The Influence of Interpolated Point Location and Density on 3D Bathymetric Models Generated by Kriging Methods: An Application on the Giglio Island Seabed (Italy)

Alcaras, Emanuele; Amoroso, Pier Paolo; Parente, Claudio

doi:10.3390/geosciences12020062

Cited by 24 publications

(21 citation statements)

References 77 publications

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“…To assess the accuracy of the results, Cross Validation (CV) is carried out. CV is a statistical validation technique to assess the performs of an interpolation algorithm (Alcaras et al, 2022).…”

Section: Accuracy Evaluationmentioning

confidence: 99%

Using Electronic Navigational Chart for 3d Bathymetric Model of the Port of Naples

Alcaras

Amoroso²,

Figliomeni³

et al. 2023

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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Abstract. Nautical charts generally report fundamental knowledge for the safety of navigation. This information also includes sea depth data reported as depth points or contour lines, which can be used to build a 3D model of the seabed. However, there are different interpolation methods for creating digital depth models, and there is no way to know in advance which of them is the best performing. The aim of this work is to compare different spatial interpolation methods applied on a dataset concerning the seabed of the Port of Naples (Italy) and extracted from the Electronic Navigational Chart (ENC) produced by the Hydrographic Institute of the Italian Navy, in scale 1:10.000. Four deterministic interpolation methods, i.e. Inverse Distance Weighting (IDW), Global Polynomial Interpolation (GPI), Local Polynomial Interpolation (LPI), Radial Basis Function (RBF), and two stochastic interpolation methods, i.e. Ordinary Kriging (OK) and Universal Kriging (UK), are applied using Geographic Information System (GIS) software. Since each method requires to set specific parameters and different options are available, e.g. the order of the polynomial function for GPI and LPI, or semi-variograms for OK and UK, twenty-three models are generated. The result quality is evaluated by Leave-One-Out cross-validation and the statistics of the residuals produced by each interpolation method in the measured points are compared and analysed. The experiments confirm that the stochastic approach is more versatile compared to deterministic approach and can produce better results, as it is testified by the great performance of the Ordinary Kriging, which produces the most accurate 3D models.

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Section: Accuracy Evaluationmentioning

confidence: 99%

Using Electronic Navigational Chart for 3d Bathymetric Model of the Port of Naples

Alcaras

Amoroso²,

Figliomeni³

et al. 2023

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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“…Assessing the accuracy of DEMs is a pending issue, especially for the submerged part of the Earth, where both density and distribution of acoustic bathymetric measurements [10] and spatial resolution (either of interpolation or of indirect gravimetric inversion) are limited. Furthermore, DEM quality is also affected by characteristics of the surface or terrain roughness, cell size or spatial resolution, and the chosen interpolation method (and decisions made about its parameters) [11,12].…”

Section: Introductionmentioning

confidence: 99%

Multigrid/Multiresolution Interpolation: Reducing Oversmoothing and Other Sampling Effects

Rodríguez‐Pérez

Sánchez-Carnero

2022

Geomatics

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Traditional interpolation methods, such as IDW, kriging, radial basis functions, and regularized splines, are commonly used to generate digital elevation models (DEM). All of these methods have strong statistical and analytical foundations (such as the assumption of randomly distributed data points from a gaussian correlated stochastic surface); however, when data are acquired non-homogeneously (e.g., along transects) all of them show over/under-smoothing of the interpolated surface depending on local point density. As a result, actual information is lost in high point density areas (caused by over-smoothing) or artifacts appear around uneven density areas (“pimple” or “transect” effects). In this paper, we introduce a simple but robust multigrid/multiresolution interpolation (MMI) method which adapts to the spatial resolution available, being an exact interpolator where data exist and a smoothing generalizer where data are missing, but always fulfilling the statistical requirement that surface height mathematical expectation at the proper working resolution equals the mean height of the data at that same scale. The MMI is efficient enough to use K-fold cross-validation to estimate local errors. We also introduce a fractal extrapolation that simulates the elevation in data-depleted areas (rendering a visually realistic surface and also realistic error estimations). In this work, MMI is applied to reconstruct a real DEM, thus testing its accuracy and local error estimation capabilities under different sampling strategies (random points and transects). It is also applied to compute the bathymetry of Gulf of San Jorge (Argentina) from multisource data of different origins and sampling qualities. The results show visually realistic surfaces with estimated local validation errors that are within the bounds of direct DEM comparison, in the case of the simulation, and within the 10% of the bathymetric surface typical deviation in the real calculation.

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“…The geoid must be derived by considering topography and its mass density variations. A GGM supports the conversion of ellipsoidal heights to orthometric heights with accuracies varying between few centimetres to even a metre (Denker et al 2009;Pavlis et al 2012;Alcaras et al 2022). There are also local geoid models that present higher level of accuracy: they are generally developed using local (surface or aerial) gravity data compared with the GNSS/levelling measurements (Sideris and She 1995;Huang et al 2007).…”

Section: Introductionmentioning

confidence: 99%

On the Accuracy of Geoid Heights Derived from Discrete GNSS/Levelling Data Using Kriging Interpolation

Alcaras

Amoroso

Falchi

et al. 2022

International Association of Geodesy Symposia

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Local geoid models presenting higher resolution than global ones are generally derived by a combination of different datasets, integrating individual pure astrogeodetic, gravimetric and GNSS/levelling solutions. To define local geoid, different interpolators may be applied starting from dataset of geoid height values. It is well known that the accuracy of the resulting models depends not only by interpolation method, but also by points numerosity and distribution. This article aims to analyse the performance of Kriging approaches in dependence of the density of the dataset. The experiments are carried out on geoid heights extracted in random way from an already existing local geoid model: different subsets are organized containing an increasing number of points in the same area and each of them is submitted to Kriging interpolations (Universal Kriging and Ordinary Kriging). The resulting models are compared with the original one and residuals are calculated to evaluate the accuracy in dependence of point density. The results demonstrate the efficiency of the Kriging methods, highlighting the possibility to achieve higher accuracy (a few centimetres) using a point density of 1 point/100 sqkm, in absence of gravity anomalies. Ordinary Kriging provides better results than Universal Kriging but the undulations between the resulting models are minimal (a few millimetres) when a high number of points is involved. Furthermore, the results highlight the limit of the leave one out Cross validation since it supplies higher residuals than direct comparison for both Universal Kriging and Ordinary Kriging, when few points are used.

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The Influence of Interpolated Point Location and Density on 3D Bathymetric Models Generated by Kriging Methods: An Application on the Giglio Island Seabed (Italy)

Cited by 24 publications

References 77 publications

Using Electronic Navigational Chart for 3d Bathymetric Model of the Port of Naples

Using Electronic Navigational Chart for 3d Bathymetric Model of the Port of Naples

Multigrid/Multiresolution Interpolation: Reducing Oversmoothing and Other Sampling Effects

On the Accuracy of Geoid Heights Derived from Discrete GNSS/Levelling Data Using Kriging Interpolation

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