Abstract
In the paper a method is suggested for a simultaneous estimation of parameters in some differential equations, describing the variation of oxygen in a small creek, and the parameter in a low pass filtering of the solar radiation input. The low pass filtering is obtained by using a simple first order filter.
The oxygen dynamics are modelled by using linear and non-linear stochastic differential equations. The modelling involves a description of the influence from variations in water temperature and solar radiation. The latter affects the oxygen level via the photo synthesis process.
It is shown that the simultaneous low pass filtering of the solar radiation data provides more precise estimates. The low pass filter compensates for the fact that the solar radiation is a high frequency signal and a point measurement, which probably is measured some distance away from the main body of the river. The estimated filter enables an on-line monitoring of water quality. Thus, immediate assessment of receiving waters, as well as of data quality, is possible.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
B.J. Cosby, G.M. Hornberger, and M.G. Kelly. Identification of photosynthesis-light models for aquatic systems. II. Application to a macrophyte dominated stream. Ecological Modelling, 23:25–51, 1984. Elsevier Science Publishers B.V., Amsterdam.
Judith L. Jacobsen and Henrik Madsen. Grey box modelling of oxygen levels in a small stream. EnvironMetrics, 7: 109–21, 1996.
Judith L. Jacobsen, Henrik Madsen, and Poul Harremoës. Modelling the dynamical effect of solar radiation on the oxygen content of a small creek. In press: EnvironMetrics,1996. (Presented at the 6th International Conference on Environmetrics in Malaysia, Dec. 1995.).
Judith L. Jacobsen, Henrik Madsen, and Poul Harremoës. Modelling the transient impact of rain events on the oxygen content of a small creek. Water, Science and Technology, 33(2):177–187, 1996. ( In: Uncertainty, Risk and Transient Pollution Events. Selected proceedings of the IAWQ Interdisciplinary Symposium).
Judith L. Jacobsen and L.M. Voss. Time series analysis and modelling of corrupted data. Master’s thesis, Institute of Mathematical Statistics and Operations Research, Technical University of Denmark, Lyngby, Denmark, 1994. No. 12/94.
Henrik Madsen and Henrik Melgaard. The mathematical and numerical methods used in CTLSM - a program for ML-estimation in stochastic, continuous time dynamical models. Technical Report No. 7/1991, Institute of Mathematical Statistics and Operations Research, Technical University of Denmark, Lyngby, Denmark, 1991.
Henrik Melgaard and Henrik Madsen. CTLSM continuous time linear stochastic modelling. In J.J. Bloem, editor, In: Workshop on Application of System Identification in Energy Savings in Buildings, pages 41–60. Institute for Systems Engineering and Informatics, Joint Research Centre, 1993.
J. Simonsen. Oxygen fluctuation in streams. PhD thesis, Department of Technical Hygiene, Technical University of Denmark, 1974.
Erik Thomsen and Niels Thyssen. Monitoring of important state variables in rivers. Vand,29(2):46–53, 1979. (In Danish: Maling og registrering of vigtige tilstandsvariabler i vandlob).
Niels Thyssen. Aspects of the oxygen dynamics of a macrophyte dominated lowland streams. In J.J. Symoens, S.S. Hooper, and P. Compére, editors, Studies on Aquatic Vascular Plants, pages 202–213. 1982.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 B. G. Teubner Stuttgart
About this chapter
Cite this chapter
Jacobsen, J.L., Madsen, H., Harremoës, P. (1997). Estimation of a low pass filter for solar radiation data. In: Brøns, M., Bendsøe, M.P., Sørensen, M.P. (eds) Progress in Industrial Mathematics at ECMI 96. European Consortium for Mathematics in Industry, vol 9. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-96688-9_4
Download citation
DOI: https://doi.org/10.1007/978-3-322-96688-9_4
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-322-96689-6
Online ISBN: 978-3-322-96688-9
eBook Packages: Springer Book Archive