Isn't it right that we use both initialization methods and the data assimilation approach to improve on the initial conditions of a model? So what are their differences?
I'm not sure to understand the question.
"data assimilation" is not for "improving on the initial conditions".
Data assimilation is used during the course of the simulation to readjust model variables to take into accound recent data.
For example in meteorology you can first initialize and run a numerical model, and then, while the model is running, data assimilation is used to have a more accurate state.
As far as I can imagine, data assimilation would be nonsense if you were able to measure the entire state of the world (then, indeed, the best thing to do would probably be to stop the current simulation and initialize a new one with the recently measured state).
But in real life you are never able to measure the complete state of the world. So you have to combine the data you have just measured with the data you have computed so far to create the current state of your model.
This is what data assimilation is about : combination of a computed state of the world and of "real" measure to create a more accurate state of the world.
Christophe's description of what data assimilation is in reality is accurate. However, data assimilation IS commonly used to create more accurate initial conditions for predicting the evolution of a system's state.
A model can be initialized (defining initial conditions for a prediction) in various ways, more or less sophisticated. For instance, you can run a model for a long time from any random state and let it adjust to some type of equilibrium. If you assume that this equilibrium state is your best estimate of current conditions, then one can use this estimate as initial conditions for a forecast. So here the model is initialized without the use of data assimilation. Of course such initial conditions should not be expected to be very accurate as models are typically not perfect leading to errors developing in the course of their integration. So data assimilation, a mathematical procedure in which information from a model and from available observations are optimally "blended" together to create an estimate of the recent state of a system (an analysis). The analyses resulting from data assimilation are expected to represent more accurately the actual state of a system as information from observations was used. These analyses are commonly used as initial conditions to produce forecasts, such as in numerical weather prediction.
A nice tutorial about data assimilation can be found at:
https://www.meted.ucar.edu/training_module.php?id=704
Hope this helps.
Cristopher is right. After initial input of parametre values, to calibrate the model data assimilation can be used so that simulation does not become unrealistic.
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