Assessing the Interactions between Chlorophyll a and Environmental Variables Using Copula Method
Publication: Journal of Hydrologic Engineering
Volume 17, Issue 4
Abstract
Eutrophication is a major water quality problem throughout the world. An understanding of the pattern of phytoplankton variation and the relationships between chlorophyll a and environmental variables can contribute to eutrophic lake management. In this study, the copula method is applied to discern the inherent relationship between chlorophyll a and environmental variables of Wulihu Lake to the north of Taihu Lake, China. The results show that the method can not only determine the correlation between chlorophyll a and environmental variables through Kendall’s but also determine the joint distribution without assuming the variables to be independent. Moreover, the return period of chlorophyll a can be obtained for given different environmental variables. This study may provide insights for policy makers wishing to improve the water quality of lakes and reservoirs.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This project was supported by the National Natural Science Fund of China (40725010 and 40730635), Water Resources Public-Warfare Project (200701024), the Research Fund for the Doctoral Program of Higher Education of China (20100091120059), and the Skeleton Young Teachers Program and Excellent Disciplines Leaders in Midlife-Youth Program of Nanjing University.
References
Akaike, H. (1974). “A new look at the statistical model identification.” IEEE Trans. Autom. ControlIETAA9, 19(6), 716–722.
Bricker, S., Longstaff, B., Dennison, W. A., Jones, K., Boicourt, C. W., and Woerner, J. (2007). “Effects of nutrient enrichment in the nation’s estuaries: A decade of change.” NOAA Coastal Ocean Program Decision Analysis Series No. 26, National Centers for Coastal Ocean Science, Silver Spring, MD.
Celik, K. (2006). “Spatial and seasonal variations in chlorophyll-nutrient relationships in the shallow hypertrophic lake Manyas, Turkey.”Environ. Monit. Assess.EMASDH, 117(1–3), 261–269.
Ceron, J. C., Jimenez-Espinosa, R., and Pulido-Bosch, A. (2000). “Numerical analysis of hydrogeochemical data: A case study (Alto Guadalentín, southeast Spain).” Appl. Geochem.APPGEY, 15(7), 1053–1067.
Chen, Y. W., Fan, C. X., Katrin, T., and Dokulil, M. (2003). “Changes of nutrients and phytoplankton chlorophyll a in a large shallow lake, Taihu, China: An 8-year investigation.” HydrobiologiaHYDRB8, 506(1–3), 273–279.
Cristofor, S., Vadineanu, A., Sarbu, A., Postolache, C., Dobre, R., and Adamescu, M. (2003). “Long-term changes of submerged macrophytes in the lower danube wetland system.” HydrobiologiaHYDRB8, 506–509(1–3), 625–634.
Cunnane, C. (1978). “Unbiased plotting positions—A review.” J. Hydrol. (Amsterdam)JHYDA7, 37(3), 205–222.
Dodds, W. K., et al. (2009). “Eutrophication of US freshwaters: analysis of potential economic damages.” Environ. Sci. Technol.ESTHAG, 43(1), 12–19.
Duan, H., et al. (2009). “Two-decade reconstruction of algal blooms in China’s Lake Taihu.” Environ. Sci. Technol.ESTHAG, 43(10), 3522–3528.
Favre, A. C., El Adlouni, S., Perreault, L., Nathalie, T., and Bernard, B. (2004). “Multivariate hydrological frequency analysis using copulas.” Water Resour. Res.WRERAQ, 40(1), W01101,.
Genest, C., and Favre, A. C. (2007). “Everything you always wanted to know about copula modeling but were afraid to ask.” J. Hydrol. Eng.JHYEFF, 12(4), 347–368.
Genest, C., and Mackay, L. (1986). “The joy of copulas: Bivariate distributions with uniform marginals.” Am. Stat.ASTAAJ, 40(4), 280–283.
Genest, C., and Rivest, L. (1993). “Statistical inference procedures for bivariate archimedean copulas.” J. Am. Stat. Assoc.JSTNAL, 88(423), 1034–1043.
Grimaldi, S., and Serinaldi, F. (2006). “Asymmetric copula in multivariate flood frequency analysis.” Adv. Water Resour.AWREDI, 29(8), 1155–1167.
Gringorten, I. I. (1963). “A plotting rule of extreme probability paper.” J. Geophys. Res.JGREA2, 68(3), 813–814.
Jia, C. R., Batterman, S., and D’Souza, J. C. (2010). “Copulas and other multivariate models of personal exposures to VOC mixtures.” Hum. Ecol. Risk Assess.HERAFR, 16(4), 873–900.
Kagalou, I., Papastergiadou, E., Tsimarakis, G., and Petridis, D. (2003). “Evaluation of the trophic state of lake pamvotis greece, a shallow urban lake.” HydrobiologiaHYDRB8, 506–509(1–3), 745–752.
Kao, S. C., and Govindaraju, R. S. (2010). “A copula-based joint deficit index for droughts.” J. Hydrol. (Amsterdam)JHYDA7, 380(1-2), 121–134.
Kershaw, J. A., Richardsa, E. W., McCarterb, J. B., and Oborna, S. (2010). “Spatially correlated forest stand structures: A simulation approach using copulas.” Comput. Electron. Agric.CEAGE6, 74(1), 120–128.
Kirchner, J. W., Feng, X., Neal, C., and Robson, A. (2004). “The fine structure of water-quality dynamics, the (high-frequency) wave of the future.” Hydrol. ProcessesHYPRE3, 18(7), 1353–1359.
Lau, S. S. S., and Lane, S. N. (2002). “Biological and chemical factors influencing shallow lake eutrophication: A long-term study.” Sci. Total Environ.STENDL, 288(3), 167–181.
Makinen, J., Kauppila, T., Jukka, M., and Juha, M. (2010). “Impacts of point source and diffuse metal and nutrient loading on three northern boreal lakes.” J. Geochem. Explor.JGCEAT, 104(1–2), 47–60.
Ministry of Environment Protection of China (MEP). (2002). “Environmental quality standards for surface water of China” 〈http://www.es.org.cn/download/35-1.pdf〉.
Ministry of Water Resources of China (MWRC). (1999). “Professional standard of a guide to water resources assessment (in Chinese).” SL/T238-1999, Beijing.
Neal, C., and Heathwaite, A. L. (2005). “Nutrient mobility within river basins: A European perspective.” J. Hydrol. (Amsterdam)JHYDA7, 304(1–4), 477–490.
Nelsen, R. B. (2006). An introduction to copulas, 2nd Ed., Springer, New York.
Organization for Economic Cooperation and Development (OECD). (1982). “Eutrophication of waters: monitoring assessment and control.” Final Rep. Cooperative Program on Monitoring of Inland Waters (Eutrophication Control), Environment Directorate, Paris.
Ozturk, A., Kurt, M., and Bilgili, A. (2010). “A copula-based BRDF model.” Comput Graphics Forum.CGFODY, 29(6), 1795–1806.
Pei, H., and Wang, Y. (2003). “Eutrophication research of West Lake, Hangzhou, China: Modeling under uncertainty.” Water Res.WATRAG, 37(2), 416–428.
Piantadosi, J., Boland, J., and Howlett, P. (2008). “Generating synthetic rainfall on various timescales-daily, monthly and yearly.” Environ. Model. Assess., 14(4), 431–438.
Raini, J. A. (2009). “Impact of land use changes on water resources and biodiversity of Lake Nakuru catchment basin, Kenya.” African Journal of EcologyAJOEDE, 47(s1), 39–45.
Romo, S., Van Donk, E., Gylstra, R., and Gulati, R. (1996). “A multivariate analysis of phytoplankton and food web changes in a shallow biomanipulated lake.” Freshwater Biol.FWBLAB, 36(3), 683–696.
Salvadori, G., and De Michele, C. (2004). “Frequency analysis via copulas: Theoretical aspects and applications to hydrological events.” Water Resour. Res.WRERAQ, 40(12), W12511,
Sklar, A. (1959). “Fonctions de repartition an dimensions et leurs marges.” Publ. Inst. Statist. Univ. Paris, 8, 229–231.
State Environmental Protection Administration of China (SEPAC). (2002). “National standard of environmental quality standard for surface water (in Chinese).” GB3838-2002, Beijing.
Strain, P. M., and Yeats, P. A. (1999). “The relationships between chemical measures and potential predictors of the eutrophication status of inlets.” Mar. Pollut. Bull.MPNBAZ, 38(12), 1163–1170.
Takamura, N., Kadono, Y., Fukushima, M., Nakagawa, M., and Baik-H, O. K. (2003). “Effects of aquatic macrophytes on water quality and phytoplankton communities in shallow lakes.” Ecological researchECRSEX, 18(4), 381–395.
Tang, J., and He, P. (2006). “A measure of dependence between random variables based on copula.” J. Jianghan Univ., 34, 5–9 (in Chinese with English abstract).
Tongeren, O. F. R., Liere, L., Gulati, R. D., Postema, G., and Bruyn, P. J. (1992). “Multivariate analysis of the plankton communities in the Loosdrecht Lakes—Relationship with the chemical-physical environment.” HydrobiologiaHYDRB8, 233(1–3), 105–117.
Wang, D., Singh, V. P., and Zhu, Y. (2007c). “Hybrid fuzzy and optimal modeling for water quality evaluation.” Water Resour. Res.WRERAQ, 43(5), W05415,.
Wang, D., Singh, V. P., Zhu, Y. S., and Wu, J. C. (2009). “Stochastic observation error and uncertainty in water quality evaluation.” Adv. Water Resour.AWREDI, 32(10), 1526–1534.
Wang, L., Zhang, J., and Wang, X. (2008). “Mutlianalysis between chlorophyll a and environmental factors in dianshan lake water.” J. Shanghai. Fish. Univ., 17, 58–64 (in Chinese with English abstract).
Wang, X., Lu, Y., He, G., Han, J., and Wang, T. (2007a). “Multivariate analysis of interactions between phytoplankton biomass and environmental variables in Taihu Lake, China.” Environ. Monit. Assess.EMASDH, 133(1-3), 243–253.
Wang, X. L., Lu, Y. L., He, G. Z., Han, J., and Wang, T. (2007b). “Exploration of relationships between phytoplankton biomass and related environmental variables using multivariate statistic analysis in a eutrophic shallow lake: A 5-year study.” J. Environ. Sci. ChinaJENSEE, 19(8), 920–927.
Yu, S., Shang, J., Zhao, J., and Guo, H. (2003). “Factor analysis and dynamics of water quality of the Songhua river, northeast China.” Water Air, Soil Pollut.WAPLAC, 144(1/4), 159–169.
Zechman, E. M., and Ranjithan, S. R. (2007). “Evolutionary computation-based approach for model error correction and calibration.” Adv. Water Resour.AWREDI, 30(5), 1360–1370.
Zhang, L., and Singh, V. P. (2007). “Bivariate rainfall frequency distributions using Archimedean copulas.” J. Hydrol. (Amsterdam)JHYDA7, 332(1–2), 93–109.
Information & Authors
Information
Published In
Copyright
© 2012. American Society of Civil Engineers.
History
Received: Aug 7, 2010
Accepted: Feb 1, 2011
Published online: Feb 3, 2011
Published in print: Apr 1, 2012
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.