Water balance models are often employed to improve understanding of drivers of change in regional hydrologic cycles. Most of these models, however, are physically-based, and few employ state-of-the-art statistical methods to reconcile measurement uncertainty and bias.
Starting in 2015, NOAA Great Lakes Environmental Research Laboratory (GLERL), along with its partners at the University of Michigan Cooperative Institute for Great Lakes Research (CIGLR), began developing a water balance model under a Bayesian Markov chain Monte Carlo framework. Through this model, we generate new estimates of monthly runoff, over-lake evaporation, over-lake precipitation, and connecting channel flows for each of the Great Lakes. The new model reconciles discrepancies between model and measurement-based estimates of each component while closing the Laurentian Great Lakes water balance.
In 2017, funding from the International Joint Commission - through their International Watersheds Initiative was received to use the model in generating a new, balanced historical (1950 - 2015) record of the Laurentian Great Lakes water balance. The project will help in resolving the regional water budget across monthly and inter-annual time scales and represents an important stepping stone towards addressing a long-standing need in the Great Lakes for clear and defensible differentiation between hydrological, climatological, geological, and anthropogenic drivers behind seasonal and long-term changes in Laurentian Great Lakes water levels.
To run these models, you will need to do the following:
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Visit the JAGS Sourceforge repository and download JAGS for your computer: https://sourceforge.net/projects/mcmc-jags/files/JAGS/
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Download the R statistical programming environment https://cran.r-project.org/
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Open R, and enter the command "install.packages(c('rjags'))", select your mirror, and install locally if necessary
Numerical summary data in comma-delimited (CSV) format of L2SWBM inferred values for the Great Lakes' water balance and components. File names are formatted as follows:
- Abbreviated lake name (superior, miHuron, clair, erie, ontario)
- Component of interest, which include Precip, Evap, Runoff, Outflow, Diversion, NBS (for St. Clair), and StorageChange (change in water level)
- '_L2SWBM_vX.csv', identifying the L2SWBM version (X) the model generated data are from
Data are formatted with the following columns (labelled):
- Year
- Month
- Median estimate
- 2.5 Quantile estimate
- 97.5 Quantile estimate
Plots in PDF format of the complete L2SWBM generated time-series along with model input data for comparison. These plots are done by decade, and thus there may be multiple plots per lake. File names are formatted as follows:
- Abbreviated lake name (superior, miHuron, clair, erie, ontario)
- 'YYYY_ZZZZ' indicating the plot spans the year YYYY to ZZZZ
- '_L2SWBM_vX.csv', identifying the L2SWBM version (X) the model generated data are from
Plots are structured such that:
- Top 3 plots for Superior, Michigan-Huron, Erie, and Ontario show data and L2SWBM Net Basin Supply (NBS) component inferences of over-lake precipitation (P), over-lake evaporation (E), and runoff (R), while the top-most plot for Lake St. Clair shows NBS
- Plots thereafter show data and model inferences for channel outflows (Q) and diversions (D)
- Bottom-most plot for all lakes shows data and model 'posterior-predictive' inferences for monthly changes in lake storage or water level (ΔH) -Legends indicate the gray bars are L2SWBM generated inferences, and horizontal segments are independent estimates of water balance components from different sources:
GLERL.AHPS.Hydromet or GLM.HMD.Hydromet indicate the estimate is derived from the NOAA-GLERL GLM-HMD:
- HUNTER, T.S., A.H. CLITES, A.D. GRONEWOLD, and K.B. CAMPBELL. Development and application of a North American Great Lakes hydrometeorological database - Part I: Precipitation, evaporation, runoff, and air temperature. Journal of Great Lakes Research 41(1):65-77 (DOI:10.1016/j.jglr.2014.4.12.006) (2015). https://www.glerl.noaa.gov/pubs/fulltext/2015/20150006.pdf
- USACE.AHPS indicates the estimate is derived from an implementation of NOAA-GLERL's Advanced Hydrologic Prediction System (AHPS) ran by the United States Army Corps of Engineers
- ECCC* indicates the estimate was generated by Environment and Climate Change Canada and one of their 2 models: 1) Canadian Precipitation Analysis (CaPA); and 2) Global Environmental Multiscale (GEM) model
*Proto indicates the estimate is from a previous model instance used in developing the prototype models described below
For precipitation and channel outflows, we included historically coordinated estimates from the Coordinating Committee on Great Lakes Basic Hydraulic and Hydrologic Data (CCGLBHHD)
IGS indicates the estimate (for channel outflow) is from an International Gauging Station, maintained by the United States Geological Survey and Water Survey Canada
For reference, we indicate the regulation limit of 91 m3/s for the Chicago Diversion with a dashed, blue line
Additionally, we compare inferred channel outflows' uncertainty to the estimated uncertainty from:
- Bruxer, J., ENG, B. and ENG, P., 2010. Uncertainty analysis of Lake Erie net basin supplies as computed using the residual method (Doctoral dissertation, MS thesis, Dept. of Civil Engineering, McMaster University, 238 pp.).
Model code, with documentation contained within the README.txt. Changes from previous versions are documented in the CHANGES_vA_vB.txt file, where A is the previous, and B is the downloaded version.
Questions about this code can be sent to NOAA-GLERL at oar.glerl.data@noaa.gov.
The code available here was developed for research purposes, the operational version of the code is maintained by the Coordinating Committee on Great Lakes Basic Hydraulic and Hydrologic Data and can be accessed here:
https://github.com/cc-hydrosub/L2SWBM
This model is being used for research by Dr. Andrew Gronewold at the University of Michigan. Please see the most recent publication here: https://doi.org/10.1038/s41597-020-00613-z
Access the research version of the code and the 1950-2019 simulations here: https://doi.org/10.7302/tx97-nn12
GRONEWOLD, A.D., J. Bruxer, D. Durnford, A.H. CLITES, J.P. SMITH, F. Segleniecks, S.S. Qian, T.S. HUNTER, and V. Fortin (2016) Hydrological drivers of record-setting water level rise on Earth's largest lake system. Water Resources Research 52(DOI:10.1002/2015WR018209). https://www.glerl.noaa.gov/pubs/fulltext/2016/20160014.pdf
SMITH, J.P. and A.D. GRONEWOLD. Development and analysis of a Bayesian water balance model for large lake systems. ArXiv. https://arxiv.org/abs/1710.10161
SMITH, J.P. and A.D. GRONEWOLD (2018) Summary Report: Development of the Large Lake Statistical Water Balance Model for Constructing a New Historical Record of the Great Lakes Water Balance. FINAL report for the International Joint Commission. https://www.glerl.noaa.gov/pubs/fulltext/2018/20180021.pdf
SMITH, J.P., A.D. Gronewold, L. Read and J.L. Crooks (2019) Large Lake Statistical Water Balance Model - Laurentian Great Lakes - 1 month time window - 1980 through 2015 monthly summary data and model output. Deep Blue, University of Michigan, Ann Arbor, MI. https://doi.org/10.7302/s6h1-d521
Do, H.X., J.P. Smith, L.M. Fry and A.D. Gronewold (2020) Seventy-year long record of monthly water balance estimates for Earth’s largest lake system. Scientific Data 7, 276. https://doi.org/10.1038/s41597-020-00613-z
Do, Hong X., J.P. SMITH, L.M. Fry and A.D. Gronewold (2020) Monthly water balance estimates for the Laurentian Great Lakes from 1950 to 2019 (v1.1). Deep Blue, University of Michigan, Ann Arbor, MI. https://doi.org/10.7302/tx97-nn12
Drew Gronewold, Associate Professor at the University of Michigan's School for Environment and Sustainability, initiated model development.
We thank Song Qian, Yves Atchade, Kerby Shedden, Edward Ionides, Vincent Fortin, Bryan Tolson, and Craig Stow for helpful discussions on Bayesian inference and alternative formulations of our water balance model. Jacob Bruxer, Frank Seglenieks, Tim Hunter, and Lauren Fry provided expert opinions and water balance data. Nicole Rice provided graphical and editorial support.
Funding was provided by the International Joint Commission (IJC) International Watersheds Initiative (IWI) to NOAA and the Cooperative Institute for Great Lakes Research (CIGLR) through a NOAA Cooperative Agreement with the University of Michigan (NA12OAR4320071); many thanks to Wendy Leger and Mike Shantz.
The use of product names, commercial and otherwise, in this paper does not imply endorsement by NOAA, NOAA-GLERL, CIGLR, or any other contributing agency or organization.
This repository is a scientific product and is not official communication of the National Oceanic and Atmospheric Administration, or the United States Department of Commerce. All NOAA GitHub project code is provided on an ‘as is’ basis and the user assumes responsibility for its use. Any claims against the Department of Commerce or Department of Commerce bureaus stemming from the use of this GitHub project will be governed by all applicable Federal law. Any reference to specific commercial products, processes, or services by service mark, trademark, manufacturer, or otherwise, does not constitute or imply their endorsement, recommendation or favoring by the Department of Commerce. The Department of Commerce seal and logo, or the seal and logo of a DOC bureau, shall not be used in any manner to imply endorsement of any commercial product or activity by DOC or the United States Government.