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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]

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]

Identifying the factors influencing wetland variations is crucial for understanding the relationship of climate change with wetland conservation and management. The wetland distribution is associated with multiple variables, and the interactions among these variables are complex. In this study, we aim to explore an interpretable and quantitative analysis of factors related to wetland spatiotemporal variations on the Tibetan Plateau (TP). By combining SHapley Additive exPlanations with a spatially stratified heterogeneity model, we propose a locally explained stratified heterogeneity (LESH) model that well reveals the effects of multiple variable interactions on the spatiotemporal variations of wetlands. The results show that topographic variables are the most important variables related to the spatial distribution of wetlands on the TP, and climatic variables are the most relevant factors for the increase in the wetland area on the TP from 2015 to 2019. In addition, the interactions among multiple variables strongly influence wetlands on the TP. Among them, when other geographic variables interact with the evaporation variable, its explanatory power on wetland distribution is significantly increased. Knowledge of wetland distribution determinants can help us understand the evolution of wetlands and the impacts of climate change on wetland variations. [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]

AbstractSpatial autoregressive (SAR) models are often used to explicitly account for the spatial dependence underlying geographic phenomena. However, traditional SAR models are specified using a single SAR coefficient, assuming constant spatial dependence over space. This assumption oversimplifies the situation where the true spatial autoregressive process varies in strength; the consequences of ignoring heterogeneous autocorrelation remain to be discussed. This study proposes a heterogeneous spatial autocorrelation model by extending the spatial lag model (SLM). The new model includes change point detection for identifying patterns of spatially varying autocorrelation strengths, a SAR coefficient matrix for representing heterogeneous spatial autocorrelation, and maximum likelihood estimation for determining multiple SAR coefficients. Monte Carlo simulations demonstrate that the proposed method is effective in modeling SAR processes with heterogeneous autocorrelation patterns, while traditional SLM inflates uncertainties in the regression coefficients when a heterogeneous autocorrelation structure is not accounted for. We further applied the new method to an empirical analysis of traffic crashes in the Greater Perth Area, Australia. The heterogeneous spatial autocorrelation model reduces model RMSE by 42% (compared with traditional SLM). Results from both simulation and empirical studies indicate that spatially varying autocorrelation strengths should be considered for SAR processes and relevant applications. [ABSTRACT FROM AUTHOR]

Due to the instantaneous field-of-view (IFOV) of the sensor and diversity of land cover types, some pixels, usually named mixed pixels, contain more than one land cover type. Soft classification can predict the portion of each land cover type in mixed pixels in the absence of spatial distribution. The spatial distribution information in mixed pixels can be solved by super resolution mapping (SRM). Typically, SRM involves two steps: soft class value estimation, which is similar to the image super resolution of image restoration, and land cover allocation. A new SRM approach utilizes a deep image prior (DIP) strategy combined with a super resolution convolutional neural network (SRCNN) to estimate fine resolution fraction images for each land cover type; then, a simple and efficient classifier is used to allocate subpixel land cover types under the constraint of the generated fine fraction images. The proposed approach can use prior information of input images to update network parameters and no longer require training data. Experiments on three different cases demonstrate that the subpixel classification accuracy of the proposed DIP-based SRM approach is significantly better than the three conventional SRM approaches and a transfer learning-based neural network SRM approach. In addition, the DIP-SRM approach performs very robustly about small-area objects within multiple land cover types and significantly reduces soft classification uncertainty. The results of this paper provide an extension for utilizing SRCNN to address SRM issues in hyperspectral images. [ABSTRACT FROM AUTHOR]

Urban forms reflect spatial structures of cities, which have been consciously and dramatically changing in China. Fast urbanisation may lead to similar urban forms due to similar habits and strategies of city planning. However, whether urban forms in China are identical or significantly different has not been empirically investigated. In this paper, urban forms are investigated based on two spatial units: city and block. The boundaries of natural cities in terms of the density of human settlements and activities are delineated with the concept of ‘redefined city’ using points of interests (POIs), and blocks are determined by road networks. Urban forms are characterised by city-block two-level spatial morphologies. Further, redefined cities are classified into four hierarchies to examine the effects of different city development stages on urban forms. The spatial morphology is explained by urbanisation variables to understand the effects. Results show that the urban forms are spatially clustered from the perspective of city-block two-level morphologies. Urban forms tend to be similar within the same hierarchies, but significantly varied among different hierarchies, which is closely related to the development stages. Additionally, the spatial dimensional indicators of urbanisation could explain 41% of the spatial morphology of redefined cities. [ABSTRACT FROM AUTHOR]

The rational function model (RFM) is widely applied to orthorectification of aerial and satellite imagery. This article proposes a newmethod named Ortho-WTLS to solve the RFM in remote-sensing imagery orthorectification. Based on a weighted total least squares (WTLS) estimator, the proposed method allows one to handle coordinates of ground control points (GCPs) that contain errors and are of unequal accuracies. This situation occurs, e.g. if GCPs are automatically selected. In the proposed model, first, the relationship of two linearization methods for an RFM with errors contained in GCPs is investigated and results in a hybrid linearization. Next, based on WTLS, RFM coefficients are estimated with an iterative computation function. Finally, the performance of the Ortho-WTLS method thus obtained is investigated using simulated images and remotely sensed images by collecting GCPs with varying errors. Experimental results show that the Ortho-WTLS method achieves a more robust estimation of model parameters and a higher orthorectification accuracy when compared with standard LS-based RFM estimation. We conclude that the quality of GCPs has a large impact on the accuracy and that an increasing number of low-precision GCPsmay lead to a decrease in orthorectification quality. [ABSTRACT FROM AUTHOR]