Interpolation Of Spatial Data Research Articles

Uncertainty quantification for impact location and force estimation in composite structures

Structural health monitoring of impact location and severity using Lamb waves has been proven to be a reliable method under laboratory conditions. However, real-life operational and environmental conditions (vibration noise, temperature changes, different impact scenarios, etc.) and measurement errors are known to generate variation in Lamb wave features which may significantly affect the accuracy of these estimates. Therefore, these uncertainties should be considered, as a deterministic approach may lead to erroneous decisions. In this article, a novel data-driven stochastic Kriging-based method for impact location and maximum force estimation, that is able to reliably quantify the output uncertainty is presented. The method utilises a novel modification of the kriging technique (normally used for spatial interpolation of geostatistical data) for statistical pattern matching and uncertainty quantification using Lamb wave features to estimate the location and maximum force of impacts. The data was experimentally obtained from a composite panel equipped with piezoelectric sensors. Comparison with a deterministic benchmark method developed in prior studies shows that the proposed method gives a more reliable estimate for experimental impacts under various simulated environmental and operational conditions by estimating the uncertainty. The developed method highlights the suitability of data-driven methods for uncertainty quantification, by taking advantage of the relationship between data points in the reference database that is a mandatory component of these methods (and is often seen as a disadvantage). By quantifying the uncertainty, there is more information for operators to reliably locate impacts and estimate the severity, leading to robust maintenance decisions.

A Comparison of Precise Fertilization Prescription Rates to a Conventional Approach Based on the Open Source GIS Software

Fertilization is one of the most important components of precision agriculture, ensuring high and stable crop yields. The process of spatial interpolation of soil sample data is recognized as a reliable method of determining the prescription rates for precise fertilization. However, the application of a free open-source geographic information system (GIS) software was often overlooked in the process. In this study, a method of precise fertilization prescription map creation was developed using an open-source GIS software to enable a wider and cheaper availability of its application. The study area covered three independent locations in Osijek-Baranja County. A method was developed for the fertilization of sugar beet with phosphorous pentoxide, but its application is universal with regard to the crop type. An ordinary kriging was determined as an optimal interpolation method for spatial interpolation, with the mean RMSE of 1.8754 and R2of 0.6955. By comparing the precision fertilization prescription rates to a conventional approach, the differences of 4.1 kg ha-1 for Location 1, 15.8 kg ha-1 for Location 2, and 11.2 kg ha-1 for Location 3 were observed. These values indicate a general deficit in soil phosphorous pentoxide, and precise fertilization could ensure its optimal content in the future sowing seasons.

Spatial interpolation of mobile positioning data for population statistics

ABSTRACT Mobile positioning is recognised to be one of the most promising new sources of data for the production of fast and cost-effective statistics regarding population and mobility. Considerable interest has been shown by government institutions in their search for a way to use mobile positioning data to produce official statistics, although to date there are only few examples of successful projects. Apart from data access and sampling, the main challenges relate to the spatial interpolation of mobile positioning data and extrapolation of recorded data to the level of the entire population. This area of work has to date received relatively little attention in the academic discussion. In the current study, we compare five different methods of spatial interpolation of mobile positioning data. The best methods of describing population distribution and size in comparison with Census data are the adaptive Morton grid and the Random forest model (R2 > 0.9), while the more widely used point-in-polygon and areal-weighted methods produce results that are far less satisfactory (R2 = 0.42; R2 = 0.35). Careful selection of spatial interpolation methods is therefore of the utmost importance for producing reliable population statistics from mobile positioning data.

How the variations of terrain factors affect the optimal interpolation methods for multiple types of climatic elements?

The spatial interpolation of meteorological data have important applications in ecological environment monitoring, such as soil erosion, ecological vulnerability evaluation. However, there are significant differences in the interpolation accuracy of climatic elements under different topographic and geomorphic conditions. Based on data of 810 meteorological stations across the country, five typical interpolation methods, namely ordinary Kriging method, inverse distance weight method, spline function method, natural neighborhood method and trend surface method, were utilized in this paper to analyze and compare the interpolation accuracy of five climate factors, namely temperature, precipitation, accumulated temperature(>10°),wind speed and sunshine hours, under different topographic and geomorphological conditions. The results showed that: (1) Ordinary kriging method of temperature had better applicability in plain, hill and medium-large undulating mountain areas for temperature while the inverse distance weight method and spline function method had higher interpolation accuracy in the platform area and the small undulating mountain area, respectively. (2) The optimal interpolation of the precipitation in plain, platform and medium-large undulating mountain areas was ordinary kriging method while the inverse distance weight method and spline function method had better applicability in small undulating mountain area. (3) For accumulated temperature (>10 °C), the spline function method had higher interpolation accuracy in plain and platform areas, while ordinary kriging method had better applicability in hilly, small and medium-large undulating mountain area al (4) The optimal spatial interpolation of wind speed in plain and hilly areas was the inverse distance weight method. The natural neighborhood method and the spline function method had the best applicability in plateau, medium-large undulating mountainous areas and small undulating mountain areas, respectively. (5) For sunshine hours, the optimal spatial interpolations in plain and hilly areas were natural neighborhood method and spline function method, respectively, while the ordinary kriging method and the inverse distance weighting method had better applicability in platform, large undulating mountainous areas and small undulating mountainous areas, respectively .

The Problem of Data Mining in Modelling Traffic Flows in a Megapolis

The article discusses the problems of using data mining in a transport model as a digital platform for analysing data on traffic flows in a megapolis, and prerequisites for creation in future of single data banks and an integrated environment for interaction of models of different levels as clusters of the digital economy, which will consider all modes of transport to assess transport demand and develop projects for organizing traffic in a megapolis.The objective of the work is to study the processes of obtaining quantitative characteristics of objects of transport modelling when creating a single electronic environment by calculating the derived parameters of the transport network of a megapolis. Quantitative spatial characteristics of an object are associated with calculating the distance from a city centre and a main street and are determined using geographic information systems entailing consequent problem of data unification and efficient data storage.As part of achieving that objective, it is shown that it is necessary to create a preprocessing and validation procedure for all primary transport data, since data sources have different formats and spatial interpolation of tracking data. For this, it is recommended to use various methods of data analysis based on GIS technologies, digital terrain modelling, topology of the road network and other objects of the transport network of a megapolis. Besides, the use of intelligent data should be preceded by formatting and grouping the source data in real time. The most common errors arise at the stage of the iterative process for obtaining quantitative characteristics of objects of transport modelling and building the optimal route in terms of travel time along a certain transport network.The existing trends of urban growth require global digitalization of all transport infrastructure objects, considering changes in the functions of the transport environment and in intensity of traffic flows. Theis entails further development and implementation of new information technologies for data processing using neural networks and other digital technologies.

Construction of three-dimensional weather radar data from volcanic eruption clouds

Analysis tools of three-dimensional weather radar data (ANT3D) was originally developed at the National Research Institute for Earth Science and Disaster prevention (NIED) to retrieve three-dimensional (3D) precipitation and wind fields for convective storms. In 2013, Kagoshima University significantly revised ANT3D for analyses of volcanic eruption clouds, mainly to improve the temporal and spatial interpolation of radar data and estimation of the advection vector, which is required for temporal interpolation. Detailed information pertaining to these algorithms is listed as additional information in this paper.•Procedures necessary for the construction of three-dimensional (3D) volcanic cloud weather radar data are described.•An algorithm based on temporal and elevation angle interpolation methods was used to create 3D constant altitude plan position indicator (3D CAPPI) data with high temporal and spatial resolution.•Two programs (ANT3D_GUI and the CAPPI viewer) are provided for readers interested in analyzing volcanic eruption cloud radar data.

Morphometric and landscape factors influencing the precipitation and temperature fields in the Western regions of Ukraine

The paper deals with the analysis of the influences of terrain morphometric parameters on the spatial distribution of temperature regime and precipitation amounts in the Western regions of Ukraine. Among the terrain morphometric parameters that presumably influence the distribution of precipitation and temperatures, the absolute elevation, the surface aspect factor and the vertical dissection index have been considered. The latter two were calculated by the respective focal operators applied to DEM. As to the precipitation amounts, the most strongly influencing factors have been the vertical dissection index, the surface aspect factor and the absolute elevation. The absolute elevation was influencing the most strongly when averaged in the 7 km moving window, while the optimal size of the moving window for the vertical dissection index has been 10 km, and 50–70 km for the aspect factor. The largest precipitation amounts are observed on north-western macroslopes, the smallest –on south-eastern ones. The multiple correlation coefficient observed was above 0.98, while the coefficient of partial correlation for the vertical dissection index was above 0.9. When only weather station located in the plains were considered separately from those in the mountains, this relationship nearly disappeared. Thereby the distribution of precipitation is mostly influenced by high-scale terrain dissection, characteristic of mountainous areas. Average monthly air temperatures, however, have shown the strongest relationship with the absolute elevation, while the vertical dissection index is having some impact, and the impact of the surface aspect factor being rather week. The influence of elevation on average monthly temperature appeared to be the strongest in summer and the weakest – in winter, probably because of the frequent development of temperature inversions. Vertical temperature gradient appeared to be lower in months when the cyclonic type of atmospheric circulation prevailed. Under the prevailing anticyclonic weather types eastern slopes were somewhat warmer than the western ones, under the prevailing cyclonic weather types – other way round. It was shown that the terrain morphometric parameters can serve as good predictors of the temperature regime and precipitation amounts and as such can be used for the purpose of the spatial interpolation of weather stations data to obtain spatially distributed data. Key words: precipitation, air temperature, morphometric parameters, multiple regression.

Assessing soil water content variation in a small mountainous catchment over different time scales and land covers using geographical variables

Soil Water Content (SWC) plays a key role in hydrological processes at the catchment scale. It is highly dependent on local variables (such as soil properties, vegetation type, and topography) and rainfall, which makes it vary in space and time. To characterize its complexity, scientists need SWC monitoring at short time-steps and at different spatial scales (plot, hillslope, sub-catchment). Today such monitoring is possible due to sensors based on geophysical methods that measure SWC at the plot scale, but assessing the space–time variation of SWC remains a challenge in mountainous catchments. This study focuses on a small headwater catchment (Laval, 0.86 km2, Draix-Bléone observatory) composed primarily of black marls in which soil water content variations are assumed to occur primarily in the subsurface (0 cm–50 cm). To characterize the catchment inner hydrological response and to identify parameters controlling hydrological processes, 14 capacitance sensors were set up to monitor SWC at a 15 min time-step at depths of 10 cm to 20 cm; this network complements classic measurements (rainfall, outflows, erosion) in various soil-landscape-hydrological units. The model LISDQS (Interpolation of Quantitative and Spatial Data) based on local topographic variables (from a 1 m resolution Digital Elevation Model) (DEM), Normalized Difference Vegetation Index (NDVI), and soil depth made it possible to estimate SWC at the plot scale and at different time scales. Estimated SWC were compared to SWC time-series collected since May 2016. Finally, this method points out how local parameters that control SWC affect this variable according to rainfall and the catchment initial soil hydric status. At the hourly and daily time scales, SWC variations were highly dependent on curvature index and NDVI during wetting period, and primarily on soil depth and NDVI during drying periods. At 15 min time steps, 7 rainfall-runoff events have been investigated. SWC variations were highly dependent on rainfall intensity and initial SWC. At the same time step, matrix flow was characterized as the main subsurface flow type during fall flood events in every monitored environment while preferential flow appeared during summer flood events and mainly in grassland.

Geoinformation system for analyzing the dynamics of extreme geomagnetic disturbances from observations of ground stations

The paper is concerned with an approach to developing a specialized web-GIS based on a microservice architecture that provides analytical control of the disturbed component of geomagnetic field variations, according to observation data from magnetic observatories and variational stations published on the SuperMAG portal <http://supermag.jhuapl.edu/>. A method of spatial interpolation of geomagnetic data implemented in the proposed web-GIS, together with the proposed scheme for ranking and interpreting them, as well as a visualization method in the form of isolines, allows a user to track the structure, observe the dynamics, identify probable regions, duration and time intervals of the occurrence of extreme geomagnetic disturbances.

Histogram via entropy reduction (HER): an information-theoretic alternative for geostatistics

Abstract. Interpolation of spatial data has been regarded in many different forms, varying from deterministic to stochastic, parametric to nonparametric, and purely data-driven to geostatistical methods. In this study, we propose a nonparametric interpolator, which combines information theory with probability aggregation methods in a geostatistical framework for the stochastic estimation of unsampled points. Histogram via entropy reduction (HER) predicts conditional distributions based on empirical probabilities, relaxing parameterizations and, therefore, avoiding the risk of adding information not present in data. By construction, it provides a proper framework for uncertainty estimation since it accounts for both spatial configuration and data values, while allowing one to introduce or infer properties of the field through the aggregation method. We investigate the framework using synthetically generated data sets and demonstrate its efficacy in ascertaining the underlying field with varying sample densities and data properties. HER shows a comparable performance to popular benchmark models, with the additional advantage of higher generality. The novel method brings a new perspective of spatial interpolation and uncertainty analysis to geostatistics and statistical learning, using the lens of information theory.

Prediction of future grassland vegetation cover fluctuation under climate change scenarios

Grasslands are subject to degradation in arid and semi-arid areas as the result of various pressures, including climate change. Therefore, spatial and temporal monitoring of vegetation cover fluctuation is needed for better understanding and management of natural resources to sustain livelihoods that depend on these grasslands. In this study, changes in vegetation cover were monitored over 1985–2015, using vegetation indices derived from the Landsat images in Chaharmahal-va-Bakhtiyari province, Iran. The percentage of vegetation cover was recorded from sampling plots in the study areas and vegetation indices were calculated from Landsat data over the study period. The relationship between vegetation cover and climate parameters (temperature (T) and precipitation (P)) was determined from precipitation maps, produced from spatial interpolation of weather stations data and temperature maps, produced by regression equation established between DEM-derived elevation and temperature. Then, a regression equation between climate variables and vegetation cover over a period of 30 years’ period was developed and applied on projected climatic variables for the 2050 under RCP2.6 and RCP8.5 scenarios. The Green Vegetation Index (GVI) was found to be the best index for estimation of vegetation cover from the correlation coefficient (r = 0.79) and model RMSE (1.98). The GVI fluctuation was associated with the fluctuation in climate variables, and this was especially evident in especially dry years (1999, 2001 and 2012). From the difference between current and future vegetation cover maps, future vegetation cover change maps were produced and vulnerable areas most likely to be impacted by climate change were identified. The results predict that vegetation cover will be reduced under both scenarios, mostly in the eastern parts of the study region, while 5–25% of vegetation cover increases are projected for some areas in the western parts of the region. Further analysis showed that currently, oak forest covers large swaths of the western parts adjacent to grasslands, but forest degradation will lead to increase of grassland areas at the expense of oak forests. Overall, substantial loss of vegetation cover is predicted in the central parts and extends to the southern parts of the province. Loss of vegetation cover would pave the way to conversion of grassland to other non-productive cover types for pastoral systems. Appropriate management programs and adaptation strategies should be designed and implemented to reduce climate change impacts on grasslands in the identified vulnerable areas.

Inverse distance weighting method optimization in the process of digital terrain model creation based on data collected from a multibeam echosounder

This paper presents the optimization of the inverse distance weighting method (IDW) in the process of creating a digital terrain model (DTM) of the seabed based on bathymetric data collected using a multibeam echosounder (MBES). There are many different methods for processing irregular measurement data into a grid-based DTM, and the most popular of these methods are inverse distance weighting (IDW), nearest neighbour (NN), moving average (MA) and kriging (K). Kriging is often considered one of the best methods in interpolation of heterogeneous spatial data, but its use is burdened by a significantly long calculation time. In contrast, the MA method is the fastest, but the calculated models are less accurate. Between them is the IDW method, which gives satisfactory accuracy with a reasonable calculation time. In this study, the author optimized the IDW method used in the process of creating a DTM seabed based on measurement points from MBES. The goal of this optimization was to significantly accelerate the calculations, with a possible additional increase in the accuracy of the created model. Several variants of IDW methods were analysed (dependent on the search radius, number of points in the interpolation, power of the interpolation and applied smoothing method). Finally, the author proposed an optimization of the IDW method, which uses a new technique of choosing the nearest points during the interpolation process (named the growing radius). The experiments presented in the paper and the results obtained show the true potential of the IDW optimized method in the case of DTM estimation.

Spatial Pythagorean-Hodograph B–Spline curves and 3D point data interpolation

This article deals with the spatial counterpart of the recently introduced class of planar Pythagorean-Hodograph (PH) B–Spline curves. Spatial Pythagorean-Hodograph B–Spline curves are odd-degree, non-uniform, parametric spatial B–Spline curves whose arc length is a B–Spline function of the curve parameter and can thus be computed explicitly without numerical quadrature. After giving a general definition for this new class of curves, we exploit quaternion algebra to provide an elegant description of their coordinate components and useful formulae for the construction of their control polygon. We hence consider the interpolation of spatial point data by clamped and closed PH B–Spline curves of arbitrary odd degree and discuss how degree-(2n+1), Cn-continuous PH B–Spline curves can be computed by optimizing several scale-invariant fairness measures with interpolation constraints.

The use of ordinary kriging and inverse distance weighted interpolation to assess the odour impact of a poultry farming

The aim of the study was to determine the usefulness of spatial data interpolation methods in analyses of the odour impact of animal husbandry facilities. The interpolation methods of data obtained from measurements using the field olfactometry technique were the ordinary kriging method (OK) and the inverse distance weighted method (IDW). The quality of the analyses that have been obtained indicates the potentially better use of the OK method in the presentation of spatial odour concentration distributions.

Modern pollen and its relationship with vegetation and climate in the Mu Us Desert and surrounding area, northern China: Implications of palaeoclimatic and palaeocological reconstruction

This study establishes the spatial and quantitative relationship between modern pollen, vegetation and climate based on 84 surface pollen samples from a nature reserve and ecological restoration area in the Mu Us Desert and surrounding areas, including seven natural vegetation types. Pollen spectra, discriminant analysis and spatial distribution patterns of the main pollen types are used to explore the relationship between pollen assemblages and vegetation types. Results show that each vegetation type can be characterized by a distinct modern pollen assemblage as follows: (1) coniferous forest: Pinus Diploxylon-type and Picea; (2) deciduous forest: Pinus Diploxylon-type, Quercus, Artemisia and Poaceae; (3) deciduous shrub: Pinus Diploxylon-type, Artemisia and Poaceae; (4) grass meadow: Poaceae and Cyperaceae; (5) grass steppe: Poaceae and Artemisia; (6) desert steppe: Chenopodiaceae, Artemisia and Poaceae; and (7) desert: Chenopodiaceae, Nitraria and Artemisia. The higher percentage and lower concentration of Pinus pollen in the Mu Us Desert can be explained by effective long-distance transport from the mountain forest, while Picea has a limited pollen dispersal ability via wind-borne dispersal. Poaceae pollen is well represented and has a higher percentage in several different types of ecological conditions. Modern pollen–climate relationships are assessed using redundancy analysis and weighted averaging partial least squares regression. Significant relationships exist between pollen assemblages and mean annual temperature (R2 = 0.67; RMSEP 1.7 °C; max. bias 2.5 °C), July precipitation (R2 = 0.58; RMSEP 17.8 mm; max. bias 26.0 mm), and January precipitation (R2 = 0.82; RMSEP 0.9 mm; max. bias 1.8 mm). Furthermore, the climate variables obtained by spatial interpolation of data from meteorological stations are used to cross-check the data reconstructed by pollen-climate transfer functions. Our work provides a more comprehensive understanding of the qualitative and quantitative relationships between modern pollen and vegetation/climate and serves as a basis for the paleovegetation and paleoclimate reconstruction in arid and semiarid regions of northern China and similar areas.

Wind speed interpolation for evapotranspiration assessment in complex topography area

Wind speed and direction are fundamental data for many application fields, such as power generation and hydrological modelling. Wind measurements are usually few and sparse; hence, spatial interpolation of wind data is required. However, in mountainous areas with complex orography, accurate interpolation of wind data should consider topographic effects. Due to computational constraints, fully physically based methods that solve thermodynamic and mass conservation equations in three dimensions cannot be applied for long-time simulations or very large areas, while fast empirical methods seem more suitable. The aim of this work is to compare fast empirical methods to interpolate wind speed against a physically based full atmospheric model in order to assess the impact of the introduced approximation in estimating the wind field and the potential evapotranspiration. Comparison is carried out over the area of the upper Po River basin, a predominantly alpine region located in northern Italy. Results show that empirical topographic correction can increase accuracy of interpolated wind speed in areas with complex topography, but it requires about 50% more computational time than simpler empirical methods that do not consider topography.

Non-parametric machine learning methods for interpolation of spatially varying non-stationary and non-Gaussian geotechnical properties

Spatial interpolation has been frequently encountered in earth sciences and engineering. A reasonable appraisal of subsurface heterogeneity plays a significant role in planning, risk assessment and decision making for geotechnical practice. Geostatistics is commonly used to interpolate spatially varying properties at un-sampled locations from scatter measurements. However, successful application of classic geostatistical models requires prior characterization of spatial auto-correlation structures, which poses a great challenge for unexperienced engineers, particularly when only limited measurements are available. Data-driven machine learning methods, such as radial basis function network (RBFN), require minimal human intervention and provide effective alternatives for spatial interpolation of non-stationary and non-Gaussian data, particularly when measurements are sparse. Conventional RBFN, however, is direction independent (i.e. isotropic) and cannot quantify prediction uncertainty in spatial interpolation. In this study, an ensemble RBFN method is proposed that not only allows geotechnical anisotropy to be properly incorporated, but also quantifies uncertainty in spatial interpolation. The proposed method is illustrated using numerical examples of cone penetration test (CPT) data, which involve interpolation of a 2D CPT cross-section from limited continuous 1D CPT soundings in the vertical direction. In addition, a comparative study is performed to benchmark the proposed ensemble RBFN with two other non-parametric data-driven approaches, namely, Multiple Point Statistics (MPS) and Bayesian Compressive Sensing (BCS). The results reveal that the proposed ensemble RBFN provides a better estimation of spatial patterns and associated prediction uncertainty at un-sampled locations when a reasonable amount of data is available as input. Moreover, the prediction accuracy of all the three methods improves as the number of measurements increases, and vice versa. It is also found that BCS prediction is less sensitive to the number of measurement data and outperforms RBFN and MPS when only limited point observations are available.

CircSpaceTime: an R package for spatial and spatio-temporal modelling of circular data

ABSTRACTCircSpaceTime is the only R package, currently available, that implements Bayesian models for spatial and spatio-temporal interpolation of circular data. Such data are often found in applications where, among the many, wind directions, animal movement directions, and wave directions are involved. To analyse such data, we need models for observations at locations and times t, as the so-called geostatistical models, providing structured dependence assumed to decay in distance and time. The approach we take begins with Gaussian processes defined for linear variables over space and time. Then, we use either wrapping or projection to obtain processes for circular data. The models are cast as hierarchical, with fitting and inference within a Bayesian framework. Altogether, this package implements work developed by a series of papers, by Jona Lasinio, Mastrantonio, Wang, and Gelfand. All procedures are written using Rcpp. Estimates are obtained by MCMC, allowing parallelized multiple chains run. The implementation of the proposed models is considerably improved on the simple routines adopted in the research papers. As original running examples, for the spatial and spatio-temporal settings, we use wind directions datasets over central Italy.

Assessment of the Twin-Tunnel Interaction Mechanism in Kenny Hill Formation Using Contraction Ratio Method

Volume loss during tunneling excavation leads to ground deformation, which can damage adjacent surfaces or subsurface structures. Thus, tunnel design with proper estimation of ground deformation and realistic geotechnical simulation is essential for large-scale urban underground construction. In this study, subsurface characterization of the tunnel excavation section in Kenny Hill Formation (KHF) was conducted to develop 3D ground model and tunnel-filtered models and obtain ground sections through the spatial interpolation of borehole data using the Inverse Distance Weighting (IDW) method. Six greenfield ground sections were selected by using the tunnel-filtered model’s configuration of tunnels and available tunneling-induced ground movement data. Conceptual models for finite element modeling were developed based on soil profiles, and the corresponding soil parameters were determined from ground sections. The strength and stiffness parameters of the Hardening Soil (HS) model were established using data from site investigation, in situ and laboratory tests, and empirical correlations with standard penetration test. The effectiveness of empirical correlations was determined through back analysis of twin-tunnel excavation in 2D finite element analysis using the contraction method and verified with monitored ground movement data. The numerical back-analyzed results of twin-tunnel excavation simulation using HS parameters obtained from a selected empirical correlation showed good agreement with construction-monitored ground movements. The application range of the values of contraction ratio was from 0.3 to 0.95%.

Spatial interpolation of marine environment data using P-MSN

ABSTRACTWhen a marine study area is large, the environmental variables often present spatially stratified non-homogeneity, violating the spatial second-order stationary assumption. The stratified non-homogeneous surface can be divided into several stationary strata with different means or variances, but still with close relationships between neighboring strata. To give the best linear-unbiased estimator for those environmental variables, an interpolated version of the mean of the surface with stratified non-homogeneity (MSN) method called point mean of the surface with stratified non-homogeneity (P-MSN) was derived. P-MSN distinguishes the spatial mean and variogram in different strata and borrows information from neighboring strata to improve the interpolation precision near the strata boundary. This paper also introduces the implementation of this method, and its performance is demonstrated in two case studies, one using ocean color remote sensing data, and the other using marine environment monitoring data. The predictions of P-MSN were compared with ordinary kriging, stratified kriging, kriging with an external drift, and empirical Bayesian kriging, the most frequently used methods that can handle some extent of spatial non-homogeneity. The results illustrated that for spatially stratified non-homogeneous environmental variables, P-MSN outperforms other methods by simultaneously improving interpolation precision and avoiding artificially abrupt changes along the strata boundaries.