Effect of interpolation methods on quantifying terrain surface roughness under different data densities

Chen, Chuanfa; Bei, Yixuan; Li, Yanyan; Zhou, Weiwei

doi:10.1016/j.geomorph.2022.108448

Cited by 10 publications

(4 citation statements)

References 49 publications

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“…Kriging aims to predict the value of the random variable z(x 0 ) at an unsampled point x 0 of a geographical region [56,57] by assuming the following model:…”

Section: Ordinary Krigingmentioning

confidence: 99%

Statistical Assessment of Some Interpolation Methods for Building Grid Format Digital Bathymetric Models

et al. 2023

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As far as the knowledge of the seabed is concerned, both for safe navigation and for scientific research, 3D models, particularly digital bathymetric models (DBMs), are nowadays of fundamental importance. This work aimed to evaluate the quality of DBMs according to the interpolation methods applied to obtain grid format 3D surfaces from scattered sample points. Other complementary factors affecting DBM vertical accuracy, such as seabed morphological complexity and surveyed points sampling density, were also analyzed by using a factorial ANOVA experimental design. The experiments were performed on a multibeam dataset provided by the Italian Navy Hydrographic Institute (IIM) with an original resolution of 1 m × 1 m grid spacing, covering a surface of 0.24 km2. Six different sectors comprising different seabed morphologies were investigated. Eight sampling densities were randomly extracted from every sector, each with four repetitions. Finally, four different interpolation methods were tested, including: radial basis multiquadric function (RBMF), ordinary kriging (OK), universal kriging (UK) and Gaussian Markov random fields (GMRF). The results demonstrated that both RBMF and OK produced very accurate DBM in areas characterized by low levels of seabed ruggedness at sampling densities of only 0.0128 points/m2 (equivalent grid spacing of 8.84 m). In contrast, a higher density of 0.1024 points/m2 (3.13 m grid spacing) was required to produce accurate DBM in areas with more complex seabed topography. On the other hand, UK and GMRF were strongly influenced by morphology and sampling density, yielding higher vertical random errors and more prone to slightly overestimate seabed depths. In addition, sampling density and morphology were the factors that most influenced the vertical accuracy of the interpolated DBM. In this sense, the highly statistically significant influence of the interaction between sampling density and morphology on the vertical accuracy of the interpolated DBM confirms the need to perform a preliminary analysis of seabed morphological complexity in order to increase, if necessary, the number of surveyed points in cases of complex morphologies.

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“…Kriging aims to predict the value of the random variable z(x 0 ) at an unsampled point x 0 of a geographical region [56,57] by assuming the following model:…”

Section: Ordinary Krigingmentioning

confidence: 99%

Statistical Assessment of Some Interpolation Methods for Building Grid Format Digital Bathymetric Models

et al. 2023

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“…Generally, these methods utilize a particular mathematical model to forecast missing data (Chen, Gao, et al., 2022). The commonly used spatial interpolator includes inverse distance weighting (IDW) (Liang et al., 2018), Kriging (Jeffrey et al., 2001), radial basis function (Chen, Bei, et al., 2022), and Point interpolation based on Biased Sentinel Hospitals Areal Disease Estimation (P‐BSHADE) (Jiang et al., 2018; Xu et al., 2013, 2022). Meanwhile, two commonly used temporal interpolation methods are simple exponential smoothing (SES) (Cheng & Lu, 2017) and autoregressive integrated moving average (Kotu & Deshpande, 2019).…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal stacking method with daily‐cycle restrictions for reconstructing missing hourly PM2.5 records

Chen,

2024

Transactions in GIS

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The reliability of hourly PM2.5 data obtained from air quality monitoring stations is compromised as a result of the missing values, thereby impeding the thorough examination of crucial information. In this paper, we present a spatiotemporal (ST) stacking machine learning (ML) method with daily‐cycle restrictions for reconstructing missing hourly PM2.5 records. First, the ST neighbors for the target station with missing values are selected at a daily scale. Subsequently, the non‐null data within the ST neighbors undergo an iterative P‐BSHADE interpolation process for re‐interpolation. Next, a stacking ML model is constructed using the re‐interpolation values and several environmental factors associated with PM2.5 as the predictors, while the observed PM2.5 is taken as the independent variable. Finally, the missing values are reconstructed by inputting the predictors into the trained stacking model. The study utilized hourly PM2.5 data in the Beijing‐Tianjin‐Hebei region as a case study to assess the effectiveness of the proposed method, using daily missing ratios of 10%, 30%, and 50%, respectively. The accuracy of the proposed method was then compared to four contemporary ST interpolation methods. The results indicate that the proposed method exhibits superior performance compared to the classical methods. Specifically, it achieves a reduction in the average root mean square error and mean absolute error by at least 40.6% and 40.1%, respectively. Additionally, the proposed method demonstrates the successful recovery of extreme values in the hourly PM2.5 records, in contrast to the classical methods which often exhibit a tendency to overestimate low values and underestimate high values. Overall, the proposed method presents a viable and efficient approach to recover missing values in the hourly PM2.5 records that demonstrate evident daily periodic patterns.

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“…Generally, interpolation is used to generate a DEM from deficient data. Currently, interpolation methods such as the nearest neighbor method, Kriging, and inverse distance weighting are used to generate DEMs [4]. However, their accuracy can degrade in regions with sparse data.…”

Section: Introductionmentioning

confidence: 99%

Comparative Analysis of Digital Elevation Model Generation Methods Based on Sparse Modeling

Fuse,

Imose

2023

Remote Sensing

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With the spread of aerial laser bathymetry (ALB), seafloor topographies are being measured more frequently. Nevertheless, data deficiencies occur owing to seawater conditions and other factors. Conventional interpolation methods generally need to produce digital elevation models (DEMs) with sufficient accuracy. If the topographic features are considered as a basis, the DEM should be reproducible based on a combination of such features. The purpose of this study is to develop new DEM generation methods based on sparse modeling. Based on a review of the definitions of sparsity, we developed DEM generation methods based on a discrete cosine transform (DCT), DCT with elastic net, K-singular value decomposition (K-SVD), Fourier regularization, wavelet regularization, and total variation (TV) minimization, and conducted a comparative analysis. The developed methods were applied to artificially deficient DEM and ALB data, and their accuracy was evaluated. Thus, as a conclusion, we can confirm that the K-SVD method is appropriate when the percentage of deficiencies is low, and that the TV minimization method is appropriate when the percentage of deficiencies is high. Based on these results, we also developed a method integrating both methods and achieved an RMSE of 0.128 m.

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Effect of interpolation methods on quantifying terrain surface roughness under different data densities

Cited by 10 publications

References 49 publications

Statistical Assessment of Some Interpolation Methods for Building Grid Format Digital Bathymetric Models

Statistical Assessment of Some Interpolation Methods for Building Grid Format Digital Bathymetric Models

Spatiotemporal stacking method with daily‐cycle restrictions for reconstructing missing hourly PM2.5 records

Comparative Analysis of Digital Elevation Model Generation Methods Based on Sparse Modeling

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