Work Description

Title: Large Lake Statistical Water Balance Model - Laurentian Great Lakes - 1 month time window - 1980 through 2015 monthly summary data and model output Open Access Deposited
Attribute Value
  • We use a Bayesian Network to assimilate multiple monthly-total estimates of the Laurentian Great Lakes -- Superior, Michigan-Huron, St. Clair, Erie, and Ontario -- water balance and components thereof, generating new estimates with quantified uncertainty.
  • Using the statistical programming package R (, and JAGS (Just Another Gibbs Sampler,, 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: Large Lake Statistical Water Balance Model (L2SWBM):

  • This data set has a shorter timespan to accommodate a prior which uses data not used in the likelihood functions.
Contact information
Funding agency
  • Other Funding Agency
Other Funding agency
  • International Joint Commission
Citations to related material
  • 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
  • Large Lake Statistical Water Balance Model (L2SWBM).
  • 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.
Resource type
Last modified
  • 06/09/2020
  • 11/27/2019
To Cite this Work:
Smith, J., Gronewold, A., Read, L., Crooks, J., School for Environment and Sustainability, U., Department of Civil and Environmental Engineering, U., Cooperative Institute for Great Lakes Research (2019). Large Lake Statistical Water Balance Model - Laurentian Great Lakes - 1 month time window - 1980 through 2015 monthly summary data and model output [Data set]. University of Michigan - Deep Blue.

Files (Count: 38; Size: 962 MB)

Files provided in this data repository:

config_record.csv - configuration file for this L2SWBM run. An R script reads this file, and performs the computations and writing of BUGS (Bayesian inference Using Gibbs Sampling) code necessary to feed into JAGS (Just Another Gibbs Sampler), which runs the model. See the following for more information:

Lunn, D.J., Thomas, A., Best, N. and Spiegelhalter, D., 2000. WinBUGS-a Bayesian modelling framework: concepts, structure, and extensibility. Statistics and computing, 10(4), pp.325-337.

Plummer, M., 2003, March. JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. In Proceedings of the 3rd international workshop on distributed statistical computing (Vol. 124, No. 125, p. 10).

- [possibly "y"][lake abbreviation][water balance component]_ALL_12FF_1980_1_2015_12_1000000_Record_F.csv - summary data files for the water balance components across all of the lakes. Lake abbreviations are as follows, with lake name first, followed by abbreviation:

-- Superior, superior
-- Michigan-Huron, miHuron
-- St. Clair, clair
-- Erie, erie
-- Ontario, ontario

-- Water balance components are as follows:

-- Precipitation, Precip
-- Evaporation, Evap
-- Runoff, Runoff
-- Connecting Channel Outflow, Outflow
-- Diversion, Diversion
-- Change in Storage, DStorePP
-- Net Basin Supply, NBS

-- Units are in millimeters over the respective lake's surface, except for connecting channel outflows, diversions, and St. Clair net basin supply.

-- The comma delimited summary files have 5 columns, which from left to right are:

-- Year
-- Month
-- Median inference
-- 2.5 percentile inference
-- 97.5 percentile inference

- L2SWBM_ALL_PP_12FF_1980_1_2015_12_1000000_Record_F.RData - The RData file for use in R to further process model output. You may load the file into R and type "ls()" to view the contents of the file. Relevant data objects are highlighted below:

-- [lake abbreviation][variable]_Prior - the data used to develop prior distributions for the specified component and lake, 1950-1979
-- [lake abbreviation][variable]_A - the data used for the analysis period and likelihood functions, 1980-2015, for the specified component and lake
-- [lake abbreviation][variable](Log)Prior[Mean, Precision, Rate, Shape] - calendar month prior distribution parameters for the specified component and lake, calculated from the prior data mentioned above
-- [lake abbreviation][variable]Src - source of data by column
-- jMod: The JAGS model in BUGS, can be used to re-initialize the model for further analysis
-- jSum: Summary statistics from the model run. Columns are - Mean, Standard Deviation, 2.5%, 25%, 50%, 75%, and 97.5% (percentiles), and the n-effective value. Variable names are typically: (possibly y)[lake abbreviation][water balance component](possibly a number to indicate observation number, and PP for Posterior Predictive)[[month of analysis]]
-- jSample: a 3000 row (samples) by n-variables column matrix of MCMC samples to further analyze

Further questions can be sent to


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