numerous causes. They may be related to the fact that the physical processes which
lie in the basis of the models are poorly known. In addition, the processes of subgrid
description are not resolved correctly. The lack of the input data or their poor
quality may also cause wrong prediction. However, the main cause is not adequate
knowledge of the physical processes in full details. In other words, the basic
equations, which are applied for modeling are not completely correct and describe
the reality only partially. Therefore, the further progress in the computer power and
facilities as well as in the development of the mathematical algorithms, and increase
in the model resolution would not necessary lead to the better prediction and
analysis of the natural phenomena. In relation to the aforementioned ideas it is
necessary to highlight that the development and further progress in the observational database will need improvements in testing and validation of the models and
correction of the model outputs towards the observations.
Eventually, one may come to a conclusion that, in order to improve substantially
the knowledge and understanding of the climate and other geophysical processes
and their predictability it is necessary to combine the mathematical models and field
data. This combination makes possible improving the modeling quality and
enriching and restoring the existing database.
The problem of the optimal combination of the data and models is known in
geophysics as the data assimilation (DA) problem. This is a non-trivial scientific
problem because the extreme solutions such as mere replacement of all the model
values with the observed data without changing the other values or simply ignoring
the observations, while the model values remain unchanged are obviously not
optimal. Indeed, if we only replace the model values by observations, the model
output field will be totally unbalanced and on next time-step it will lead to large
false fluxes, which may completely destroy the model. On the contrary, leaving the
model values unchanged and ignoring the observations may result in a completely
wrong output, which would appear far from reality.
In meteorology and oceanography, the DA-problems have been ongoing during
several decades. Originally these problems came into consideration in the end of
1960s. Apparently, one of the first results was reported by Gandin [6]. He proposed
the objective analysis method to correct the model output based on the linear
interpolation ideas. This idea turned out very fruitful and this method became
widely used [7]. Further, the DA-methods became an important part of the
numerical weather prediction. However, there is a big gap between the theoretical
sophisticated approaches and their practical realizations in the numerical algorithms. Even a very well-developed theoretical idea faces serious difficulties to be
implemented in practice. Due to this and other causes the DA-problems remain
actual.
The DA-methods are divided into two big groups; namely the variational and
dynamical-stochastic methods. The first group is referred, for example, in [15], its
modern realizations are known as a 4D-var scheme. The second group of methods
is mostly represented in literature as the Kalman-filter approach, for example, in [5].
There are, also, several hybrid schemes, combining both approaches [1, 12].
Numerical Realization of Hybrid Data Assimilation Algorithm …
449
lie in the basis of the models are poorly known. In addition, the processes of subgrid
description are not resolved correctly. The lack of the input data or their poor
quality may also cause wrong prediction. However, the main cause is not adequate
knowledge of the physical processes in full details. In other words, the basic
equations, which are applied for modeling are not completely correct and describe
the reality only partially. Therefore, the further progress in the computer power and
facilities as well as in the development of the mathematical algorithms, and increase
in the model resolution would not necessary lead to the better prediction and
analysis of the natural phenomena. In relation to the aforementioned ideas it is
necessary to highlight that the development and further progress in the observational database will need improvements in testing and validation of the models and
correction of the model outputs towards the observations.
Eventually, one may come to a conclusion that, in order to improve substantially
the knowledge and understanding of the climate and other geophysical processes
and their predictability it is necessary to combine the mathematical models and field
data. This combination makes possible improving the modeling quality and
enriching and restoring the existing database.
The problem of the optimal combination of the data and models is known in
geophysics as the data assimilation (DA) problem. This is a non-trivial scientific
problem because the extreme solutions such as mere replacement of all the model
values with the observed data without changing the other values or simply ignoring
the observations, while the model values remain unchanged are obviously not
optimal. Indeed, if we only replace the model values by observations, the model
output field will be totally unbalanced and on next time-step it will lead to large
false fluxes, which may completely destroy the model. On the contrary, leaving the
model values unchanged and ignoring the observations may result in a completely
wrong output, which would appear far from reality.
In meteorology and oceanography, the DA-problems have been ongoing during
several decades. Originally these problems came into consideration in the end of
1960s. Apparently, one of the first results was reported by Gandin [6]. He proposed
the objective analysis method to correct the model output based on the linear
interpolation ideas. This idea turned out very fruitful and this method became
widely used [7]. Further, the DA-methods became an important part of the
numerical weather prediction. However, there is a big gap between the theoretical
sophisticated approaches and their practical realizations in the numerical algorithms. Even a very well-developed theoretical idea faces serious difficulties to be
implemented in practice. Due to this and other causes the DA-problems remain
actual.
The DA-methods are divided into two big groups; namely the variational and
dynamical-stochastic methods. The first group is referred, for example, in [15], its
modern realizations are known as a 4D-var scheme. The second group of methods
is mostly represented in literature as the Kalman-filter approach, for example, in [5].
There are, also, several hybrid schemes, combining both approaches [1, 12].
Numerical Realization of Hybrid Data Assimilation Algorithm …
449