Spatial Prediction Accuracy Research Articles

Integrating Soil Compaction Impacts of Tramlines Into Soil Erosion Modelling: A Field-Scale Approach

Soil erosion by water is one of the main soil degradation processes worldwide, which leads to declines in natural soil fertility and productivity especially on arable land. Despite advances in soil erosion modelling, the effects of compacted tramlines are usually not considered. However, tramlines noticeably contribute to the amount of soil eroded inside a field. To quantify these effects we incorporated high-resolution spatial tramline data into modelling. For simulation, the process-based soil erosion model EROSION3D has been applied on different fields for a single rainfall event. To find a reasonable balance between computing time and prediction quality, different grid cell sizes (5, 1, and 0.5 m) were used and modelling results were compared against measured soil loss. We found that (i) grid-based models like E3D are able to integrate tramlines, (ii) the share of measured erosion between tramline and cultivated areas fits well with measurements for resolution ≤1 m, (iii) tramline erosion showed a high dependency to the slope angle and (iv) soil loss and runoff are generated quicker within tramlines during the event. The results indicate that the integration of tramlines in soil erosion modelling improves the spatial prediction accuracy, and therefore, can be important for soil conservation planning.

Correction of in-situ portable X-ray fluorescence (PXRF) data of soil heavy metal for enhancing spatial prediction

Heavy metal data measured by portable X-ray fluorescence (PXRF), especially by in-situ PXRF, are usually affected by multiple soil factors, such as soil moisture (SM), soil organic matter (SOM), and soil particle size (SPZ). Thus, a correction may be needed. However, traditionally-used correction methods, such as non-spatial linear regression (LR), cannot effectively correct the spatially non-stationary influences of the related soil factors on PXRF analysis. Moreover, these correction methods are not robust to outliers. In this study, robust geographically weighted regression (RGWR) was used to correct in-situ and ex-situ PXRF data of soil Pb in a peri-urban agricultural area of Wuhan City, China. The accuracy of the corrected PXRF data by RGWR was compared with those by non-spatial and spatial but non-robust methods (i.e., LR and GWR). In addition, to find an appropriate method of using the corrected PXRF data for more accurate spatial prediction, we compared robust ordinary kriging with the corrected PXRF data as part of hard data (ROK-CPXRF) and robust ordinary cokriging with the corrected PXRF data as auxiliary soft data (RCoK-CPXRF). Results showed that (i) RGWR obtained higher correction accuracy than LR and GWR on both the in-situ and ex-situ PXRF data; (ii) the accuracy of the RGWR-corrected in-situ PXRF data was increased nearly to that of the RGWR-corrected ex-situ PXRF data; (iii) given the same amount of sample data, ROK-CPXRF obtained higher prediction accuracy than RCoK-CPXRF. It is concluded that the methods suggested in this study may largely promote the application of in-situ PXRF technique for rapid and accurate soil heavy metal investigation in large-scale areas.

High precision and fast solution method for linearized assembly contact point of geometric error surface

The geometric error modeling method for assembly[1] proposes a feasible basis for the assembly process considering manufacturing error. However, contacting two mounting surfaces with geometric error and finding their actual contact points are two main difficulties in the study of real three-dimensional parts assembly methods. A high-precision and fast solution method for linearized assembly contact points considering geometric errors is proposed by calculating the point cloud spatial pose of the actual contact surface. This method is suitable for spatial pose calculation in high precision plane assembly of rigid parts, which enables fast, accurate and quantitative solution of the positional relationship of components during assembly and measurement, and improves the accuracy and efficiency of spatial pose prediction and control.

Soil type spatial prediction from Random Forest: different training datasets, transferability, accuracy and uncertainty assessment

ABSTRACT: Different uses of soil legacy data such as training dataset as well as the selection of soil environmental covariables could drive the accuracy of machine learning techniques. Thus, this study evaluated the ability of the Random Forest algorithm to predict soil classes from different training datasets and extrapolate such information to a similar area. The following training datasets were extracted from legacy data: a) point data composed of 53 soil samples; b) 30 m buffer around the soil samples, and soil map polygons excluding: c) 20 m; and d) 30 m from the boundaries of polygons. These four datasets were submitted to principal component analysis (PCA) to reduce multidimensionality. Each dataset derived a new one. Different combinations of predictor variables were tested. A total of 52 models were evaluated by means of error of models, prediction uncertainty and external validation for overall accuracy and Kappa index. The best result was obtained by reducing the number of predictors with the PCA along with information from the buffer around the points. Although Random Forest has been considered a robust spatial predictor model, it was clear it is sensitive to different strategies of selecting training dataset. Effort was necessary to find the best training dataset for achieving a suitable level of accuracy of spatial prediction. To identify a specific dataset seems to be better than using a great number of variables or a large volume of training data. The efforts made allowed for the accurate acquisition of a mapped area 15.5 times larger than the reference area.

An Appraisal on the Interpolation Methods Used for Predicting Spatial Variability of Field Hydraulic Conductivity

Knowledge of spatial variability of soil hydraulic conductivity is a key parameter for hydrological modeling. Spatial variability of soil hydraulic conductivity, Ks is attributed to soil heterogeneities associated with texture/structure, different initial conditions, meteorological changes, and clogging. The spatial variability is quantified by employing interpolation methods to point measurements performed in the field. There are not many studies reported in the literature that deals with the critical evaluation of the relative performance of different interpolation methods for predicting spatial variability of hydraulic conductivity. The primary objective of this study is to perform a critical evaluation of five interpolation methods, namely Kriging, Inverse Distance Weighted, Natural Neighbor, Spline and Trend for the spatial prediction of hydraulic conductivity. The accuracy of different methods was assessed by comparing the predicted values with the measured hydraulic conductivity of selected locations. It was noted that the Kriging method with exponential model gave a better spatial prediction as compared to other methods. The spatial variability of Ks was found to be in the same pattern as that of the percentage variation of the sand fraction for both the sites investigated in this study. It was further noted that the prediction of Ks was found to be more precise for those stations with a higher percentage of sand. A sudden transition of soil type from sand to silt was found to influence the accuracy of spatial prediction.

Design of an integrated climatic assessment indicator (ICAI) for wheat production: A case study in Jiangsu Province, China

Agro-meteorological condition plays a fundamental role in crop production. For a specific region, the comprehensive effects of multiple meteorological factors are important indicators for the climatic suitability of the crops. To evaluate the synthetic effects, an integrated climatic assessment indicator (ICAI) are developed in Jiangsu Province, China. A newly produced meteorological assimilation driving datasets (CMADS V1.0) combined with observation data are used in establishing the indicator. The procedure to construct the indicator involves building statistical crop models by meteorological factors and determining the indicator values by classification. In modeling, two machine learning algorithms: Random Forest (RF) and Support Vector Machine (SVM) are compared and the classification model of RF is chosen to build ICAI due to its better performance in the independent test set. To determine a reasonable division in classification, distribution detection of climatic yield is carried out and Monte Carlo simulations are applied for the Kolmogorov–Smirnov (KS) test. The generated indicator includes three values: yield loss, normal and yield increment, with the spatial and temporal prediction accuracy from 67.86% to 100% in the test set for the Northern, Central and Southern Jiangsu. The ICAI are used to estimate the past climatic suitability of winter wheat and the future suitability under global warming conditions in Jiangsu Province. The results show that the climate in 1990s has more adverse effects on wheat production than the other two sub-periods in Northern and Southern Jiangsu. The adaptability of wheat production in Southern Jiangsu has improved greatly to the local environments during the past three decades. In addition, when annual temperature accelerates upwards, both possibilities of yield loss in Northern Jiangsu and yield increment in Southern Jiangsu will increase. Therefore, more concerns should be given to the North in future warming climate, while yield potential in the South may be further improved in this circumstance.

Spatial Analysis of Accidental Oil Spills Using Heterogeneous Data: A Case Study from the North-Eastern Ecuadorian Amazon

Accidental oil spills were assessed in the north-eastern Ecuadorian Amazon, a rich biodiversity and cultural heritage area. Institutional reports were used to estimate oil spill volumes over the period 2001–2011. However, we had to make with heterogeneous and incomplete data. After statistically discriminating well- and poorly-documented oil blocks, some spill factors were derived from the former to spatially allocate oil spills where fragmentary data were available. Spatial prediction accuracy was assessed using similarity metrics in a cross-validation approach. Results showed 464 spill events (42.2/year), accounting for 10,000.2 t of crude oil, equivalent to annual discharges of 909.1 (±SD = 1219.5) t. Total spill volumes increased by 54.8% when spill factors were used to perform allocation to poorly-documented blocks. Resulting maps displayed pollution ‘hotspots’ in Dayuma and Joya de Los Sachas, with the highest inputs averaging 13.8 t km−2 year−1. The accuracy of spatial prediction ranged from 32 to 97%, depending on the metric and the weight given to double-zeros. Simulated situations showed that estimation accuracy depends on variabilities in incident occurrences and in spill volumes per incident. Our method is suitable for mapping hazards and risks in sensitive ecosystems, particularly in areas where incomplete data hinder this process.

Data Association Methodology to Improve Spatial Predictions in Alternative Marketing Circuits in Ecuador.

This work proposes a methodology that reduces the error of future estimations in commercialization based on multivariate spatial prediction techniques (cokriging) considering the products with strong associations. It is based on the Apriori algorithm to find association rules in sales of agricultural products of local markets. Results show the improvement in spatial prediction accuracy after using the best association rules.

Influence of Sampling Point Discretization on the Regional Variability of Soil Organic Carbon in the Red Soil Region, China

Research on the regional variability of soil organic carbon (SOC) has focused mostly on the influence of the number of soil sampling points and interpolation methods. Little attention has typically been paid to the influence of sampling point discretization. Based on dense soil sampling points in the red soil area of Southern China, we obtained four sample discretization levels by a resampling operation. Then, regional SOC distributions were obtained at four levels by two interpolation methods: ordinary Kriging (OK) and Kriging combined with land use information (LuK). To evaluate the influence of sample discretization on revealing SOC variability, we compared the interpolation accuracies at four discretization levels with uniformly distributed validation points. The results demonstrated that the spatial distribution patterns of SOC were roughly similar, but the contour details in some local areas were different at the various discretization levels. Moreover, the predicted mean absolute errors (MAE) and root mean square errors (RMSE) of the two Kriging methods all rose with an increase in discretization. From the lowest to the largest discretization level, the MAEs of OK and LuK rose from 4.47 and 3.02 g kg−1 to 5.46 and 3.54 g kg−1, and the RMSEs rose from 5.13 and 3.95 g kg−1 to 5.76 and 4.76 g kg−1, respectively. Though the trend of prediction errors varied with discretization levels, the interpolation accuracies of the two Kriging methods were both influenced by the sample discretization level. Furthermore, the spatial interpolation uncertainty of OK was more sensitive to the discretization level than that of the LuK method. Therefore, when the spatial distribution of SOC is predicted using Kriging methods based on the same sample quantity, the more uniformly distributed sampling points are, the more accurate the spatial prediction accuracy of SOC will be, and vice versa. The results of this study can act as a useful reference for evaluating the uncertainty of SOC spatial interpolation and making a soil sampling scheme in the red soil region of China.

The estimation of sampling density in improving geostatistical prediction for geotechnical characterization

ABSTRACT Optimum sampling grid was established using geostatistical estimation in order to improve the accuracy of spatial prediction to characterize Rock Quality Designation (RQD). Ordinary Kriging (OK) present in the software GEOVIA Surpac™ module was implemented to undertake geostatistical estimation. The cross-validation method was used to determine the level of accuracy in the process of establishing the optimum sampling density. Generally, the optimal sampling density for this project is 50.1 m, although taking into consideration the results of cross-validation it is deduced that the sampling density laying within 50.1m to 235.68 m is ideal for this project to characterize the RQD. Taking into account the cost of geotechnical drilling, the leave one out cross-validation (LOOCV) method can be used to establish the range of sampling density for RQD. The study area was subdividing into three scenarios and each scenario had training and testing samples for the application of cross-validation technique.

A weekly, continually updated dataset of the probability of large wildfires across western US forests and woodlands

Abstract. There is broad consensus that wildfire activity is likely to increase in western US forests and woodlands over the next century. Therefore, spatial predictions of the potential for large wildfires have immediate and growing relevance to near- and long-term research, planning, and management objectives. Fuels, climate, weather, and the landscape all exert controls on wildfire occurrence and spread, but the dynamics of these controls vary from daily to decadal timescales. Accurate spatial predictions of large wildfires should therefore strive to integrate across these variables and timescales. Here, we describe a high spatial resolution dataset (250 m pixel) of the probability of large wildfires ( > 405 ha) across forests and woodlands in the contiguous western US, from 2005 to the present. The dataset is automatically updated on a weekly basis using Google Earth Engine and a continuous integration pipeline. Each image in the dataset is the output of a random forest machine-learning algorithm, trained on random samples of historic small and large wildfires and represents the predicted conditional probability of an individual pixel burning in a large fire, given an ignition or fire spread to that pixel. This novel workflow is able to integrate the near-term dynamics of fuels and weather into weekly predictions while also integrating longer-term dynamics of fuels, the climate, and the landscape. As a continually updated product, the dataset can provide operational fire managers with contemporary, on-the-ground information to closely monitor the changing potential for large wildfire occurrence and spread. It can also serve as a foundational dataset for longer-term planning and research, such as the strategic targeting of fuels management, fire-smart development at the wildland–urban interface, and the analysis of trends in wildfire potential over time. Weekly large fire probability GeoTiff products from 2005 to 2017 are archived on the Figshare online digital repository with the DOI https://doi.org/10.6084/m9.figshare.5765967 (available at https://doi.org/10.6084/m9.figshare.5765967.v1). Weekly GeoTiff products and the entire dataset from 2005 onwards are also continually uploaded to a Google Cloud Storage bucket at https://console.cloud.google.com/storage/wffr-preds/V1 (last access: 14 September 2018) and are available free of charge with a Google account. Continually updated products and the long-term archive are also available to registered Google Earth Engine (GEE) users as public GEE assets and can be accessed with the image collection ID users/mgray/wffr-preds within GEE.

Regional-scale back-analysis using TRIGRS: an approach to advance landslide hazard modeling and prediction in sparse data regions

Landslides in Kerala, India, have been shown to be preceded not only by critical rainfall over a short period but also a much longer period of elevated pore pressure. Such rainfall-triggered landslides are difficult to monitor due to a lack of adequate data on the locations of failures and precipitation. Here, a method is presented using Transient Rainfall Infiltration and Grid-based Regional Slope stability (TRIGRS) as a tool to model the relationship between critical rainfall and antecedent pore pressure as they relate to slope stability, which can be useful for hazard assessment in sparse data regions. This is demonstrated by parameterizing the model with a combination of regional data sources, remote sensing, and temporal back-analysis based on two known failure events (June 2004 and July 2007). Ranges of possible geotechnical and hydraulic parameters were obtained from various local and regional sources, and soil thickness was modeled as a function of slope angle. Rainfall was estimated using satellite microwave radiometry data. For back-analysis, combinations of cohesion, friction angle, and water table depth were then tested in TRIGRS using trial and error until the predicted and observed failure times coincided for the two failure events. While the spatial prediction accuracy of the model is low and multiple solution sets are expected to exist, the results confirm that information regarding the critical pre-failure conditions and stability changes over time can be derived despite data-poor circumstances. Future studies can be undertaken extending this method to characterize many parameter combinations and incorporate more failure cases to develop probabilistic early-warning thresholds.

Mapping invasion potential using ensemble modelling. A case study on Yushania maling in the Darjeeling Himalayas

Biological invasion is considered the subsequent most important threat to biodiversity after habitat destruction and is documented as a main cause of global biodiversity loss and species extinction. Species distribution models can be used to identify areas that are at risk for invasions by harmful invasive alien species (IAS) if IAS have not yet spread to all suitable habitats. We tested the potential of combining two or more independent but complementary modelling methods to enhance the accuracy of spatial predictions. We used the modelling tools Maxent, GARP and BIOCLIM with presence-only data of the IAS Yushania maling (Maling bamboo), from Darjeeling, Himalaya to develop distribution maps. Modelling tools were chosen based on their performance with presence-only data (Area under curve (AUC) > 0.7) as well as their differences in underlying modelling concept and statistics. The models combine occurrence records with topographic, climatic, and vegetative predictors derived from satellite data. By combining the 3 selected models in an ensemble approach we were able to minimize the spatial uncertainty related to suitable habitat prediction for Yushania maling. While both GARP and BIOCLIM consistently performed at an AUC > 0.7, both our ensemble model and Maxent performed better with an AUC of 0.95 and 0.94 respectively. Moderately and highly suitable habitats for Yushania maling predicted by models correlated well with survey records except for GARP, where we found the model to over-predict suitability outside of the species’ known ecological niche. Our findings identify the best modelling approach enhancing overall explanatory power of habitat suitability models. Our findings show that an ensemble approach should be used to ensure appropriate mitigation measures are applied in the appropriate places, enhancing overall effectiveness both ecologically as well as economically. It was shown that Yushania maling is indeed a threat to the ecosystems in the region, and while the species’ potential habitat may decrease in some areas with climate change, other areas will become more suitable for it.

The optimal sampling design for littoral habitats modelling: A case study from the north-western Mediterranean.

Species distribution models (SDMs) have been used to predict potential distributions of habitats and to model the effects of environmental changes. Despite their usefulness, currently there is no standardized sampling strategy that provides suitable and sufficiently representative predictive models for littoral marine benthic habitats. Here we aim to establish the best performing and most cost-effective sample design to predict the distribution of littoral habitats in unexplored areas. We also study how environmental variability, sample size, and habitat prevalence may influence the accuracy and performance of spatial predictions. For first time, a large database of littoral habitats (16,098 points over 562,895 km of coastline) is used to build up, evaluate, and validate logistic predictive models according to a variety of sampling strategies. A regularly interspaced strategy with a sample of 20% of the coastline provided the best compromise between usefulness (in terms of sampling cost and effort) and accuracy. However, model performance was strongly depen upon habitat characteristics. The proposed sampling strategy may help to predict the presence or absence of target species or habitats thus improving extensive cartographies, detect high biodiversity areas, and, lastly, develop (the best) environmental management plans, especially in littoral environments.

Using sequential indicator simulation method to define risk areas of soil heavy metals in farmland.

The heavy metals in soil have serious impacts on safety, ecological environment and human health due to their toxicity and accumulation. It is necessary to efficiently identify the risk area of heavy metals in farmland soil, which is of important significance for environment protection, pollution warning and farmland risk control. We collected 204 samples and analyzed the contents of seven kinds of heavy metals (Cu, Zn, Pb, Cd, Cr, As, Hg) in Zengcheng District of Guangzhou, China. In order to overcame the problems of the data, including the limitation of abnormal values and skewness distribution and the smooth effect with the traditional kriging methods, we used sequential indicator simulation method (SISIM) to define the spatial distribution of heavy metals, and combined Hakanson index method to identify potential ecological risk area of heavy metals in farmland. The results showed that: (1) Based on the similar accuracy of spatial prediction of soil heavy metals, the SISIM had a better expression of detail rebuild than ordinary kriging in small scale area. Compared to indicator kriging, the SISIM had less error rate (4.9%-17.1%) in uncertainty evaluation of heavy-metal risk identification. The SISIM had less smooth effect and was more applicable to simulate the spatial uncertainty assessment of soil heavy metals and risk identification. (2) There was no pollution in Zengcheng's farmland. Moderate potential ecological risk was found in the southern part of study area due to enterprise production, human activities, and river sediments. This study combined the sequential indicator simulation with Hakanson risk index method, and effectively overcame the outlier information loss and smooth effect of traditional kriging method. It provided a new way to identify the soil heavy metal risk area of farmland in uneven sampling.

Acquiring Common Sense Spatial Knowledge Through Implicit Spatial Templates

Spatial understanding is a fundamental problem with wide-reaching real-world applications. The representation of spatial knowledge is often modeled with spatial templates, i.e., regions of acceptability of two objects under an explicit spatial relationship (e.g., "on," "below," etc.). In contrast with prior work that restricts spatial templates to explicit spatial prepositions (e.g., "glass on table"), here we extend this concept to implicit spatial language, i.e., those relationships (generally actions) for which the spatial arrangement of the objects is only implicitly implied (e.g., "man riding horse"). In contrast with explicit relationships, predicting spatial arrangements from implicit spatial language requires significant common sense spatial understanding. Here, we introduce the task of predicting spatial templates for two objects under a relationship, which can be seen as a spatial question-answering task with a (2D) continuous output ("where is the man w.r.t. a horse when the man is walking the horse?"). We present two simple neural-based models that leverage annotated images and structured text to learn this task. The good performance of these models reveals that spatial locations are to a large extent predictable from implicit spatial language. Crucially, the models attain similar performance in a challenging generalized setting, where the object-relation-object combinations (e.g., "man walking dog") have never been seen before. Next, we go one step further by presenting the models with unseen objects (e.g., "dog"). In this scenario, we show that leveraging word embeddings enables the models to output accurate spatial predictions, proving that the models acquire solid common sense spatial knowledge allowing for such generalization.

Robust variogram estimation combined with isometric log-ratio transformation for improved accuracy of soil particle-size fraction mapping

Mapping soil particle-size fractions (psf) plays an important role in regional hydrological, ecological, geological, agricultural and environmental studies. To map soil compositional data like soil psf, interpolators such as compositional kriging and the combination of log-ratio transformations with ordinary kriging or cokriging were developed. In addition, robust estimators were proposed for these interpolators to improve the variogram models. However, few studies have focused on how to choose log-ratio transformation, kriging, cokriging, or robust variogram estimation methods based on data characteristics to achieve optimal performance when mapping soil psf by comprehensive comparative analysis. Here, we selected different compositional kriging, log-ratio kriging, log-ratio cokriging and log-ratio cokriging methods combined with a robust variogram estimator to improve the accuracy of spatial predictions of soil psf when using 262 soil samples from the upper reaches of the Heihe River in China. In this study, a comprehensive comparative analysis of soil psf maps generated by using different interpolators is presented, and appropriate methods for mapping psf based on the characteristics of the available data are explored. The results show that using isometric log-ratio (ILR) transformation with different interpolators can achieve relatively better performance than the other log-ratio transformation methods. In addition, combining the interpolators with robust variogram estimators significantly improve the prediction accuracy compared with using standard estimators, which presented reasonable and smooth transitions when mapping soil psf. Combining ILR cokriging with a robust variogram estimator had the best accuracy, with the lowest root mean squared error (sand, 10.50%; silt, 11.24%; clay, 7.32%), an Aitchison's distance of 0.76, a standardized residual sum of squares of 0.70 and a relatively higher rate of correctly predicting soil texture types 90.04%. In the future, guideline for using log-ratio transformation methods with linear regression, a generalized linear model or random forest should be developed and combined with ancillary variables to improve the interpolators.

Spatial prediction of basal area and volume in Eucalyptus stands using Landsat TM data: an assessment of prediction methods

BackgroundIn fast-growing forests such as Eucalyptus plantations, the correct determination of stand productivity is essential to aid decision making processes and ensure the efficiency of the wood supply chain. In the past decade, advances in remote sensing and computational methods have yielded new tools, techniques, and technologies that have led to improvements in forest management and forest productivity assessments. Our aim was to estimate and map the basal area and volume of Eucalyptus stands through the integration of forest inventory, remote sensing, parametric, and nonparametric methods of spatial prediction.MethodsThis study was conducted in 20 5-year-old clonal stands (362 ha) of Eucalyptus urophylla S.T.Blake x Eucalyptus camaldulensis Dehnh. The stands are located in the northwest region of Minas Gerais state, Brazil. Basal area and volume data were obtained from forest inventory operations carried out in the field. Spectral data were collected from a Landsat 5 TM satellite image, composed of spectral bands and vegetation indices. Multiple linear regression (MLR), random forest (RF), support vector machine (SVM), and artificial neural network (ANN) methods were used for basal area and volume estimation. Using ordinary kriging, we spatialised the residuals generated by the spatial prediction methods for the correction of trends in the estimates and more detailing of the spatial behaviour of basal area and volume.ResultsThe ND54 index was the spectral variable that had the best correlation values with basal area (r = − 0.91) and volume (r = − 0.52) and was also the variable that most contributed to basal area and volume estimates by the MLR and RF methods. The RF algorithm presented smaller basal area and volume errors when compared to other machine learning algorithms and MLR. The addition of residual kriging in spatial prediction methods did not necessarily result in relative improvements in the estimations of these methods.ConclusionsRandom forest was the best method of spatial prediction and mapping of basal area and volume in the study area. The combination of spatial prediction methods with residual kriging did not result in relative improvement of spatial prediction accuracy of basal area and volume in all methods assessed in this study, and there is not always a spatial dependency structure in the residuals of a spatial prediction method. The approaches used in this study provide a framework for integrating field and multispectral data, highlighting methods that greatly improve spatial prediction of basal area and volume estimation in Eucalyptus stands. This has potential to support fast growth plantation monitoring, offering options for a robust analysis of high-dimensional data.

More Data or a Better Model? Figuring Out What Matters Most for the Spatial Prediction of Soil Carbon

Core Ideas Sample size is the major driving factor of prediction accuracy of soil carbon. The prediction accuracy increases at a decreasing rate with increasing sample sizes. Larger sample sizes deliver equally good prediction accuracy despite the model type. Model type affects the reproducibility (precision) of the predictions. Uncertainty of model predictions decreases with increasing sample sizes. Modeling techniques used in digital soil carbon mapping encompass a variety of algorithms to address spatial prediction problems such as spatial non‐stationarity, nonlinearity and multi‐colinearity. A given study site can inherit one or more such spatial prediction problems, necessitating the use of a combination of statistical learning algorithms to improve the accuracy of predictions. In addition, the training sample size may affect the accuracy of the model predictions. The effect of varying sample size on model accuracy has not been widely studied in pedometrics. To help fill this gap, we examined the behavior of multiple linear regression (MLR), geographically weighted regression (GWR), linear mixed models (LMMs), Cubist regression trees, quantile regression forests (QRFs), and extreme learning machine regression (ELMR) under varying sample sizes. The results showed that for the study site in the Hunter Valley, Australia, the accuracy of spatial prediction of soil carbon is more sensitive to training sample size compared to the model type used. The prediction accuracy initially increases exponentially with increasing sample size, eventually reaching a plateau. Different models reach their maximum predictive potential at different sample sizes. Furthermore, the uncertainty of model predictions decreases with increasing training sample sizes.

A composite spatial predictor via local criteria under a misspecified model

Spatial prediction and variable selection for the study area are both important issues in geostatistics. If spatially varying means exist among different subareas, globally fitting a spatial regression model for observations over the study area may be not suitable. To alleviate deviations from spatial model assumptions, this paper proposes a methodology to locally select variables for each subarea based on a locally empirical conditional Akaike information criterion. In this situation, the global spatial dependence of observations is considered and the local characteristics of each subarea are also identified. It results in a composite spatial predictor which provides a more accurate spatial prediction for the response variables of interest in terms of the mean squared prediction errors. Further, the corresponding prediction variance is also evaluated based on a resampling method. Statistical inferences of the proposed methodology are justified both theoretically and numerically. Finally, an application of a mercury data set for lakes in Maine, USA is analyzed for illustration.