Bilinear surface smoothing for spatial interpolation with optional incorporation of an explanatory variable. Part 1:Theory

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.

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[English]

Bilinear surface smoothing is an alternative concept which provides flexible means for spatial interpolation. Interpolation is accomplished by means of fitting a bilinear surface into a regression model with known break points and adjustable smoothing terms. Additionally, as an option, the incorporation in an objective manner, of the influence of an explanatory variable available at a considerable denser dataset is possible. The parameters involved in each case (with or without an explanatory variable) are determined by a nonparametric approach based on the generalized cross-validation (GCV) methodology. A convenient search technique of the smoothing parameters was achieved by transforming them in terms of tension parameters, with values restricted in the interval [0, 1). The mathematical framework, the computational implementation and details concerning both versions of the methodology, as well as practical aspects of their application are presented and discussed. In a companion paper, examples using both synthesized and real world (hydrological) data are presented to illustrate the methodology. The proposed mathematical framework constitutes a simple alternative to existing spatial interpolation methodologies.

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See also: http://dx.doi.org/10.1080/02626667.2015.1051980

Our works referenced by this work:

1. D. Koutsoyiannis, Broken line smoothing: A simple method for interpolating and smoothing data series, Environmental Modelling and Software, 15 (2), 139–149, 2000.
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 2: Application to synthesized and rainfall data, Hydrological Sciences Journal, 61 (3), 527–540, doi:10.1080/02626667.2015.1080826, 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 2: Application to synthesized and rainfall data, Hydrological Sciences Journal, 61 (3), 527–540, doi:10.1080/02626667.2015.1080826, 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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