From electronic navigational chart data to sea-bottom models: Kriging approaches for the Bay of Pozzuoli

<p class="Abstract">Electronic Navigational Charts (ENCs), official databases created by a national hydrographic office and included in Electronic Chart Display and Information System (ECDIS), supply, among essential indications for safe navigation, data about sea-bottom morphology in terms of depth points and isolines. Those data are very useful to build bathymetric 3D models: applying interpolation methods, it is possible to produce a continuous representation of the seafloor for supporting studies concerning different aspects of a marine area, such as directions and intensity of currents, sensitivity of habitats and species, etc. Many interpolation methods are available in literature for bathymetric data modelling: among them kriging ones are extremely performing, but require deep analysis to define input parameters, i.e. semi-variogram models. This paper aims to analyze kriging approaches for depth data concerning the Bay of Pozzuoli. The attention is focused on the role of semi-variogram models for Ordinary and Universal kriging. Depth data included in two ENCs, namely IT400129 and IT400130, are processed using Geostatistical Analyst, an extension of ArcGIS 10.3.1 (ESRI). The results testify the relevance of the choice of the mathematical functions of the semi-variogram: Stable Model supplies, for this case study, the best performance in terms of depth accuracy for both Ordinary and Universal kriging.</p>

The Application of Semi Variogram and Ordinary Kriging in Determining the Cohesion and Clay Percentage Distribution in Hilly Area of Sabah, Malaysia

Ordinary Kriging (OK) is one of the geostatistical methods, which were used in the variation types of mapping, which related to the soil. Compliment by semi variogram models, OK has become one of the most sought out method for the digital mapping, which applied Geographical Information System (GIS) as a main approach. Four semi variogram models, which are spherical, exponential, circular and gaussian would be applied to determine the best model for the mapping purposes, with Root-Mean-Squared-Error (RMSE) as a performance indicator. The value of the cohesion and clay percentage will be based according to the related depth. Each semi variogram model will be applied to determine the best model for each depth, whether it is cohesion or clay percentage, and producing a map, as a result. This mapping would be an alternative to the geological mapping, whereby it would show the range of the cohesion and clay percentage values rather than soil types.

Weekly Mapping of Sea Ice Freeboard in the Ross Sea from ICESat-2

NASA’s ICESat-2 has been providing sea ice freeboard measurements across the polar regions since October 2018. In spite of the outstanding spatial resolution and precision of ICESat-2, the spatial sparsity of the data can be a critical issue for sea ice monitoring. This study employs a geostatistical approach (i.e., ordinary kriging) to characterize the spatial autocorrelation of the ICESat-2 freeboard measurements (ATL10) to estimate weekly freeboard variations in 2019 for the entire Ross Sea area, including where ICESat-2 tracks are not directly available. Three variogram models (exponential, Gaussian, and spherical) are compared in this study. According to the cross-validation results, the kriging-estimated freeboards show correlation coefficients of 0.56–0.57, root mean square error (RMSE) of ~0.12 m, and mean absolute error (MAE) of ~0.07 m with the actual ATL10 freeboard measurements. In addition, the estimated errors of the kriging interpolation are low in autumn and high in winter to spring, and low in southern regions and high in northern regions of the Ross Sea. The effective ranges of the variograms are 5–10 km and the results from the three variogram models do not show significant differences with each other. The southwest (SW) sector of the Ross Sea shows low and consistent freeboard over the entire year because of the frequent opening of wide polynya areas generating new ice in this sector. However, the southeast (SE) sector shows large variations in freeboard, which demonstrates the advection of thick multiyear ice from the Amundsen Sea into the Ross Sea. Thus, this kriging-based interpolation of ICESat-2 freeboard can be used in the future to estimate accurate sea ice production over the Ross Sea by incorporating other remote sensing data.

Spatial dependency of groundwater quality in Benin City, Edo State, Nigeria using semi-variogram models

Water quality is a worldwide concern especially water for human consumption. Regular monitoring and tools should be developed, to ensure continuous assessment of the level of concentration of chemical constituents prevalent in water. This will guide against health dangers and risks associated with water of low quality. The research focus on using semi-variogram models to measure the degree of spatial dependency of sampled boreholes for prediction of the concentration of water quality parameters at un-sampled locations because of the cumbersome nature of assessing the whole boreholes in Benin City. One hundred and ten (110) different domestic boreholes were systematically sampled and analyzed in laboratory for determination of the concentration of some chemical water quality parameters which include Electrical Conductivity (EC), Total Dissolve Solids (TDS), Bicarbonate (HCO3), Sodium (Na), Potassium (K), Calcium (Ca), Magnesium (Mg), etc. Laboratory examination of boreholes water quality parameters were carried out in wet and dry seasons. Geographical locations of sampled boreholes were also determined. The obtained experimental results were utilized in investigating the spatial structure of the boreholes using semi-variogram models which include spherical, exponential, Gaussian etc. Exponential model was the most fitted model. The borehole water quality parameters exhibited high degree of spatial dependency in EC, TDS, HCO3, Na, K, Ca. Mg, Cl, P, and NO3 in both seasons with ratio < 25% therefore, interpolation technique can be employed to produce spatial variation quality map of boreholes in Benin City as a monitoring technique to detect contamination or changes in water quality.

Recreation and terrain effect on the spatial variation of the apparent soil electrical conductivity in an urban park

Recreation is an important cultural ecosystem service and is able to significantly affect soil heterogeneity and vegetation functioning. This study investigated the role of the relief and tree stand density in the apparent soil electrical conductivity variation within an urban park. The most suitable variogram models were assessed to evaluate the autocorrelation of the regression models. The map of the spatial variability of apparent soil electrical conductivity was built on the basis of the most suitable variogram. The experimental polygon was located in the Botanical Garden of Oles Honchar Dnipro National University (Dnipro City, Ukraine). The experimental polygon was formed by a quasi-regular grid of measurement locations located about 30 m apart. The measurements of the apparent electrical conductivity of the soil in situ were made in May 2018 at 163 points. On average, the value of soil apparent electric conductivity within the investigated polygon was 0.55 dSm/m and varied within 0.17–1.10 dSm/m. Such environment predictors as tree stand density, relief altitude, topographic wetness index, and potential of relief to erosion were able to explain 48% of the observed variability of soil electrical conductivity. The relief altitude had the greatest influence on the variation of soil electrical conductivity, which was indicated with the highest values of beta regression coefficients. The most important trend of the electric conductivity variation was due to the influence of relief altitude and this dependence was nonlinear. The smallest values of the soil electrical conductivity were recorded in the highest and in lowest relief positions, and the largest values were detected in the relief slope. Recreational load can also be explained by the geomorphology predictors and tree stand density data. These predictors can explain 32% of the variation of recreational load. The variogram was built both for the soil apparent electrical conductivity dataset and for the residuals of the regression model. As a result of the procedure of the models’ selection on the basis of the AIC we obtained the best estimation of the variogram models parameters for the electrical conductivity and for the regression residuals of the electrical conductivity. The level of recreation was correlated statistically significantly with the apparent soil electrical conductivity. The residuals of regression models in which geomorphological indicators and tree stand density were used as predictors have a higher correlation level than the original variables. The soil electrical conductivity may be a sensitive indicator of the recreation load.

Basics of geostatistical analyses with GIS

The goal of Geostatistic is to predict the spatial distribution of a property. In this topic we are going to study two types of Spatial Analysis: i) Conventional Analysis (Nongeostatistical); ii) Spatial Continuity Analysis (Geostatistical). We will also try to understand what are Experimental variograms (Nugget; Range and Sill), Variogram models (basic variogram functions) and Estimation (Kriging). The video includes an Exercise. The materials for this topic are a slide presentation, a video with an exercise resolution using geostatistics and two guidebooks.