The Effect of Soil Sampling Density and Spatial Autocorrelation on Interpolation Accuracy of Chemical Soil Properties in Arable Cropland

Knowledge of the relationship between soil sampling density and spatial autocorrelation with interpolation accuracy allows more time- and cost-efficient spatial analysis. Previous studies produced contradictory observations regarding this relationship, and this study aims to determine and explore under which conditions the interpolation accuracy of chemical soil properties is affected. The study area covered 823.4 ha of agricultural land with 160 soil samples containing phosphorus pentoxide (P2O5) and potassium oxide (K2O) values. The original set was split into eight subsets using a geographically stratified random split method, interpolated using the ordinary kriging (OK) and inverse distance weighted (IDW) methods. OK and IDW achieved similar interpolation accuracy regardless of the soil chemical property and sampling density, contrary to the majority of previous studies which observed the superiority of kriging as a deterministic interpolation method. The primary dependence of interpolation accuracy to soil sampling density was observed, having R2 in the range of 56.5–83.4% for the interpolation accuracy assessment. While this study enables farmers to perform efficient soil sampling according to the desired level of detail, it could also prove useful to professions dependent on field sampling, such as biology, geology, and mining.

Density estimation with Gaussian processes for gravitational wave posteriors

ABSTRACT The properties of black hole and neutron-star binaries are extracted from gravitational waves (GW) signals using Bayesian inference. This involves evaluating a multidimensional posterior probability function with stochastic sampling. The marginal probability distributions of the samples are sometimes interpolated with methods such as kernel density estimators. Since most post-processing analysis within the field is based on these parameter estimation products, interpolation accuracy of the marginals is essential. In this work, we propose a new method combining histograms and Gaussian processes (GPs) as an alternative technique to fit arbitrary combinations of samples from the source parameters. This method comes with several advantages such as flexible interpolation of non-Gaussian correlations, Bayesian estimate of uncertainty, and efficient resampling with Hamiltonian Monte Carlo.

Adaptive Directional Cubic Convolution for Integrated Circuit Chip Defect Image Interpolation

An adaptive directional cubic convolution interpolation method for integrated circuit (IC) chip defect images is proposed in this paper, to meet the challenge of preserving edge and texture information. In the proposed method, Otsu thresholding technique is employed to distinguish strong edge pixels from weak ones and texture regions, and estimate the direction of strong edges, adaptively. Boundary pixels are pre-interpolated using the original bicubic interpolation method to help improve the interpolation accuracy of the interior pixels. The experimental results of both classic test images and IC chip defect images demonstrate that the proposed method outperforms the competing methods with better edge and texture preservation, interpolation quality, more natural visual effect of the interpolated images and reasonable computational time. The proposed method can provide high quality IC chip images for defect detection and has been successfully applied on practical vision inspection for IC chips

Ingestion of GNSS-Derived ZTD and PWV for Spatial Interpolation of PM2.5 Concentration in Central and Southern China

With the increasing application of global navigation satellite system (GNSS) technology in the field of meteorology, satellite-derived zenith tropospheric delay (ZTD) and precipitable water vapor (PWV) data have been used to explore the spatial coverage pattern of PM2.5 concentrations. In this study, the PM2.5 concentration data obtained from 340 PM2.5 ground stations in south-central China were used to analyze the variation patterns of PM2.5 in south-central China at different time periods, and six PM2.5 interpolation models were developed in the region. The spatial and temporal PM2.5 variation patterns in central and southern China were analyzed from the perspectives of time series variations and spatial distribution characteristics, and six types of interpolation models were established in central and southern China. (1) Through correlation analysis, and exploratory regression and geographical detector methods, the correlation analysis of PM2.5-related variables showed that the GNSS-derived PWV and ZTD were negatively correlated with PM2.5, and that their significances and contributions to the spatial analysis were good. (2) Three types of suitable variable combinations were selected for modeling through a collinearity diagnosis, and six types of models (geographically weighted regression (GWR), geographically weighted regression kriging (GWRK), geographically weighted regression—empirical bayesian kriging (GWR-EBK), multiscale geographically weighted regression (MGWR), multiscale geographically weighted regression kriging (MGWRK), and multiscale geographically weighted regression—empirical bayesian kriging (MGWR-EBK)) were constructed. The overall R2 of the GWR-EBK model construction was the best (annual: 0.962, winter: 0.966, spring: 0.926, summer: 0.873, and autumn: 0.908), and the interpolation accuracy of the GWR-EBK model constructed by inputting ZTD was the best overall, with an average RMSE of 3.22 μg/m3 recorded, while the GWR-EBK model constructed by inputting PWV had the highest interpolation accuracy in winter, with an RMSE of 4.5 μg/m3 recorded; these values were 2.17% and 4.26% higher than the RMSE values of the other two types of models (ZTD and temperature) in winter, respectively. (3) The introduction of the empirical Bayesian kriging method to interpolate the residuals of the models (GWR and MGWR) and to then correct the original interpolation results of the models was the most effective, and the accuracy improvement percentage was better than that of the ordinary kriging method. The average improvement ratios of the GWRK and GWR-EBK models compared with that of the GWR model were 5.04% and 14.74%, respectively, and the average improvement ratios of the MGWRK and MGWR-EBK models compared with that of the MGWR model were 2.79% and 12.66%, respectively. (4) Elevation intervals and provinces were classified, and the influence of the elevation and the spatial distribution of the plane on the accuracy of the PM2.5 regional model was discussed. The experiments showed that the accuracy of the constructed regional model decreased as the elevation increased. The accuracies of the models in representing Henan, Hubei and Hunan provinces were lower than those of the models in representing Guangdong and Guangxi provinces.

Development and Assessment of the Monthly Grid Precipitation Datasets in China

Based on the high-quality homogenized precipitation data from all 2,419 national weather stations in China, the climatology and anomaly percentage fields are derived, and then the digital elevation model (DEM) is employed to reduce the influence of elevation on the spatial interpolation accuracy of precipitation due to the unique topography in China. Then, the gradient plus inverse distance squared (GIDS) method and the inverse distance squared (IDS) method are used to grid the climatology field and the anomaly percentage field, respectively, and the 0.5 × 0.5° gridded datasets during 1961–2018 in China are obtained by combining them together. The evaluation shows that the mean absolute error (MAE) between the analysis value and the observation is 15.8 mm/month. The MAE in South China is generally higher than that in North China, and the MAE is obviously larger in summer than in other seasons. Specifically, 94.6, 54.4, 4.6, and 53.8% of the MAE are below 10 mm/month in winter (DJF), spring (MAM), summer (JJA), and autumn (SON), respectively, and 99.5, 79.9, 22.8, and 82.1% of them are less than 20 mm/month. The MAE over China in four seasons is 3.8, 13.2, 33.5, and 12.7 mm/month, respectively. This dataset has the potential of broad application prospects in the evaluations of weather and climate models and satellite products.

Maps, trends, and temperature sensitivities—phenological information from and for decreasing numbers of volunteer observers

Phenology serves as a major indicator of ongoing climate change. Long-term phenological observations are critically important for tracking and communicating these changes. The phenological observation network across Germany is operated by the National Meteorological Service with a major contribution from volunteering activities. However, the number of observers has strongly decreased for the last decades, possibly resulting in increasing uncertainties when extracting reliable phenological information from map interpolation. We studied uncertainties in interpolated maps from decreasing phenological records, by comparing long-term trends based on grid-based interpolated and station-wise observed time series, as well as their correlations with temperature. Interpolated maps in spring were characterized by the largest spatial variabilities across Bavaria, Germany, with respective lowest interpolated uncertainties. Long-term phenological trends for both interpolations and observations exhibited mean advances of −0.2 to −0.3 days year−1 for spring and summer, while late autumn and winter showed a delay of around 0.1 days year−1. Throughout the year, temperature sensitivities were consistently stronger for interpolated time series than observations. Such a better representation of regional phenology by interpolation was equally supported by satellite-derived phenological indices. Nevertheless, simulation of observer numbers indicated that a decline to less than 40% leads to a strong decrease in interpolation accuracy. To better understand the risk of declining phenological observations and to motivate volunteer observers, a Shiny app is proposed to visualize spatial and temporal phenological patterns across Bavaria and their links to climate change–induced temperature changes.

Estimation of the spatial climate comfort distribution using tourism climate index (TCI) and inverse distance weighting (IDW) (case study: Fars Province, Iran)

This article was conducted to perform a temporal and spatial analysis in order to identify suitable climatic regions for tourism. We investigated tourism climate conditions in Fars province from 2006 to 2016 using tourism climate index (TCI). Also, modified inverse distance weighting (IDW) interpolation is applied to generate the optimal spatial pattern of the TCI distribution. The relationship between the interpolation accuracy and a critical IDW parameter, called power value (β), was evaluated for optimization. The results revealed that during four months of May, April, October, and November, 70–83% of cities in Fars province show excellent and ideal climatic comfort. In the four months of July, December, January, and March, about 45–54% of Fars province provide good and very good conditions for tourism activities. The spatial distribution of TCI also shows that the cities in the northern part generally have the most desirable conditions during the hot season, while the southern cities of Fars province are more suitable for tourism during the cold season. Also, analysis of optimization steps demonstrated that power value (β) affects interpolation accuracy. As our study suggests, using the optimal power values (β) of 1 and 2 can lead to optimal spatial interpolation of the TCI distribution. Overall, we found IDW and TCI as reliable tools for assessing bioclimatic comfort conditions, considering β-value as an influential factor that should be evaluated to achieve optimal interpolation results.

Application of Dynamically Constrained Interpolation Methodology in Simulating National-Scale Spatial Distribution of PM2.5 Concentrations in China

Numerous studies have revealed that the sparse spatiotemporal distributions of ground-level PM2.5 measurements affect the accuracy of PM2.5 simulation, especially in large geographical regions. However, the high precision and stability of ground-level PM2.5 measurements make their role irreplaceable in PM2.5 simulations. This article applies a dynamically constrained interpolation methodology (DCIM) to evaluate sparse PM2.5 measurements captured at scattered monitoring sites for national-scale PM2.5 simulations and spatial distributions. The DCIM takes a PM2.5 transport model as a dynamic constraint and provides the characteristics of the spatiotemporal variations of key model parameters using the adjoint method to improve the accuracy of PM2.5 simulations. From the perspective of interpolation accuracy and effect, kriging interpolation and orthogonal polynomial fitting using Chebyshev basis functions (COPF), which have been proved to have high PM2.5 simulation accuracy, were adopted to make a comparative assessment of DCIM performance and accuracy. Results of the cross validation confirm the feasibility of the DCIM. A comparison between the final interpolated values and observations show that the DCIM is better for national-scale simulations than kriging or COPF. Furthermore, the DCIM presents smoother spatially interpolated distributions of the PM2.5 simulations with smaller simulation errors than the other two methods. Admittedly, the sparse PM2.5 measurements in a highly polluted region have a certain degree of influence on the interpolated distribution accuracy and rationality. To some extent, adding the right amount of observations can improve the effectiveness of the DCIM around existing monitoring sites. Compared with the kriging interpolation and COPF, the results show that the DCIM used in this study would be more helpful for providing reasonable information for monitoring PM2.5 pollution in China.

High Accuracy Interpolation of DEM Using Generative Adversarial Network

Digital elevation model (DEM) interpolation is aimed at predicting the elevation values of unobserved locations, given a series of collected points. Over the years, the traditional interpolation methods have been widely used but can easily lead to accuracy degradation. In recent years, generative adversarial networks (GANs) have been proven to be more efficient than the traditional methods. However, the interpolation accuracy is not guaranteed. In this paper, we propose a GAN-based network named gated and symmetric-dilated U-net GAN (GSUGAN) for improved DEM interpolation, which performs visibly and quantitatively better than the traditional methods and the conditional encoder-decoder GAN (CEDGAN). We also discuss combinations of new techniques in the generator. This shows that the gated convolution and symmetric dilated convolution structure perform slightly better. Furthermore, based on the performance of the different methods, it was concluded that the Convolutional Neural Network (CNN)-based method has an advantage in the quantitative accuracy but the GAN-based method can obtain a better visual quality, especially in complex terrains. In summary, in this paper, we propose a GAN-based network for improved DEM interpolation and we further illustrate the GAN-based method’s performance compared to that of the CNN-based method.

Continuous body 3-D reconstruction of limbless animals

ABSTRACTLimbless animals such as snakes, limbless lizards, worms, eels and lampreys move their slender, long bodies in three dimensions to traverse diverse environments. Accurately quantifying their continuous body's 3-D shape and motion is important for understanding body–environment interactions in complex terrain, but this is difficult to achieve (especially for local orientation and rotation). Here, we describe an interpolation method to quantify continuous body 3-D position and orientation. We simplify the body as an elastic rod and apply a backbone optimization method to interpolate continuous body shape between end constraints imposed by tracked markers. Despite over-simplifying the biomechanics, our method achieves a higher interpolation accuracy (∼50% error) in both 3-D position and orientation compared with the widely used cubic B-spline interpolation method. Beyond snakes traversing large obstacles as demonstrated, our method applies to other long, slender, limbless animals and continuum robots. We provide codes and demo files for easy application of our method.