Introduction
Data assimilation deals with the mixing of measurements weighted by their certainty, i.e. the inverse of their error variance. In this chapter, we illustrate this concept on three simple examples. The standard formalism of data assimilation is sckeched in the first section. The examples provides an illustration of the "Best Linear Unbiased Estimation" (BLUE) data assimilation method.
In the first example, the concept of correlation error matrix is illustrated with the simple example of clock time estimation. One considers time measurement as the realization of two independent or correlated gaussian random variables.
In the second example, the velocity of a hydraulic jump is estimated with the measurement of one water heigh in an open channel.
In the last example, one estimates the water filling and discharge capacity of a trank with sequential measurements of its water height.
Hand-ons with python programs are proposed for each example.