Bilinear surface smoothing for spatial interpolation with optional incorporation of an explanatory variable. Part 2: Application to synthesized and rainfall data

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.

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[English]

The non-parametric mathematical framework of Bilinear Surface Smoothing (BSS) methodology provides flexible means for spatial (two dimensional) interpolation of variables. As presented in a companion paper, interpolation is accomplished by means of fitting consecutive bilinear surfaces into a regression model with known break points and adjustable smoothing terms defined by means of angles formed by those bilinear surfaces. Additionally, the second version of the methodology (BSSE) incorporates, in an objective manner, the influence of an explanatory variable available at a considerable denser dataset. In the present study, both versions are explored and illustrated using both synthesized and real world (hydrological) data, and practical aspects of their application are discussed. Also, comparison and validation against the results of commonly used spatial interpolation methods (Inverse Distance Weighted, Spline, Ordinary Kriging and Ordinary Cokriging) is performed in the context of the real world application. In every case, the method’s efficiency to perform interpolation between data points that are interrelated in a complicated manner was confirmed. Especially during the validation procedure presented in the real world case study, BSSE yielded very good results, outperforming those of the other interpolation methods. Given the simplicity of the approach, the proposed mathematical framework overall performance is quite satisfactory, indicating its applicability for diverse tasks of scientific and engineering hydrology and beyond.

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See also: http://dx.doi.org/10.1080/02626667.2015.1080826

Our works referenced by this work:

1. D. Koutsoyiannis, and P. Marinos, Final Report of Phase B, Evaluation of Management of the Water Resources of Sterea Hellas - Phase 2, Report 32, 95 pages, Department of Water Resources, Hydraulic and Maritime Engineering – National Technical University of Athens, Athens, September 1995.
2. D. Koutsoyiannis, Broken line smoothing: A simple method for interpolating and smoothing data series, Environmental Modelling and Software, 15 (2), 139–149, 2000.
3. 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.
4. 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.

Our works that reference this work:

1. 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.
2. N. Malamos, I. L. Tsirogiannis, A. Tegos, A. Efstratiadis, and D. Koutsoyiannis, Spatial interpolation of potential evapotranspiration for precision irrigation purposes, 10th World Congress on Water Resources and Environment "Panta Rhei", Athens, European Water Resources Association, 2017.
3. N. Malamos, I. L. Tsirogiannis, A. Tegos, A. Efstratiadis, and D. Koutsoyiannis, Spatial interpolation of potential evapotranspiration for precision irrigation purposes, European Water, 59, 303–309, 2017.
4. N. Malamos, and D. Koutsoyiannis, Field survey and modelling of irrigation water quality indices in a Mediterranean island catchment: A comparison between spatial interpolation methods, Hydrological Sciences Journal, 63 (10), 1447–1467, doi:10.1080/02626667.2018.1508874, 2018.

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