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The explanation of spatial errors in geospatial modelling has long been a challenge. This study introduces an index that captures the complexity of local spatial distribution, which can partially provide insight into spatial errors. While previous studies have explored the complexity of geographical data from various perspectives, there is limited knowledge on assessing the complexity while taking spatial dependence into account. This study proposes a measure of geocomplexity, i.e. the spatial local complexity indicator, which characterizes the complexity of local spatial patterns while considering spatial neighbor dependence. We used both aspatial and spatial models to estimate the economic inequality in Australia, and applied the spatial local complexity indicator to explain spatial errors in these models. Results show that the developed geocomplexity indicator, using a binary spatial matrix, can effectively explain spatial errors arising from models, including 17%-47% of errors in aspatial models and 14% in a spatial model. The experiments in this study support our hypothesis that geocomplexity is an essential component in explaining spatial errors. The proposed geocomplexity indicator, along with our hypothesis, has the potential for advancing the understanding complex geospatial systems and enabling applications in various fields related to spatial data analysis. [ABSTRACT FROM AUTHOR]

Understanding geographical characteristics of distribution patterns and spatial association is essential for spatial statistical inference such as factor exploration and spatial prediction. The geographical similarity principle was recently developed to explain the association between geographical variables. It describes the comprehensive degree of approximation of a geographical structure instead of explicit relationships between variables. However, there are still challenges for geographical similarity-based methods. For instance, all samples are used for prediction, leading to increased calculation burden and reduced prediction accuracy due to the noise and unrelated data in large spatial data sets. This study develops a geographically optimal similarity (GOS) model for accurate and reliable spatial prediction based on the geographical similarity principle. In GOS, the geographical configurations are first characterized, and similarities between unknown and known observation locations are assessed. Next, an optimal threshold is determined to select a small number of observations with optimal similarities for the prediction at each unknown location. Finally, a reliable uncertainty assessment approach is developed to assess and map uncertainties of GOS predictions. A new R package "geosimilarity" is developed to conduct GOS models. In this study, GOS is implemented in predicting spatial distributions of trace elements in a mining region in Australia. Results show that GOS can use a small number of observations to derive more accurate and reliable spatial predictions than linear regression and basic configuration similarity models. In addition, pattern characteristics of predictions can be improved by GOS by eliminating the phenomenon wherein predictions are clustered near mean values and contain striped textures. Therefore, GOS demonstrates greater potential for implementing the geographical similarity principle in spatial predictions by bringing information from samples with relatively high similarities at any location across space for more accurate and effective predictions in broader fields and practice. [ABSTRACT FROM AUTHOR]

Spatial heterogeneity refers to uneven distributions of geographical variables. Spatial interpolation methods that utilize spatial heterogeneity are sensitive to the way in which spatial heterogeneity is characterized. This study developed a Generalized Heterogeneity Model (GHM) for characterizing local and stratified heterogeneity within variables and to improve interpolation accuracy. GHM first divides a study area into multiple spatial strata according to the sample values and locations of a variable. Then, GHM estimates simultaneously the spatial variations of the variable within and between the spatial strata. Finally, GHM interpolates unbiased estimates and uncertainty at unsampled locations. We demonstrated the GHM by predicting the spatial distributions of marine chlorophyll in Townsville, Queensland, Australia. Results show that GHM improved both the overall interpolation accuracy across the study area and along strata boundaries compared with previous interpolation models. GHM also avoided bull's eye patterns and abrupt changes along strata boundaries. In future studies, GHM has the potential to be integrated with machine learning and advanced algorithms to improve spatial prediction accuracy for studies in broader fields. [ABSTRACT FROM AUTHOR]

Small data samples are still a critical challenge for spatial predictions. Land use regression (LUR) is a widely used model for spatial predictions with observations at a limited number of locations. Studies have demonstrated that LUR models can overcome the limitation exhibited by other spatial prediction models which usually require greater spatial densities of observations. However, the prediction accuracy and robustness of LUR models still need to be improved due to the linear regression within the LUR model. To improve LUR models, this study develops a land use quantile regression (LUQR) model for more accurate spatial predictions for small data samples. The LUQR is an integration of the LUR and quantile regression, which both have advantages in predictions with a small data set of samples. In this study, the LUQR model is applied in predicting spatial distributions of annual mean PM 2.5 concentrations across the Greater Sydney Region, New South Wales, Australia, with observations at 19 valid monitoring stations in 2020. Cross validation shows that the goodness-of-fit can be improved by 25.6–32.1% by LUQR models when compared with LUR, and prediction root mean squared error (RMSE) and mean absolute error (MAE) can be reduced by 10.6–13.4% and 19.4–24.7% by LUQR models, respectively. This study also indicates that LUQR is a more robust model for the spatial prediction with small data samples than LUR. Thus, LUQR has great potentials to be widely applied in spatial issues with a limited number of observations. [ABSTRACT FROM AUTHOR]

Geographical variables are usually not independent of each other. Hence, it is necessary to investigate the effect of interactions among explanatory variables on a response variable to characterize spatially enhanced or weakened relationships among all variables. The geographical detector (GD) model identifies zones for each explanatory variable, divides the study area into spatial units by overlapping these zones, and quantifies spatial associations as the power of interactive determinant (PID) between a response variable and explanatory variables. Consequently, the PID values depend upon the distributions of explanatory variables (i.e. spatial characteristics) and the subsequent division of spatial units out of these explanatory variables. This study has therefore proposed an Interactive Detector for Spatial Associations (IDSA) to optimize spatial division and improve PID. IDSA utilizes spatial autocorrelation of each explanatory variable and optimizes spatial units based on spatial fuzzy overlay to compute PID. We test the IDSA on both a simulation study and practical case that analyzes road deterioration in Australia. Results showed that the IDSA model could effectively assess the PID while existing GD overestimated PID. Hence, the IDSA improves the GD with refined spatial units based on explanatory variables to enhance their local spatial associations with a response variable. [ABSTRACT FROM AUTHOR]

Road infrastructure performance is closely associated with passengers and freight transportation systems and socio-economic development. The performance of road infrastructure is commonly measured by sensor-monitored indicators, and the ability of monitored indicators in revealing actual performance is generally determined by decision makers and road users. However, it is usually unreliable to directly apply monitored indicators in road performance evaluation, due to the limited aspects of individual sensor-monitored indicators, and potential biases and uncertainties of human experience. To address the issues, this study proposes a model-driven fuzzy spatial multi-criteria decision making (MFSD) approach to derive a comprehensive and accurate indicator of sustainable road performance. In this study, the MFSD approach is applied in exploring the road network in the Wheatbelt region in Western Australia, Australia. Spatial variables of road properties, traffic vehicles and climate conditions are used as criteria in the decision making. Four sensor monitored indicators are collected for estimating contributions of criteria. Results show that the MFSD-based indicator can more comprehensively and accurately characterize sustainable road infrastructure performance. In the study area, the MFSD-based indicator can improve 30.46% of the correlation with road maintenance cost compared with roughness, which is the optimal sensor monitored indicator. At the local government areas, the MFSD-based indicator can explain 45.8% of practical road maintenance cost. Sensitivity analysis from multiple aspects indicates that MFSD is a reliable and accurate method in decision making. The proposed method and analysis have broad potentials in the network-level sustainable infrastructure management. Image 1 • Propose an MFSD method to generate sustainable road infrastructure performance indicators. • MFSD-based indicator can describe comprehensive performance of road infrastructure. • MFSD is a model-driven approach that reduces potential biases of human decisions. • Sensitivity analysis shows that the MFSD is a reliable decision-making method. • MFS-AHP is more capable of differentiating the relative importance of alternatives MFS-TOPSIS. [ABSTRACT FROM AUTHOR]

Road infrastructure is important to the well-being and economic health of all nations. The performance of road pavement infrastructure is sophisticated and affected by numerous factors and varies greatly across different roads. Large scale spatial analysis for assessing road infrastructure performance is increasingly required for road management, therefore multi-source factors, including satellite remotely sensed climate and environmental data, and ground-monitored vehicles observations, are collected as explanatory variables. Different from the traditional point or area based geospatial attributes, the performance of pavement infrastructure is the line segment based spatial data. Thus, a segment-based spatial stratified heterogeneity method is utilized to explore the comprehensive impacts of vehicles, climate, properties of road and socioeconomic conditions on pavement infrastructure performance. Segment-based optimal discretization is applied on discretizing segment-based pavement data, and a segment-based geographical detector is utilized to assess the spatial impacts of variables and their interactions. Results show that the segment-based methods can more reasonably and accurately describe the characteristics of line segment based spatial data and assess the spatial associations. The two major categories of factors associated with pavement damage are the variables of traffic vehicles and heavy vehicles in particular, and climate and environmental conditions. Meanwhile, the interactions between the explanatory variables in these two categories have much more influence than the single explanatory variables, and the interactions can explain more than half of the pavement damage. This study highlights the great potential of remote sensing based large scale spatial analysis of road infrastructures. The approach in this study provides new ideas for spatial analysis for segmented geographical data. The findings indicate that the quantified comprehensive impacts of variables are practical for wise decision-making for road design, construction and maintenance. [ABSTRACT FROM AUTHOR]