much of this is based on
earlier papers (e.g. Lorenc, 1986). The novelty of this paper is its bringing together
of these in a simple didactic form, following the agreed notation of Ide et al.
(1997), with very simple examples to aid in the physical interpretation ofthe analysis equations.
In the second half ofthe paper the analysis is extended to handle gross observational errors, described by a non-Gaussian error distribution. Again, much of this
is based on earlier papers (Lorenc and Hammon, 1988, Dharssi et al., 1992, Ingleby
and Lorenc, 1993). Various practical methods can be derived using Bayesian ideas;
they are compared using a very simple example.
5.2 What is Data Assimilation?
There are insufficient observations at any one time to determine the state of the
atmosphere. So if we want a detailed complete picture, we need additional information. This is available as knowledge ofthe behaviour and probable structure of
the atmosphere. For instance the knowledge of the typical structure of a frontal
depression enables a human to draw an "analysis" of the atmospheric state, based
on scattered observations. To advance beyond this subjective approach, the behaviour of the atmosphere is embodied in a computer model. In particular, knowledge
of the evolution with time is embodied in a forecast model. This enables us to use
observations distributed in time. The model also provides a consistent means of
representing the atmosphere. Assimilation is the process of finding the model representation which is most consistent with the observations.
Usually, data assimilation proceeds sequentially in time. The model organises
and propagates forward the information from previous observations. The information from new observations is used to modify the model state, to be as consistent as
possible with them and the previous information. It is the experience with operational assimilation for Numerical Weather Prediction (NWP) that there is usually
Quality Control
ANDREW c. LORENC
The Met. Office, Bracknell, England
5.1 Introduction
In this paper we discuss the basic physics of the atmospheric data assimilation
problem, in order to understand the important factors to be considered in its mathematical solution. The key mathematical technique, the optimal combination of
information, is also approached from its Bayesian basics. Much of this is based on
earlier papers (e.g. Lorenc, 1986). The novelty of this paper is its bringing together
of these in a simple didactic form, following the agreed notation of Ide et al.
(1997), with very simple examples to aid in the physical interpretation ofthe analysis equations.
In the second half ofthe paper the analysis is extended to handle gross observational errors, described by a non-Gaussian error distribution. Again, much of this
is based on earlier papers (Lorenc and Hammon, 1988, Dharssi et al., 1992, Ingleby
and Lorenc, 1993). Various practical methods can be derived using Bayesian ideas;
they are compared using a very simple example.
5.2 What is Data Assimilation?
There are insufficient observations at any one time to determine the state of the
atmosphere. So if we want a detailed complete picture, we need additional information. This is available as knowledge ofthe behaviour and probable structure of
the atmosphere. For instance the knowledge of the typical structure of a frontal
depression enables a human to draw an "analysis" of the atmospheric state, based
on scattered observations. To advance beyond this subjective approach, the behaviour of the atmosphere is embodied in a computer model. In particular, knowledge
of the evolution with time is embodied in a forecast model. This enables us to use
observations distributed in time. The model also provides a consistent means of
representing the atmosphere. Assimilation is the process of finding the model representation which is most consistent with the observations.
Usually, data assimilation proceeds sequentially in time. The model organises
and propagates forward the information from previous observations. The information from new observations is used to modify the model state, to be as consistent as
possible with them and the previous information. It is the experience with operational assimilation for Numerical Weather Prediction (NWP) that there is usually