Data assimilation

Authored by: Veronica J. Berrocal

Handbook of Environmental and Ecological Statistics

Print publication date:  September  2017
Online publication date:  January  2019

Print ISBN: 9781498752022
eBook ISBN: 9781315152509
Adobe ISBN:

10.1201/9781315152509-7

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Abstract

The evolution in time of environmental systems, in particular, geophysical ones, can be described via systems of partial differential equations. In most cases, these equations, that can be either linear or non-linear, embody the physical laws that are assumed to govern the temporal dynamics of the system, and need initial, and in some cases, boundary conditions in order to be integrated forward in time and thus predict the next state of the system. Often, observations of the initial states are not completely available. This was recognized in the seventeenth and eighteenth centuries by mathematicians and astronomers, among which Euler, Lagrange and Laplace, who were trying to determine the orbits of comets and planets using Newton’s laws of gravitation [43]. In particular, in his book “Theory of Motion of Heavenly Bodies”, Gauss elaborated how available observations of the physical system – in his case, the location of the comet Ceres with respect to the Sun – were not easily translatable into initial conditions for the variables of the governing dynamic equations. In particular, he noted that in order to obtain the best approximation to the (dynamical) behavior of environmental systems, more observations than the minimum number of observations required to solve the (partial) differential equations were needed. More specifically, Gauss wrote ”[..] since all our observations and measurements are nothing more than approximations to the truth, the same must be true of all calculations resting on them, and the highest of all computations made concerning concrete phenomena must be to approximate, as nearly as practicable, to the truth. But this can be accomplished in no other way than by suitable combination of more observations than the number absolutely requisite for the determination of unknown quantities” [43], thus, in some ways, setting the basis for data assimilation, or combination of various sources of information.

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