Performance Of Ordinary Kriging Research Articles

Performance of spatial interpolation methods in predicting GNSS zenith total delay

This study proposes an alternative approach to the grid-wise VMF1 over Europe, through spatial interpolation of the site-wise VMF1 product. The performance of Ordinary Kriging and IDW was evaluated for predicting ZTD. Using 2020 data collected at 24 GNSS stations, two scenarios were constructed for February and August. Ordinary Kriging and IDW predictions were performed by making model adjustments via performance metrics and method successes were compared. The results showed that the ordinary kriging achieved a success rate of 83.2 %, while the IDW method achieved 77.1 % success. We compared the results with the grid-wise VMF1 to control the accuracy of spatial interpolations. Finally, the methods proposed as alternatives to gridded VMF1 were verified through the CSRS-PPP(ZTD). Ordinary-Kriging (RMSEFeb: [0.92–2.95 cm]; RMSEAug: [1.76–3.85 cm]) was in better compliance with the CSRS-PPP(ZTD), compared to the grid-wise VMF1 (RMSEFeb: [1.59–3.01 cm]; RMSEAug: [2.32–3.93 cm]). These results support that the quality of gridded products can be improved by spatial interpolations.

Practical implications in the interpolation methods for constructing the regional mean sea surface model in the eastern Mediterranean Sea

Abstract This investigation estimates a regional Mean Sea Surface (MSS) model, named SY21MSS, over the eastern Mediterranean Sea using satellite altimetry data from nine Exact Repeat Missions (ERM) and two Geodetic Missions (GM). Two interpolation methods, Least Squares Collocation (LSC) and Ordinary Kriging (OK), were employed, and statistical metrics were applied to assess their performance within a 15 km buffer from the coast. The comparison between LSC and OK techniques in the context of regional MSS modeling primarily centers on the covariance functions used by these methods. Furthermore, generalized cross-validation results indicate that OK outperforms LSC in this region. Consequently, the study recommends adopting the Kriging-based model for calculating regional MSS models in this region due to its superior performance. The investigation further explored the disparities between estimated regional MSS models and the global model DTU18MSS, highlighting a pronounced similarity between OK-SY21MSS and DTU18MSS, as evidenced by a lesser standard deviation (SD) difference compared to LSC-SY21MSS. The practical implications of this research underscore the importance of selecting an appropriate interpolation technique based on data characteristics and study area specifics. While both LSC and OK techniques are deemed viable for MSS modeling, the study emphasizes the superior performance of OK, particularly concerning covariance functions. Additionally, the results emphasize caution when applying global models in regions with significant local variations.

A Geostatistical Approach to Predict the Average Annual Rainfall of Bangladesh

In this paper we tried to fit a predictive model for the average annual rainfall of Bangladesh through a geostatistical approach. From geostatistical point of view, we studied the spatial dependence pattern of average annual rainfall data (measured in mm) collected from 246 stations of Bangladesh. We have employed kriging or spatial interpolation for rainfall data. The data reveals a linear trend when investigated, so by fitting a linear model we tried to remove the trend and, then we used the trend-free data for further calculations. Four theoretical semivariogram models Exponential, Spherical, Gaussian and Matern were used to explain the spatial variation among the average annual rainfall. These models are chosen according to the pattern of empirical semivariogram. The prediction performance of Ordinary kriging with these four fitted models are then compared through ����-fold cross-validation and it is found that Ordinary Kriging performs better when the spatial dependency in average annual rainfall of Bangladesh is modeled through Gaussian semivariogram model.

Spatial variation of shear strength properties incorporating auxiliary variables

Soil shear strength is a critical parameter in slope stability. Shear strength properties may vary significantly over large areas. Thus, the spatial estimates of shear strength properties are necessary for deterministic slope susceptibility mapping over large areas. However, measurements of shear strength parameters are often limited as compared to other soil properties such as Atterberg limit, bulk density and grain size distribution. Multivariate methods have been shown to improve prediction accuracy, but these methods have rarely been used to predict shear strength. In this study, attempts were made to evaluate the effectiveness of using the aforementioned soil properties in predicting the spatial variation of shear strength properties: effective cohesion (c’) and effective friction angle (ϕ’). The performance of ordinary kriging (OK), Random Forest (RF) and regression kriging (RK) in predicting c’ and ϕ’ of residual soils in Singapore were compared and evaluated. In addition, the sensitivity of the three methods to the sample size was investigated. The results of RF analysis revealed that the northing coordinate and percentage of fines were the most important variables for predicting ϕ’. The spatial coordinates and ϕ’ were also important variables for predicting c’. The predicted c’ and ϕ’ using RF and RK resulted in higher spatial heterogeneity than OK. Overall, RF had the smallest error as compared to OK and RK in predicting c’ and ϕ’ at all sample sizes, except for the prediction of ϕ’ using the largest sample size. This study also showed that RF and RK were more sensitive to sample size than OK. These results highlight the benefits of using auxiliary variables when mapping shear strength properties.

Assessing the Sensitivity of Site-Specific Lime and Gypsum Recommendations to Soil Sampling Techniques and Spatial Density of Data Collection in Australian Agriculture: A Pedometric Approach

There is currently limited understanding surrounding the spatial accuracy of soil amelioration advice as a function of sampling density at the sub-field scale. Consequently, soil-based decisions are often made using a data limiting approach, as the value proposition of soil data collection has not been well described. The work presented here investigates the spatial errors of gypsum and lime recommendations based on industry-standard blanket-rate and zone-based variable rate application, as well as the more advanced pedometric approaches – ordinary kriging (OK) and regression kriging (RK). All methods were tested at sampling densities between 0.1–3 samples/ha for a 108 ha broadacre site in central NSW, Australia. Whilst previous work has tested the effect of sampling density on the spatial predictive performance of OK and RK, here we assess prediction accuracy as the error associated with soil management decisions based on their results (i.e., the over- and under-application error of gypsum and lime applications) in conjunction with the RMSE of prediction for soil pH and exchangeable sodium percentage (ESP). The uncertainty of each method is also tested to observe the effect of random initialisation on predictive performance. Results indicated that RK provided superior spatial predictions across all sampling densities for the application of gypsum and lime, with a blanket-rate application providing the worse results, with over- and under-application errors exceeding 200 t and 300 t respectively for 40–60 cm treatment for the entire field. Interestingly, the spatial accuracy of amendment application increased to a sampling density of 0.5 samples/ha for RK, with minimal improvement thereafter, suggesting that meaningful soil amelioration advice can be attained proximal to this density.

Using Kriging incorporated with wind direction to investigate ground-level PM2.5 concentration

Conventional interpolation methods, such as spatial averaging, nearest neighbor, inverse distance weight and ordinary Kriging (OK); for estimating the spatial distribution of ground-level particulate matter (PM) data, do not account for the wind direction for estimating the spatial distribution of PM2.5. In this work, an interpolation algorithm, Win-OK accounting for the wind direction, is developed. In contrast to ordinary Kriging where all locations (irrespective of the wind direction) in the vicinity of a site is considered, the new algorithm (Win-OK) predicts the value at a certain location based on the measured values at locations upwind as determined by the wind direction. This new methodology, Win-OK is validated by applying it to analyze the hourly spatial distribution of ground-level PM2.5 concentrations during Chinese New Year and Chinese National Day in 2017 in Xinxiang city, China. The performance of OK and Win-OK are compared by using them to build PM2.5 concentration heat-maps. A “leave-one-out” cross validation methodology is used to calculate the root-mean-square error (RMSE) and standard deviation for evaluating both algorithms. The results show that OK sometimes gives an extremely high RMSE value using a Gaussian semi-variance model, and the standard deviation significantly deviates from the measured values. Win-OK was found to more accurately predict the PM2.5 spatial distribution in a specific sector. The performance of Win-OK is more stable than OK as established by comparing the calculated RMSE and standard deviation from predictions of both algorithms. Win-OK with a spherical semi-variance model is the most accurate method investigated here for deriving the spatial distribution of ground-level PM2.5. The new algorithm developed here could improve the prediction accuracy of PM2.5 spatial distribution by considering the effect of wind direction.

Land use change effects on soil quality and biological fertility: A case study in northern Iran

The present work mainly focused to investigate the effects of land use change from natural forest (NF) to arable lands (AL), citrus gardens < 10 years old (CG < 10), citrus gardens > 10 years old (CG > 10) and paddy fields (PF) on soil physical, chemical, and biological properties in northern Iran. Moreover, soil fertility was mapped by ordinary kriging (OK) method based on the biological fertility index (BFI), which is based on soil organic matter (SOM), soil basal respiration (CbasR), cumulated soil respiration (CumR), microbial biomass carbon (Cmic), metabolic quotient (qCO2) and mineralization quotient (qM). The performance of OK was assessed by the relative root mean square error (RRMSE, %). Results indicated that land use change significantly influenced most soil properties. Soil organic carbon (SOC) and soil total nitrogen (TN) stocks decreased with land use changes compared to NF. In particular, SOC stocks decreases were lower in AL (29%) and higher in CG < 10 (48%) land uses. TN stocks ranged from 6.0 Mg ha−1 in CG > 10–11.0 Mg ha−1 in NF. BFI was higher in the NF (26 as average, range 24–29) compared to the other land uses (19–22 as average, range 13–26). The range was Good-High in NF and PF, Medium-High in the other land uses. Positive and negative correlations were found among the different soil parameters. OK method interpolated BFI and qCO2 with the lowest (13.69%) and highest (55.65%) RRMSE, respectively. We can conclude that mapping of the BFI is effective to indicate where to adopt a more sustainable management in the agricultural lands for improving soil quality and reducing soil degradation in these areas.

Spatial analysis of chromium in southwestern part of Iran: probabilistic health risk and multivariate global sensitivity analysis.

This study was concerned with chromium as a potential carcinogenic contaminant in 64 wells located in five aquifers, southwest of Iran. A probabilistic health risk assessment indicated a high risk to the local residents including adults and children in the study area. A sequential sensitivity analysis and a novel approach known as multivariate global sensitivity analysis using both principal component analysis and B-spline were applied to investigate the behavior of health risk model along time considering four independent input parameters in the risk equation. In this context, based on the results of sensitivity analysis, concentration of chromium in drinking water (Cw) and body weight (W) were the most influential parameters. Random forest (RF) was used as a variable selection method to choose the most influential parameters for the prediction of chromium. Five parameters, among 13 water quality variables, including phosphate, nitrate, fluoride, manganese and iron were selected by RF as the most important parameters for spatial prediction. Hybrid methods of RF and ordinary kriging (RFOK) and RF and inverse distance weighting (RFIDW) were then applied for spatial prediction of Cr using the secondary variables. The RFOK and RFIDW were more efficient than that of ordinary kriging (OK) with respect to a cross-validation algorithm. For instance, in terms of relative root mean squared error, the performance of OK was improved from 31.72 to 23.21 and 23.61 for RFOK and RFIDW, respectively.

Statistical comparison of various interpolation algorithms for reconstructing regional grid ionospheric maps over China

This paper presents a quantitative comparison of several widely used interpolation algorithms, i.e., Ordinary Kriging (OrK), Universal Kriging (UnK), planar fit and Inverse Distance Weighting (IDW), based on a grid-based single-shell ionosphere model over China. The experimental data were collected from the Crustal Movement Observation Network of China (CMONOC) and the International GNSS Service (IGS), covering the days of year 60–90 in 2015. The quality of these interpolation algorithms was assessed by cross-validation in terms of both the ionospheric correction performance and Single-Frequency (SF) Precise Point Positioning (PPP) accuracy on an epoch-by-epoch basis. The results indicate that the interpolation models perform better at mid-latitudes than low latitudes. For the China region, the performance of OrK and UnK is relatively better than the planar fit and IDW model for estimating ionospheric delay and positioning. In addition, the computational efficiencies of the IDW and planar fit models are better than those of OrK and UnK.

Spatial interpolation model of soil organic carbon density considering land-use and spatial heterogeneity.

Soil organic carbon pool is an important component of terrestrial carbon pool. Soil organic carbon pool and its dynamic change have important influence on carbon cycle in terrestrial ecosystem. Soil organic carbon density (SOCD) is an important parameter of soil carbon storage, and it is also an important index to evaluate farmland soil quality. Accurate prediction of regional organic carbon density spatial distribution is of great significance to the development of precision agriculture. A total of 242 farmland soil samples collected from the Jianghan Plain were used to explore the effects of land use types on the spatial distribution of SOCD in plain areas. Moreover, in the presence of spatial heterogeneity and spatial outliers of SOCD, three Kriging approaches combining land use types were used for the spatial prediction of SOCD. They were dummy variable regression Kriging (DV_RK), mean centering ordinary Kriging (MC_OK1) and median centering ordinary Kriging (MC_OK2). Results showed that the difference of land use types between paddy field and irrigable land was one of the reasons for the spatial heterogeneity of SOCD in the study area, resulting in spatial non-stationary characteristics of SOCD and lowering the performance of OK. DV_RK, MC_OK1 and MC_OK2, however, eliminating the impacts of SOCD spatialheterogeneity caused by land use types while modeling, enhancing the model stability. Therefore, the prediction accuracy of these three models was higher than that of ordinary Kriging (OK). Moreover, MC_OK2 outperformed the others in terms of model reliability, prediction accuracy and the ability to explain the total variance of SOCD. In summary, as an easily accessed auxiliary variable, land use type could effectively decrease the effects of spatial heterogeneity and spatial outliers on SOCD spatial interpolation model, improving the prediction performance and reducing the model uncertainty. SOCD map with higher quality could also be achieved to help reveal the spatial characteristics of SOCD for guiding the agricultural production.

Mapping soil electric conductivity using Bayesian kriging: A case study from Qasur, Pakistan

Quality of soil data is vital to formulate agricultural policies at different scales. Current agricultural applications in Pakistan depend however, on average values of soil estimates over larger areas. In this work, model-based ordinary kriging (OK) and Bayesian kriging (BK) to interpolate soil data is used. The aim is to compare the two different methods for the accuracy of soil data prediction. For this soils were sampled for Electrical Conductivity (EC, dSm–1) at 759 different locations in the rural agricultural areas of Qasur Tehsil, Pakistan. Cross validation was used to compare the performance of OK and BK. Our results show strong skewness and spatial dependency of soil EC values in heterogeneous regions. Box-Cox transformation successfully reduced the level of skewness in the soil EC data (from 14.1 to 0.11). Contrary to OK, under-estimation of soil EC values was not evident in the BK interpolation. Mean square prediction error for BK (1.45) was significantly reduced as compared to that for OK (6.1). Considering these findings, BK is a better model to explain the sub-regional soil EC variability and estimating strategies for sustainable agricultural planning in Pakistan.

Spatial Interpolation for Real-Time Rainfall Field Estimation in Areas with Complex Topography

AbstractFor many hydrological applications interpolation of point rainfall measurements is needed. One such application is flood early warning, particularly where spatially distributed hydrological models are used. Operation in real time poses challenges to the interpolation procedure, as this should then both be automatic and efficiently provide robust interpolation of gauged data. The differences in performance of ordinary kriging, universal kriging, and kriging with external drift with individual and pooled variograms were assessed for 139 daily datasets with significant precipitation in a study area in Bogotá, Colombia. Interpolators were compared using the percentage of variability explained and the root-mean-square error found in cross validation, aiming at identifying a procedure for real-time interpolation. The results showed that interpolators using pooled variograms provide a performance comparable to when the interpolators were applied to the storms individually, showing that they can be used successfully for interpolation in real-time operation in the study area. The analysis identified limitations in the use of kriging with external drift. Only when the adjusted R2 between the secondary variables and precipitation is higher than the percentage of variability explained found in ordinary kriging, then kriging with external drift provided a consistent improvement. This interpolator was found to give a lower performance in all other cases. The distribution of precipitation over basins of interest for each of the storms, derived through sampling rainfall fields generated through conditional Gaussian simulation, shows that, while differences between the interpolators may appear to be significant, the variability of the precipitation volume is less significant.

Evaluating the Performance of Ordinary Kriging in Mapping Soil Salinity

AbstractThe performance of ordinary kriging (OK) is impacted by different factors that characterize the data sets being interpolated. The following factors were investigated as part of this study to evaluate the performance of OK in mapping soil salinity: (1) sampling density (field scale, subbasin scale, and subbasin scale merged with field scale); (2) spatial point patterns (random, aggregated, and regular); (3) spatial and no spatial autocorrelations; (4) normal and skewed distributions; and (5) homogeneity and heterogeneity. The objective of this study is to evaluate the performance of the OK model against each of the aforementioned factors. To achieve this objective, 36 different data sets were selected from data collected from 1999 to 2008 in a study area in the Lower Arkansas River Valley in Colorado. These data sets were selected to represent the different factors used to evaluate the performance of OK, in which each factor is represented by three different data sets. Assessments of the OK model r...

Geostatistical regionalization of daily runoff forecasts in Norway

The national flood forecasting service in Norway applies the conceptual HBV model in 117 catchments of different scales. Daily runoff forecasts from these 117 catchments are regionalized for nationwide qualitative flood risk regionalization displayed in a map. The regionalization is performed without considering scale dependency in runoff response in different-sized catchments. We developed a simple catchment classification approach that allows the incorporation of catchment scale into qualitative runoff forecasting regionalization by geostatistical methods such as ordinary kriging (OK) and inverse distance weighting (IDW). Slightly improved regionalization results were obtained using this classification approach. We further evaluated the predictive performance of OK as this is the current operational approach for qualitative runoff forecast regionalization used in Norway. The results suggest that OK regularly predicts correct tendencies in runoff development and often with small errors. However, the results further suggest that the runoff normalization procedure (which is necessary to make runoff data comparable) provides another source of errors in flood risk regionalization. We also compare the predictive performance of OK with IDW as a less complex method and top-kriging (TK), which is an approach especially developed for interpolating river network-related data. The validation results show that TK performs best, whereas OK tends to perform only slightly better than IDW.

Criteria to compare estimation methods of regionalized compositions

The additive logratio (alr) transformation has been used in several case studies to predict regionalized compositions using standard geostatistical estimation methods such as ordinary kriging and ordinary cokriging. It is a simple method that allows application to transformed data all the body of knowledge available for geostatistical analysis of coregionalizations without a constant sum constraint. To compare the performance of methods, it is customary to use a univariate crossvalidation approach based on the leaving-one-out technique to evaluate the performance for each attribute separately. For multivariate observations this approach is difficult to interpret in terms of overall performance. Therefore, we propose using appropriate distances in real space and in the simplex, to improve the crossvalidation approach and, going a step forward, to adapt the concept of stress from multidimensional scaling to obtain a global measure of performance for each method. The Lyons West oil field of Kansas is used to illustrate the impactof using different distances in the performance of ordinary kriging versus ordinary cokriging.