  Data Assimilation (DA) is a computational tool that uses value from the model
and the real measurement to arrive to an optimally acceptable value. Rather,
this technique relies on the idea of Kalman gain. We point out that DA has two
different perspectives based on the type of problem. In this paper, we look
into two problem types: 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.
