Data Assimilation: Two Different Perspectives Based on the Initial-Condition Dependence

Both theory and real data are what we tend to use for engineering purposes. Data Assimilation (DA) is a computational tool that uses value from the model and the real measurement to arrive to an optimally acceptable value. The work in this paper is motivated by the fact that DA needs to be tailored based on the dependence of the problem on the initial condition. We point out that DA has two different perspectives based on the type of problem: one that does not rely on the initial condition, and the other that is initial condition dependent. Data Assimilation is demonstrated on two examples: runoff monitoring and forecasting in the city of Dhaka (initial condition independent) and convection in the atmosphere (initial condition dependent). We show that standard DA works well for problems with no initial condition dependence and piecewise DA is to be utilized when the problem has initial condition dependence. In the first example, we exploited standard Data Assimilation to arrive at values that are more realistic than the ones from the model and the observations. The second example is where we devised a method to find the dynamics of the system in a piecewise manner in Data Assimilation framework and noticed that the data assimilated dynamics (even due to noisy initial condition) is in good agreement with the true dynamics for a reasonable extent of time in future.