You have data, you have a simulation model, then you should probably look into data assimilation. 

The term "Data Assimilation" depicts all the methods stemming from statistics and optimisation used to guide a numerical model towards a flow of observations and make a prediction that adds more value to them. The data assimilation methods are commonly used in geosciences (weather, oceanography, climate as well as oil and gas reservoirs) but are also increasingly being used outside of this community for non-geophysical systems confronted to analogous conceptual difficulties (big data, nonlinear and chaotic behaviour). Besides, the models and observations used in the geosciences are undergoing drastic technological changes that question the use of traditional methods. The new review paper from the data assimilation group at the Nansen Center (Carrassi et al. 2018) provides a complete theoretical background of data assimilation and an exhaustive discussion of their application set up in the ambition to allow a non-expert to choose an adequate data assimilation method and deploy it successfully for a realistic application.  

Figure: Required data assimilation (DA) method versus model resolution and prediction time horizon; examples of corresponding natural phenomena are also shown for illustrative purposes. The degree of sophistication of the DA grows commensurately with the increase in prediction time horizon and the decrease of the model grid size.

- The purpose of this article is to provide a comprehensive, state-of-the-art overview of the methods and challenges of data assimilation (DA) in the geosciences. We aim the article at geoscientists confronted with the problem of combining data with models and need to learn DA, but who are intimidated by the vast, and technical, literature. This work may guide them through a first journey into the topic while being at the same time as complete and precise as possible, say Laurent Bertino and Alberto Carrassi, the two authors from the Nansen Center (NERSC). 

The (scientific) abstract of the paper: 

 We commonly refer to state estimation theory in geosciences as data assimilation (DA). This term encompasses the entire sequence of operations that, starting from the observations of a system, and from additional statistical and dynamical information (such as a dynamical evolution model), provides an estimate of its state. DA is standard practice in numerical weather prediction, but its application is becoming widespread in many other areas of climate, atmosphere, ocean, and environment modeling; in all circumstances where one intends to estimate the state of a large dynamical system based on limited information. While the complexity of DA, and of the methods thereof, stands on its interdisciplinary nature across statistics, dynamical systems, and numerical optimization, when applied to geosciences, an additional difficulty arises by the continually increasing sophistication of the environmental models. Thus, in spite of DA being nowadays ubiquitous in geosciences, it has so far remained a topic mostly reserved to experts. We aim this overview article at geoscientists with a background in mathematical and physical modeling, who are interested in the rapid development of DA and its growing domains of application in environmental science, but so far have not delved into its conceptual and methodological complexities.

Citation: 

Carrassi A, Bocquet M, Bertino L, Evensen G. Data assimilation in the geosciences: An overview of methods, issues, and perspectives. WIREs Clim Change. 2018;9:e535. https://doi.org/10.1002/wcc.535