Using the statistical programming package R ( https://cran.r-project.org/), and JAGS (Just Another Gibbs Sampler, http://mcmc-jags.sourceforge.net/), we processed multiple estimates of the Laurentian Great Lakes water balance components -- over-lake precipitation, evaporation, lateral tributary runoff, connecting channel flows, and diversions -- feeding them into prior distributions (using data from 1950 through 1979), and likelihood functions. The Bayesian Network is coded in the BUGS language. Water balance computations assume that monthly change in storage for a given lake is the difference between beginning of month water levels surrounding each month. For example, the change in storage for June 2015 is the difference between the beginning of month water level for July 2015 and that for June 2015., More details on the model can be found in the following summary report for the International Watersheds Initiative of the International Joint Commission, where the model was used to generate a new water balance historical record from 1950 through 2015: https://www.glerl.noaa.gov/pubs/fulltext/2018/20180021.pdf. Large Lake Statistical Water Balance Model (L2SWBM): https://www.glerl.noaa.gov/data/WaterBalanceModel/, and This data set has a shorter timespan to accommodate a prior which uses data not used in the likelihood functions.
Smith, J., Gronewald, A. et al. Summary Report: Development of the Large Lake Statistical Water Balance Model for Constructing a New Historical Record of the Great Lakes Water Balance. Submitted to: The International Watersheds Initiative of the International Joint Commission. Accessible at https://www.glerl.noaa.gov/pubs/fulltext/2018/20180021.pdf, Large Lake Statistical Water Balance Model (L2SWBM). https://www.glerl.noaa.gov/data/WaterBalanceModel/, and Gronewold, A.D., Smith, J.P., Read, L. and Crooks, J.L., 2020. Reconciling the water balance of large lake systems. Advances in Water Resources, p.103505.