Studies on the Impacts of 3D-VAR Assimilation of Satellite Observations on the Simulation of Monsoon Depressions over India - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 634

organization of cumulus convection associated with a tropical cyclone. Monsoon
depressions generally weaken in intensity after reaching the central parts of India.
These then weaken to low pressure systems and move in a west-northwest direction
and merge with the seasonal low over northwest India ( Sikka 1980 ).

26.2 Data Assimilation

Geophysical (atmospheric/oceanic) information is essentially utilized to test hypoth-
esis (i.e. testing our understanding of the system), attribute cause and effect (i.e. to
understand the cause of geophysical events) and to make forecasts, i.e. to predict
future geophysical events ( Lahoz et al. 2010 ). Broadly, the geophysical information
is available through two broad sources, namely, (1) “observation” which are nothing
but measurements of the geophysical system, and (2) “models”, which have been
built based on the earlier “measurements” gathered of the system as well as our
understanding of the evolution of the geophysical system. It is true that both
observations and models have errors. The model errors arise due to the fact that the
models are imperfect in the sense that our understanding of the physical processes
associated with the geophysical system is somewhat “incomplete”. Furthermore,
model errors also appear due to the need to limit resolution of the digitization of
the continuous governing equations due to computational costs. The observational
errors are characterized as random, systematic and also due to representativeness
( Lahoz et al. 2010 ). Furthermore, the “observations” have gaps since the measure-
ments of the system are in general discrete in space and time. It is logical to fill
the gaps in the “observation” by using the information based on the behaviour
of the system, namely the “models”. A methodology of objectively combining
“observations” and “model” information to yield an “optimum” or “best estimate”
of the geophysical system is called “data assimilation”.
The basic premise in the data assimilation methodology is that combining
“observations” and “model” information together with knowledge of their respective
errors will yield combined information that is more valuable than the individual
information, provided the process of combining both the information is robust.
In data assimilation, the model takes the information from the observation and
propagates this information to unobserved regions successfully filling in the so
called “gaps” in the observation. Data assimilation can also provide estimation
of unobserved quantities. While Panofsky ( 1949 ) utilized polynomial functions
to fit to the observation values, in the early development of objective analysis of
meteorological data, Gilchrist and Cressman ( 1954 ) improved the above method by
introducing the concept of “region of influence” for each observation. Gilchrist and
Cressman also proposed the use of a background field from a previous forecast.
Bergthorsson and Doos ( 1955 ) optimized the weights given to each observation
based on the accuracy of the various types of observations while Cressman ( 1959 )
proposed variation of above method involving multiple iterations of the analysis.
This was followed by data assimilation method based on “optimal interpolation”