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Encyclopedia > Data assimilation

Data assimilation (DA) is a method used in the weather forecasting process in which observations of the current (and possibly, past) weather are combined with a previous forecast for that time to produce the meteorological `analysis'; the best estimate of the current state of the atmosphere. Weatherman redirects here. ...

More generally, Data assimilation is a method to use observations in the forecasting process.

In weather forecasting there are 2 main types of data assimilation: 3 dimensional (3DDA) and 4 dimensional (4DDA). In 3DDA only those observations are used available at the time of analyses. In 4DDA the past observations are included (thus, time dimension added).

The first data assimilation methods were called the "objective analyses" (e.g., Cressman algorithm). This was in contrast to the "subjective analyses", when (in the past practice) numerical weather predictions (NWP) forecasts were arbitrarily corrected by meteorologists. The objective methods used simple interpolation approaches, and thus were the kind of 3DDA methods. The similar 4DDA methods, called "nudging" also exist (e.g. in MM5 NWP model). They are based on the simple idea of Newtonian relaxation. The idea is to add in the right part of dynamical equations of the model the term, proportional to the difference of the calculated meteorological variable and the observation value. This term, that has a negative sign "keeps" the calculated state vector closer to the observations.

The first breakdown in the field of data assimilation was introducing by L.Gandin (1963) with the "statistical interpolation" (or "optimal interpolation" ) method. It developed the previous ideas of Kolmogorov. That method is the 3DDA method and is the kind of regression analyses, which utilizes the information about the spatial distributions of covariance functions of the errors of the "first guess" field (previous forecast) and "true field". These functions are never known. However, the different approximations were assumed.

In fact optimal interpolation algorithm is the reduced version of the Kalman filtering (KF) algorithm, when the covariance matrices are not calculated from the dynamical equations, but are pre-determined in advance. The Kalman filter (named after its inventor, Rudolf Kalman) is an efficient recursive computational solution for tracking a time-dependent state vector with noisy equations of motion in real time by the least-squares method. ...

When this was recognised the attempts to introduce the KF algorithms as a 4DDA tool for NWP models were done. However, this was (and remains) a very difficult task, since the full version of KF algorithm requires solution of the enormous large number of additional equations. In connection with that the special kind of KF algorithms (suboptimal) for NWP models were developed.

Another significant advance in the development of the 4DDA methods was utilizing the optimal control theory (variational approach) in the works of Le Dimet and Talagrand, 1986, based on the previous works of G. Marchuk. The significant advantage of the variational approaches is that the meteorological fields satisfy the dynamical equations of the NWP model and at the same time they minimize the functional, characterizing their difference from observations. Thus, the problem of constrained minimization is solved. The 3DDA variational methods also exist (e.g., Sasaki, 1958). Optimal control theory is a mathematical field that is concerned with control policies that can be deduced using optimization algorithms. ...

As it was shown by Lorenc, 1986, the all abovementioned kinds of 4DDA methods are in some limit equivalent. I.e., under some assumptions they minimize the same cost functional. However, these assumptions never fulfill.

The rapid development of the various data assimilation methods for NWP is connected to the two main points in the field of numerical weather prediction: 1. Utilizing the observations currently seems to be the most promicing challange to improve the quality of the forecasts at the different scales (from the planetary scale to the local city, or even street scale) 2. The number of different kinds of observations (sodars, radars, sattelite) is rapidly growing.

The DA methods are currently used not also in weather forecasting, but in different environmental forecasting problems, e.g. in hydrological forecasting. Basically the same types of DA methods, as those, described above are in use there.

Data assimilation is the challange for the every forecasting problem.

References: 1. R. Daley, Atmospheric data analyses, Cambridge University Press,1991. 2. MM5 community model homepage: http://www.mmm.ucar.edu/mm5/

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