Broken line smoothing: A simple method for interpolating and smoothing data series

D. Koutsoyiannis, Broken line smoothing: A simple method for interpolating and smoothing data series, Environmental Modelling and Software, 15 (2), 139–149, 2000.

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[English]

A technique is proposed for smoothing a broken line fit, with known break points, to observational data. It will be referred to as "broken line smoothing". The smoothness term is defined by means of the angles formed by the consecutive segments of the broken line, and is given an adjustable weight. The roughness of the resulting broken line can then be controlled by appropriately tuning the weight of smoothness term and the number of straight-line segments. The broken line smoothing can be used for data analysis in several applications as an alternative to other methods such as locally weighted regression and smoothing splines. The mathematical background and details of the method as well as practical aspects of its application are presented and discussed. Also, several examples using both synthesised and real world (hydrological and climatological) data are presented to explore and illustrate the methodology.

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See also: http://dx.doi.org/10.1016/S1364-8152(99)00026-2

Our works referenced by this work:

1. G. Tsakalias, and D. Koutsoyiannis, Stage-discharge curves and derivation of discharges, Evaluation of Management of the Water Resources of Sterea Hellas - Phase 2, Report 19, 125 pages, Department of Water Resources, Hydraulic and Maritime Engineering – National Technical University of Athens, Athens, September 1995.
2. M. Spethogianni, Applications of the dendrochronology to hydrology and climatology, Diploma thesis, 88 pages, Department of Water Resources, Hydraulic and Maritime Engineering – National Technical University of Athens, Athens, October 1996.

Our works that reference this work:

1. D. Zarris, and D. Koutsoyiannis, Evaluating sediment yield estimations from large-scale hydrologic systems using the rating curve concept, RMZ - Materials and Geoenvironment, 52 (1), 157–159, 2005.
2. N. Malamos, and D. Koutsoyiannis, Broken line smoothing for data series interpolation by incorporating an explanatory variable with denser observations: Application to soil-water and rainfall data, Hydrological Sciences Journal, doi:10.1080/02626667.2014.899703, 2015.
3. N. Malamos, and D. Koutsoyiannis, Bilinear surface smoothing for spatial interpolation with optional incorporation of an explanatory variable. Part 1:Theory, Hydrological Sciences Journal, 61 (3), 519–526, doi:10.1080/02626667.2015.1051980, 2016.
4. N. Malamos, and D. Koutsoyiannis, Bilinear surface smoothing for spatial interpolation with optional incorporation of an explanatory variable. Part 2: Application to synthesized and rainfall data, Hydrological Sciences Journal, 61 (3), 527–540, doi:10.1080/02626667.2015.1080826, 2016.

Other works that reference this work (this list might be obsolete):

1. Liu, N., H.X. Chen, L.F. Shu, R.W. Zong, B. Yao and M. Statheropoulos, Gaussian smoothing strategy of thermogravimetric data of biomass materials in an air atmosphere, Industrial & Engineering Chemistry Research, 43 (15), 4087-4096, 2004.
2. #Zarris, D., and E. Lykoudi, Analysis of sediment discharge data of the upper Acheloos river, Proceedings of the 7th Panhellenic Geografical Conference of the Hellenic Geographical Society (7PGC/HGS), Mytilene, Greece, 1-8, 2004.
3. #Zarris, D., E. Lykoudi and D. Panagoulia, Assessing the impacts of sediment yield on the sustainability of major hydraulic systems, Proceedings of Protection and Restoration of the Environment VIII (PROTECTION2006), Mykonos, Greece, 2006.
4. #Zarris, D., Analysis of the environmental flow requirement incorporating the effective discharge concept, Proceedings of the 6th International Symposium on Environmental Hydraulics, Athens, 1125–1130, International Association of Hydraulic Research, National Technical University of Athens, 2010.
5. #Wang, X., and S. Zhang, Application research on denoising based on wavelet in data acquisition of impact drilling system, 2010 2nd International Conference on Signal Processing Systems (ICSPS), IEEE, 1, 479-483, doi: 10.1109/ICSPS.2010.5555539, 2010.
6. Jalbert, J., T. Mathevet and A.-C. Favre, Temporal uncertainty estimation of discharges from rating curves using a variographic analysis, Journal of Hydrology, 397 (1-2), 83-92, DOI: 10.1016/j.jhydrol.2010.11.031, 2011.
7. Zarris, D., M. Vlastara and D. Panagoulia, Sediment delivery assessment for a transboundary Mediterranean catchment: The example of Nestos River catchment, Water Resources Management, 25 (14), 3785-3803, 2011.
8. Fenicia, F., D. Kavetski and H. H. G. Savenije, Elements of a flexible approach for conceptual hydrological modeling: 1. Motivation and theoretical development, Water Resour. Res., 47, W11510, doi: 10.1029/2010WR010174, 2011.
9. #Zarris, D., E. Lykoudi and D. Panagoulia, Sediment yield assessment in Greece, Sediment Transport Modeling in Hydrological Watersheds and Rivers, Istanbul, Turkey, November 2012, Vol. 1, 10.13140/2.1.4318.9444, 2012.
10. Schettino, A., Magan: A new approach to the analysis and interpretation of marine magnetic anomalies, Computers & Geosciences, 39, 135-144, 2012.
11. Ghenim, A. N., and A. Megnounif, Estimation de la précision de la relation en puissance reliant la concentration au débit liquide, Revue «Nature & Technologie». C- Sciences de l'Environnement, 09, 54-60, 2013.

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