What is data assimilation really solving, and how is the calculation actually done?

Data assimilation is a procedure in which observations are combined with models. The observations correct model errors on the one hand, and the models extrapolate the data information in space, time, and among different properties on the other. The result of assimilation is generally a more complete and more accurate description of the state of the modeled system than those obtained by either observations or model simulations alone. However, data assimilation is not a panacea for correcting every model error or for compensating all deficiencies of observations.