Abstract
The Chesapeake Bay is one of the most widely studied bodies of water in the United States and around the world. Routine monitoring of water quality indicators (e.g., salinity) relies on fixed sampling stations throughout the Bay. Utilizing this rich monitoring data, various methods produce surface predictions of water quality indicators to further characterize the health of the Bay as well as to support wildlife and human health research studies. Bayesian approaches for geostatistical modelling are becoming increasingly popular and can be preferred over frequentist approaches because full and exact inference can be computed, along with more accurate characterization of uncertainty. Traditional geostatistical prediction methods assume a Euclidean distance between two points when characterizing spatial dependence as a function of distance. However, Euclidean approaches may not be appropriate in estuarine environments when water-land boundaries are crossed during the modelling process. In this study, we compare stationary and barrier INLA geostatistical models with a classic kriging geostatistical model to predict salinity in the Chesapeake Bay during 4 months in 2019. Cross-validation is conducted for each approach to evaluate model performance based on prediction accuracy and precision. The results provide evidence that the two Bayesian-based models outperformed ordinary kriging, especially when examining prediction accuracy (most notably in the tributaries). We also suggest that the non-Euclidean model accounts for the appropriate water-based distances between sampling locations and is likely better at characterizing the uncertainty. However, more complex bodies of water may better showcase the capabilities and efficacy of the physical barrier INLA model.
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References
Abramowitz, M., & Stegun, I. A. (1972). Handbook of mathematical functions with formulas, graphs, and mathematical tables. National Bureau of Standards Applied Mathematics Series 55. Tenth Printing.
Bakka, H., Vanhatalo, J., Illian, J. B., Simpson, D., & Rue, H. (2019). Non-stationary Gaussian models with physical barriers. Spatial Statistics, 29, 268–288.
Blangiardo, M., & Cameletti, M. (2015). Spatial and spatio-temporal Bayesian models with R-INLA. John Wiley & Sons.
Boisvert, J. B., & Deutsch, C. V. (2011). Programs for kriging and sequential Gaussian simulation with locally varying anisotropy using non-Euclidean distances. Computers and Geosciences, 37(4), 495–510.
Chesapeake Bay Program. (2021). Data hub: CBP GIS datasets. Chesapeake Bay Program. https://www.chesapeakebay.net/what/data. Accessed 16 June 2021.
Cressie, N. (2015). Statistics for spatial data. John Wiley & Sons.
Curriero, F. C. (2006). On the use of non-Euclidean distance measures in geostatistics. Mathematical Geology, 38, 907–926.
Davis, B. J., & Curriero, F. C. (2019). Development and evaluation of geostatistical methods for non-Euclidean-based spatial covariance matrices. Mathematical Geosciences, 51(6), 767–791.
Davis, B. J., Jacobs, J. M., Davis, M. F., Schwab, K. J., DePaola, A., & Curriero, F. C. (2017). Environmental determinants of Vibrio parahaemolyticus in the Chesapeake Bay. Applied and Environmental Microbiology, 83(21), e01147-e1217.
Delmelle, E.M., & Desjardins, M.R., (2020). Point pattern analysis. In: Kobayashi, A. (Ed.), International Encyclopedia of Human Geography, 2nd edition. vol. 10, Elsevier, pp. 171–179.
EPA. (1996). Recommended guidelines for sampling and analyses in the Chesapeake Bay monitoring program. EPA.
Fuglstad, G. A., Simpson, D., Lindgren, F., & Rue, H. (2019). Constructing priors that penalize the complexity of Gaussian random fields. Journal of the American Statistical Association, 114(525), 445–452.
Gelfand, A. E., & Banerjee, S. (2017). Bayesian modeling and analysis of geostatistical data. Annual Review of Statistics and Its Application, 4, 245–266.
Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (1995). Bayesian data analysis. Chapman and Hall/CRC.
Jat, P., & Serre, M. L. (2016). Bayesian Maximum Entropy space/time estimation of surface water chloride in Maryland using river distances. Environmental Pollution, 219, 1148–1155.
Krige, D. G. (1951). A statistical approach to some basic mine valuation problems on the Witwatersrand. Journal of the Southern African Institute of Mining and Metallurgy, 52(6), 119–139.
Li, J., & Heap, A. D. (2014). Spatial interpolation methods applied in the environmental sciences: A review. Environmental Modelling and Software, 53, 173–189.
Lindgren, F., & Rue, H. (2015). Bayesian spatial modelling with R-INLA. Journal of Statistical Software, 63(19), 1–25.
Lindgren, F., Rue, H., & Lindström, J. (2011). An explicit link between Gaussian fields and Gaussian Markov random fields: The stochastic partial differential equation approach. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 73(4), 423–498.
Løland, A., & Høst, G. (2003). Spatial covariance modelling in a complex coastal domain by multidimensional scaling. Environmetrics: The Official Journal of the International Environmetrics Society, 14(3), 307–321.
Martins, T. G., Simpson, D., Lindgren, F., & Rue, H. (2013). Bayesian computing with INLA: New features. Computational Statistics and Data Analysis, 67, 68–83.
Mohammad Mehr, A. (2020). Prediction and anomaly detection in water quality with explainable hierarchical learning through parameter sharing (Doctoral dissertation, University of British Columbia).
Moores, M., & Mengersen, K. (2014). Bayesian approaches to spatial inference: Modelling and computational challenges and solutions. In AIP Conference Proceedings (Vol. 1636, No. 1, pp. 112–117). American Institute of Physics.
Moraga, P., (2019). Geospatial health data: Modeling and visualization with R-INLA and shiny. CRC Press.
Murphy, R. R., Curriero, F. C., & Ball, W. P. (2010). Comparison of spatial interpolation methods for water quality evaluation in the Chesapeake Bay. Journal of Environmental Engineering, 136(2), 160–171.
Oliver, M. A., & Webster, R. (2015). Basic steps in geostatistics: The variogram and kriging (pp. 15–42). Springer International Publishing.
Olson M, CBPS. (2012). Guide to using Chesapeake Bay Program water quality monitoring data. Chesapeake Bay Program, Annapolis, MD.
Peng, Z., Hu, Y., Liu, G., Hu, W., Zhang, H., & Gao, R. (2020). Calibration and quantifying uncertainty of daily water quality forecasts for large lakes with a Bayesian joint probability modelling approach. Water Research, 185, 116162.
Peterson, E. E., & Urquhart, N. S. (2006). Predicting water quality impaired stream segments using landscape-scale data and a regional geostatistical model: A case study in Maryland. Environmental Monitoring and Assessment, 121(1), 615–638.
Pourmozaffar, S., Tamadoni Jahromi, S., Rameshi, H., Sadeghi, A., Bagheri, T., Behzadi, S., Gozari, M., Zahedi, M. R., & Abrari Lazarjani, S. (2020). The role of salinity in physiological responses of bivalves. Reviews in Aquaculture, 12(3), 1548–1566.
Rathbun, S. L. (1998). Spatial modelling in irregularly shaped regions: kriging estuaries. Environmetrics: The Official Journal of the International Environmetrics Society, 9(2), 109–129.
Rue, H., Martino, S., & Chopin, N. (2009). Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 71(2), 319–392.
Serre, M. L., Carter, G., & Money, E. (2004). Geostatistical space/time estimation of water quality along the Raritan river basin in New Jersey. In Developments in water science (Vol. 55, pp. 1839–1852). Elsevier.
Sherman, M. (2011). Spatial statistics and spatio-temporal data: Covariance functions and directional properties. John Wiley & Sons.
Acknowledgements
We would like to thank the anonymous reviewer for their suggestions which ultimately improved the quality of this paper.
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This work is supported by the National Institute of Allergy and Infectious Diseases [grant number 1R01AI123931—01A1].
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Michael R. Desjardins: conceptualization, methodology, investigation, software, validation, formal analysis, data curation, writing—original draft preparation, visualization. Benjamin J.K. Davis: conceptualization, writing—reviewing and editing, resources, supervision. Frank C. Curriero: conceptualization, methodology, writing—review and editing, supervision, methodology, funding acquisition.
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Desjardins, M.R., Davis, B.J.K. & Curriero, F.C. Evaluating the performance of Bayesian geostatistical prediction with physical barriers in the Chesapeake Bay. Environ Monit Assess 196, 255 (2024). https://doi.org/10.1007/s10661-024-12401-y
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DOI: https://doi.org/10.1007/s10661-024-12401-y