In the context of data assimilation, a synthetic experiment typically refers to using outputs from a model to represent observations. These synthetic observations are then assimilated back into the model with error perturbations applied (either to inputs or directly to states).

The general idea is that the simulation which produced the observations is designated as representing the truth, and the perturbed simulation produces erroneous output. Given that we have full control in defining the truth and defining errors in these experiments (which is not so easy in real world applications), they are useful for studying the impacts of assimilation on a model, based on how well assimilation of the synthetic observations can retrieve the truth outputs series from the perturbed/erroneous one.