Application of the Beer–Lambert Model to Attenuation of Photosynthetically Active Radiation in a Shallow, Eutrophic Lake
dc.contributor.author | Weiskerger, Chelsea J. | |
dc.contributor.author | Rowe, Mark D. | |
dc.contributor.author | Stow, Craig A. | |
dc.contributor.author | Stuart, Dack | |
dc.contributor.author | Johengen, Tom | |
dc.date.accessioned | 2019-01-15T20:29:42Z | |
dc.date.available | 2020-01-06T16:40:59Z | en |
dc.date.issued | 2018-11 | |
dc.identifier.citation | Weiskerger, Chelsea J.; Rowe, Mark D.; Stow, Craig A.; Stuart, Dack; Johengen, Tom (2018). "Application of the Beer–Lambert Model to Attenuation of Photosynthetically Active Radiation in a Shallow, Eutrophic Lake." Water Resources Research 54(11): 8952-8962. | |
dc.identifier.issn | 0043-1397 | |
dc.identifier.issn | 1944-7973 | |
dc.identifier.uri | https://hdl.handle.net/2027.42/147097 | |
dc.description.abstract | Models of primary production in aquatic systems must include a means to estimate subsurface light. Such models often use the Beer–Lambert law, assuming exponential attenuation of light with depth. It is further assumed that the diffuse attenuation coefficient may be estimated as a summation of scattering/absorbing constituent concentrations multiplied by their respective specific attenuation coefficients. While theoretical deviations from these assumptions have been documented, it is useful to consider the empirical performance of this common approach. Photosynthetically active radiation (PAR) levels and water quality conditions were recorded weekly from six to eight monitoring stations in western Lake Erie between 2012 and 2016. Exponential PAR extinction models yielded a mean attenuation coefficient of 1.55 m (interquartile range = 0.74–1.90 m). While more complex light attenuation models are available, analysis of residuals indicated that the simple Beer–Lambert model is adequate for shallow, eutrophic waters similar to western Lake Erie (R2 > 0.9 for 96% of samples). Three groups of water quality variables were predictive of PAR attenuation: total and nonvolatile suspended particles, dissolved organic substances (dissolved organic carbon and chromophoric dissolved organic matter), and organic solids (volatile suspended solids and chlorophyll). Multiple regression models using these variables predicted 3–90% of the variability in PAR attenuation, with a median adjusted R2 = 0.86. Explanatory variables within these groups may substitute for each other while maintaining similar model performance, indicating that various combinations of water quality variables may be useful to predict PAR attenuation, depending on availability within a model framework or monitoring program.Key PointsThe Beer–Lambert law effectively models photosynthetically active radiation in western Lake Erie, despite some systematic deviationsField‐obtained water quality parameters can predict photosynthetically active radiation attenuation with a high degree of confidenceSuspended particle concentration is most predictive of photosynthetically active radiation attenuation in this turbid, eutrophic basin | |
dc.publisher | American Public Health Association | |
dc.publisher | Wiley Periodicals, Inc. | |
dc.subject.other | Beer–Lambert law | |
dc.subject.other | western Lake Erie | |
dc.subject.other | biophysical model applications | |
dc.subject.other | water quality | |
dc.subject.other | photosynthetically active radiation | |
dc.title | Application of the Beer–Lambert Model to Attenuation of Photosynthetically Active Radiation in a Shallow, Eutrophic Lake | |
dc.type | Article | en_US |
dc.rights.robots | IndexNoFollow | |
dc.subject.hlbsecondlevel | Natural Resources and Environment | |
dc.subject.hlbtoplevel | Science | |
dc.description.peerreviewed | Peer Reviewed | |
dc.description.bitstreamurl | https://deepblue.lib.umich.edu/bitstream/2027.42/147097/1/wrcr23654_am.pdf | |
dc.description.bitstreamurl | https://deepblue.lib.umich.edu/bitstream/2027.42/147097/2/wrcr23654-sup-0001-2018WR023024-SI.pdf | |
dc.description.bitstreamurl | https://deepblue.lib.umich.edu/bitstream/2027.42/147097/3/wrcr23654.pdf | |
dc.identifier.doi | 10.1029/2018WR023024 | |
dc.identifier.source | Water Resources Research | |
dc.identifier.citedreference | Safaie, A., Wendzel, A., Ge, Z. F., Nevers, M. B., Whitman, R. L., Corsi, S. R., & Phanikumar, M. S. ( 2016 ). Comparative evaluation of statistical and mechanistic models of Escherichia coli at beaches in southern Lake Michigan. Environmental Science & Technology, 50 ( 5 ), 2442 – 2449. https://doi.org/10.1021/acs.est.5b05378 | |
dc.identifier.citedreference | Mouw, C., & Barnett, A. ( 2014 ). CDOM Absorption—Sample Collection and Analysis (pp. 1 – 9 ). MI: Michigan Technological University Houghton. | |
dc.identifier.citedreference | Paulson, C. A., & Simpson, J. J. ( 1977 ). Irradiance measurements in upper ocean. Journal of Physical Oceanography, 7 ( 6 ), 952 – 956. https://doi.org/10.1175/1520‐0485(1977)007<0952:IMITUO>2.0.CO;2 | |
dc.identifier.citedreference | Pegau, W. S., Gray, D., & Zaneveld, J. R. V. ( 1997 ). Absorption and attenuation of visible and near‐infrared light in water: Dependence on temperature and salinity. Applied Optics, 36 ( 24 ), 6035 – 6046. https://doi.org/10.1364/AO.36.006035 | |
dc.identifier.citedreference | Pierson, D. C., Kratzer, S., Strombeck, N., & Hakansson, B. ( 2008 ). Relationship between the attenuation of downwelling irradiance at 490 nm with the attenuation of PAR (400 nm–700 nm) in the Baltic Sea. Remote Sensing of Environment, 112 ( 3 ), 668 – 680. https://doi.org/10.1016/j.rse.2007.06.009 | |
dc.identifier.citedreference | Porta, D., Fitzpatrick, M. A. J., & Haffner, G. D. ( 2005 ). Annual variability of phytoplankton primary production in the western basin of Lake Erie (2002–2003). Journal of Great Lakes Research, 31, 63 – 71. https://doi.org/10.1016/S0380‐1330(05)70305‐1 | |
dc.identifier.citedreference | Rowe, M. D., Anderson, E. J., Vanderploeg, H. A., Pothoven, S. A., Elgin, A. K., Wang, J., & Yousef, F. ( 2017 ). Influence of invasive quagga mussels, phosphorus loads, and climate on spatial and temporal patterns of productivity in Lake Michigan: A biophysical modeling study. Limnology and Oceanography, 62 ( 6 ), 2629 – 2649. https://doi.org/10.1002/lno.10595 | |
dc.identifier.citedreference | Rowe, M. D., Anderson, E. J., Wynne, T. T., Stumpf, R. P., Fanslow, D. L., Kijanka, K., Vanderploeg, H. A., Strickler, J. R., & Davis, T. W. ( 2016 ). Vertical distribution of buoyant Microcystis blooms in a Lagrangian particle tracking model for short‐term forecasts in Lake Erie. Journal of Geophysical Research: Oceans, 121, 5296 – 5314. https://doi.org/10.1002/2016JC011720 | |
dc.identifier.citedreference | Saulquin, B., Hamdi, A., Gohin, F., Populus, J., Mangin, A., & d’Andon, O. F. ( 2013 ). Estimation of the diffuse attenuation coefficient K‐dPAR using MERIS and application to seabed habitat mapping. Remote Sensing of Environment, 128, 224 – 233. https://doi.org/10.1016/j.rse.2012.10.002 | |
dc.identifier.citedreference | Siegel, D. A., Maritorena, S., Nelson, N. B., & Behrenfeld, M. J. ( 2005 ). Independence and interdependencies among global ocean color properties: Reassessing the bio‐optical assumption. Journal of Geophysical Research, 110, C07011. https://doi.org/10.1029/2004JC002527 | |
dc.identifier.citedreference | Smith, R. C., & Baker, K. S. ( 1978 ). Optical classification of natural waters. Limnology and Oceanography, 23 ( 2 ), 260 – 267. https://doi.org/10.4319/lo.1978.23.2.0260 | |
dc.identifier.citedreference | Smith, R. E. H., Hiriart‐Baer, V. P., Higgins, S. N., Guildford, S. J., & Charlton, M. N. ( 2005 ). Planktonic primary production in the offshore waters of dreissenid‐infested Lake Erie in 1997. Journal of Great Lakes Research, 31, 50 – 62. https://doi.org/10.1016/S0380‐1330(05)70304‐X | |
dc.identifier.citedreference | Smith, W. O. ( 1982 ). The relative importance of chlorophyll, dissolved and particulate material, and seawater to the vertical extinction of light. Estuarine, Coastal and Shelf Science, 15 ( 4 ), 459 – 465. https://doi.org/10.1016/0272‐7714(82)90054‐3 | |
dc.identifier.citedreference | Speziale, B. J., Schreiner, S. P., Giammatteo, P. A., & Schindler, J. E. ( 1984 ). Comparison of N,N‐dimethylformamide, dimethylsulfoxide, and acetone for extraction of phytoplankton chlorophyll. Canadian Journal of Fisheries and Aquatic Sciences, 41 ( 10 ), 1519 – 1522. https://doi.org/10.1139/f84‐187 | |
dc.identifier.citedreference | Stavn, R. H. ( 1988 ). Lambert‐Beer law in ocean waters: Optical‐properties of water and of dissolved/suspended material, optical energy budgets. Applied Optics, 27 ( 2 ), 222 – 231. https://doi.org/10.1364/AO.27.000222 | |
dc.identifier.citedreference | Stefan, H. G., Cardoni, J. J., Schiebe, F. R., & Cooper, C. M. ( 1983 ). Model of light penetration in a turbid lake. Water Resources Research, 19 ( 1 ), 109 – 120. https://doi.org/10.1029/WR019i001p00109 | |
dc.identifier.citedreference | Stramski, D., Bricaud, A., & Morel, A. ( 2001 ). Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community. Applied Optics, 40 ( 18 ), 2929 – 2945. https://doi.org/10.1364/AO.40.002929 | |
dc.identifier.citedreference | Stumpf, R. P., Wynne, T. T., Baker, D. B., & Fahnenstiel, G. L. ( 2012 ). Interannual variability of cyanobacterial blooms in Lake Erie. PLoS One, 7 ( 8 ), 11. | |
dc.identifier.citedreference | Swain, A. ( 1980 ). Material budgets in Lake Chicot, Arkansas, University of Mississippi, Oxford. | |
dc.identifier.citedreference | Twardowski, M. S., Boss, E., Macdonald, J. B., Pegau, W. S., Barnard, A. H., & Zaneveld, J. R. V. ( 2001 ). A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters. Journal of Geophysical Research, 106 ( C7 ), 14,129 – 14,142. https://doi.org/10.1029/2000JC000404 | |
dc.identifier.citedreference | USEPA ( 2005 ). Method 415.3: Measurement of total organic carbon, dissolved organic carbon and specific UV absorbance at 254 nm in source water and drinking water. Washington, DC: United States Environmental Protection Agency. | |
dc.identifier.citedreference | Verhamme, E. M., Redder, T. M., Schlea, D. A., Grush, J., Bratton, J. F., & DePinto, J. V. ( 2016 ). Development of the Western Lake Erie ecosystem model (WLEEM): Application to connect phosphorus loads to cyanobacteria biomass. Journal of Great Lakes Research, 42 ( 6 ), 1193 – 1205. https://doi.org/10.1016/j.jglr.2016.09.006 | |
dc.identifier.citedreference | Wang, M. Z., Lyzenga, D. R., & Klemas, V. V. ( 1996 ). Measurement of optical properties in the Delaware estuary. Journal of Coastal Research, 12 ( 1 ), 211 – 228. | |
dc.identifier.citedreference | Xu, J. T., Hood, R. R., & Chao, S. Y. ( 2005 ). A simple empirical optical model for simulating light attenuation variability in a partially mixed estuary. Estuaries, 28 ( 4 ), 572 – 580. https://doi.org/10.1007/BF02696068 | |
dc.identifier.citedreference | APHA ( 1998 ). Standard Methods for the Examination of Water and Wastewater. Washington, DC: American Public Health Association. | |
dc.identifier.citedreference | Beletsky, D., Schwab, D. J., Roebber, P. J., McCormick, M. J., Miller, G. S., & Saylor, J. H. ( 2003 ). Modeling wind‐driven circulation during the March 1998 sediment resuspension event in Lake Michigan. Journal of Geophysical Research, 108 ( C2 ), 3038. https://doi.org/10.1029/2001JC001159 | |
dc.identifier.citedreference | Binding, C. E., Greenberg, T. A., Watson, S. B., Rastin, S., & Gould, J. ( 2015 ). Long term water clarity changes in North America’s Great Lakes from multi‐sensor satellite observations. Limnology and Oceanography, 16, 1976 – 1995. | |
dc.identifier.citedreference | Bocaniov, S. A., Leon, L. F., Rao, Y. R., Schwab, D. J., & Scavia, D. ( 2016 ). Simulating the effect of nutrient reduction on hypoxia in a large lake (Lake Erie, USA‐Canada) with a three‐dimensional lake model. Journal of Great Lakes Research, 42 ( 6 ), 1228 – 1240. https://doi.org/10.1016/j.jglr.2016.06.001 | |
dc.identifier.citedreference | Borsuk, M. E., & Stow, C. A. ( 2000 ). Bayesian parameter estimation in a mixed‐order model of BOD decay. Water Research, 34 ( 6 ), 1830 – 1836. https://doi.org/10.1016/S0043‐1354(99)00346‐2 | |
dc.identifier.citedreference | Branco, A. B., & Kremer, J. N. ( 2005 ). The relative importance of chlorophyll and colored dissolved organic matter (CDOM) to the prediction of the diffuse attenuation coefficient in shallow estuaries. Estuaries, 28 ( 5 ), 643 – 652. https://doi.org/10.1007/BF02732903 | |
dc.identifier.citedreference | Buiteveld, H. ( 1995 ). A model for calculation of diffuse light attenuation (PAR) and Secchi depth. Netherlands Journal of Aquatic Ecology, 29 ( 1 ), 55 – 65. https://doi.org/10.1007/BF02061789 | |
dc.identifier.citedreference | Cerco, C. F., & Meyers, M. ( 2000 ). Tributary refinements to Chesapeake Bay model. Journal of Environmental Engineering‐Asce, 126 ( 2 ), 164 – 174. https://doi.org/10.1061/(ASCE)0733‐9372(2000)126:2(164) | |
dc.identifier.citedreference | Chandler, D. C. ( 1942 ). Limnological studies of western Lake Erie II. Light penetration and its relation to turbidity. Ecology, 23 ( 1 ), 41 – 52. https://doi.org/10.2307/1930871 | |
dc.identifier.citedreference | Chen, C. S., Liu, H. D., & Beardsley, R. C. ( 2003 ). An unstructured grid, finite‐volume, three‐dimensional, primitive equations ocean model: Application to coastal ocean and estuaries. Journal of Atmospheric and Oceanic Technology, 20 ( 1 ), 159 – 186. https://doi.org/10.1175/1520‐0426(2003)020<0159:AUGFVT>2.0.CO;2 | |
dc.identifier.citedreference | Christian, D., & Sheng, Y. P. ( 2003 ). Relative influence of various water quality parameters on light attenuation in Indian River lagoon. Estuarine, Coastal and Shelf Science, 57 ( 5–6 ), 961 – 971. https://doi.org/10.1016/S0272‐7714(03)00002‐7 | |
dc.identifier.citedreference | Dahl, J. A., Graham, D. M., Dermott, R., Johannsson, O. E., Millard, E. S., & Myles, D. D. ( 1995 ). Lake Erie 1993, western, west central and eastern basins: Change in trophic status, and assessment of the abundance, biomass and production of the lower trophic levels. Canadian Technical Report of Fisheries and Aquatic Sciences, 2070 ( i‐xii ), 1 – 118. | |
dc.identifier.citedreference | Dennison, W. C., Orth, R. J., Moore, K. A., Stevenson, J. C., Carter, V., Kollar, S., Bergstrom, P. W., & Batiuk, R. A. ( 1993 ). Assessing water‐quality with submersed aquatic vegetation. Bioscience, 43 ( 2 ), 86 – 94. https://doi.org/10.2307/1311969 | |
dc.identifier.citedreference | Devlin, M. J., Barry, J., Mills, D. K., Gowen, R. J., Foden, J., Sivyer, D., Greenwood, N., Pearce, D., & Tett, P. ( 2009 ). Estimating the diffuse attenuation coefficient from optically active constituents in UK marine waters. Estuarine, Coastal and Shelf Science, 82 ( 1 ), 73 – 83. https://doi.org/10.1016/j.ecss.2008.12.015 | |
dc.identifier.citedreference | Ensor, D. S., & Pilat, M. J. ( 1971 ). Effect of particle size distribution on light transmittance measurement. American Industrial Hygiene Association Journal, 32 ( 5 ), 287 – 292. https://doi.org/10.1080/0002889718506462 | |
dc.identifier.citedreference | Fitzpatrick, M. A. J., Munawar, M., Leach, J. H., & Haffner, G. D. ( 2007 ). Factors regulating primary production and phytoplankton dynamics in western Lake Erie. Fundamental and Applied Limnology, 169 ( 2 ), 137 – 152. https://doi.org/10.1127/1863‐9135/2007/0169‐0137 | |
dc.identifier.citedreference | Ge, Z. F., Whitman, R. L., Nevers, M. B., Phanikumar, M. S., & Byappanahalli, M. N. ( 2012 ). Nearshore hydrodynamics as loading and forcing factors for Escherichia coli contamination at an embayed beach. Limnology and Oceanography, 57 ( 1 ), 362 – 381. https://doi.org/10.4319/lo.2012.57.1.0362 | |
dc.identifier.citedreference | Gordon, H. R. ( 1989 ). Can the Lambert‐Beer law be applied to the diffuse attenuation coefficient of ocean water? Limnology and Oceanography, 34 ( 8 ), 1389 – 1409. https://doi.org/10.4319/lo.1989.34.8.1389 | |
dc.identifier.citedreference | Gordon, H. R., & McCluney, W. R. ( 1975 ). Estimation of depth of sunlight penetration in sea for remote‐sensing. Applied Optics, 14 ( 2 ), 413 – 416. https://doi.org/10.1364/AO.14.000413 | |
dc.identifier.citedreference | Hondzo, M., & Stefan, H. G. ( 1993 ). Lake water temperature simulation‐model. Journal of Hydraulic Engineering, 119 ( 11 ), 1251 – 1273. https://doi.org/10.1061/(ASCE)0733‐9429(1993)119:11(1251) | |
dc.identifier.citedreference | Houser, J. N. ( 2006 ). Water color affects the stratification, surface temperature, heat content, and mean epilimnetic irradiance of small lakes. Canadian Journal of Fisheries and Aquatic Sciences, 63 ( 11 ), 2447 – 2455. https://doi.org/10.1139/f06‐131 | |
dc.identifier.citedreference | Hutchinson, G. E., & Edmondson, Y. H. ( 1957 ). A Treatise on Limnology. New York: Wiley, University of California. | |
dc.identifier.citedreference | Ingle, J. D., & Crouch, S. R. ( 1988 ). Spectrochemical Analysis. Prentice Hall, NJ. Englewood Cliffs. | |
dc.identifier.citedreference | Jerlov, N. G. ( 1968 ). Optical Oceanography. Amsterdam: Elsevier Publishing Company. | |
dc.identifier.citedreference | Ji, R. B., Davis, C., Chen, C. S., & Beardsley, R. ( 2008 ). Influence of local and external processes on the annual nitrogen cycle and primary productivity on Georges Bank: A 3‐D biological‐physical modeling study. Journal of Marine Systems, 73 ( 1–2 ), 31 – 47. https://doi.org/10.1016/j.jmarsys.2007.08.002 | |
dc.identifier.citedreference | Karlsson, J., Bystrom, P., Ask, J., Ask, P., Persson, L., & Jansson, M. ( 2009 ). Light limitation of nutrient‐poor lake ecosystems. Nature, 460 ( 7254 ), 506 – 509. https://doi.org/10.1038/nature08179 | |
dc.identifier.citedreference | Kemp, W. M., Boynton, W. R., Adolf, J. E., Boesch, D. F., Boicourt, W. C., Brush, G., Cornwell, J. C., Fisher, T. R., Glibert, P. M., Hagy, J. D., Harding, L. W., Houde, E. D., Kimmel, D. G., Miller, W. D., Newell, R. I. E., Roman, M. R., Smith, E. M., & Stevenson, J. C. ( 2005 ). Eutrophication of Chesapeake Bay: Historical trends and ecological interactions. Marine Ecology Progress Series, 303, 1 – 29. https://doi.org/10.3354/meps303001 | |
dc.identifier.citedreference | Kirk, J. T. O. ( 1983 ). Light and Photosynthesis in Aquatic Ecosystems (Vol. i‐xi, pp. 1 – 401 ). Cambridge: Cambridge University Press. | |
dc.identifier.citedreference | Kirk, J. T. O. ( 1984 ). Dependence of relationship between inherent and apparent optical properties of water on solar altitude. Limnology and Oceanography, 29 ( 2 ), 350 – 356. https://doi.org/10.4319/lo.1984.29.2.0350 | |
dc.identifier.citedreference | Markager, S., & Vincent, W. F. ( 2000 ). Spectral light attenuation and the absorption of UV and blue light in natural waters. Limnology and Oceanography, 45 ( 3 ), 642 – 650. https://doi.org/10.4319/lo.2000.45.3.0642 | |
dc.identifier.citedreference | McMahon, T. G., Raine, R. C. T., Fast, T., Kies, L., & Patching, J. W. ( 1992 ). Phytoplankton biomass, light attenuation and mixing in the Shannon estuary, Ireland. Journal of the Marine Biological Association of the United Kingdom, 72 ( 03 ), 709 – 720. https://doi.org/10.1017/S0025315400059464 | |
dc.identifier.citedreference | Medrano, E. A., Uittenbogaard, R. E., Pires, L. M. D., van de Wiel, B. J. H., & Clercx, H. J. H. ( 2013 ). Coupling hydrodynamics and buoyancy regulation in Microcystis aeruginosa for its vertical distribution in lakes. Ecological Modelling, 248, 41 – 56. https://doi.org/10.1016/j.ecolmodel.2012.08.029 | |
dc.identifier.citedreference | Mitchell, B. G., Kahru, M., Wieland, J., & Stramska, M. ( 2003 ). In J. L. Mueller, G. S. Fargion, & C. R. McClain (Eds.), Ocean Optics Protocols of Satellite Ocean Color Sensor Validation (pp. 39 – 64 ). Greenbelt, MD, USA: NASA. | |
dc.identifier.citedreference | Mobley, C. D., Stramski, D., Bissett, W. P., & Boss, E. ( 2004 ). Optical modeling of ocean water: Is the case 1‐case 2 classification still useful? Oceanography, 17 ( 2 ), 61 – 67. | |
dc.identifier.citedreference | Morel, A. ( 1988 ). Optical modeling of the upper ocean in relation to its biogenous matter content (case I waters). Journal of Geophysical Research, 93 ( C9 ), 10,749 – 10,768. https://doi.org/10.1029/JC093iC09p10749 | |
dc.identifier.citedreference | Morel, A., & Prieur, L. ( 1977 ). Analysis of variations in ocean color. Limnology and Oceanography, 22 ( 4 ), 709 – 722. https://doi.org/10.4319/lo.1977.22.4.0709 | |
dc.identifier.citedreference | Mortimer, C. H. ( 1987 ). 50 years of physical investigations and related limnological studies on Lake Erie, 1928–1977. Journal of Great Lakes Research, 13 ( 4 ), 407 – 435. https://doi.org/10.1016/S0380‐1330(87)71664‐5 | |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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