Flexible Spatial Model Research Articles

Generalized sinh-Gaussian random fields

The aim of this contribution is to propose new flexible spatial models based on a class of generalized sinh transformations. Our proposal greatly extends the Gaussian random field mainly in terms of asymmetry, heavy tail behavior, and bimodality. We demonstrate that we obtain a valid random field. We ensure that it is mean square continuous. We derive explicit expressions for the moments, the covariance function, the skewness, and the kurtosis of the random fields. In comparison with the available skew-Gaussian models, the proposed models could capture a greater amount of skewness and also accommodate clustered spatial outliers. The proposed models are computationally very tractable within the Bayesian framework here adopted. They are compared with the Gaussian and skew-Gaussian spatial models through simulation studies and an application to the spatial prediction of weekly rainfall near Darwin, Australia. The result suggests that the predictive performance in terms of different criteria under our method tends to be smaller than those obtained from the competing ones.

Computer modeling and software research of car and engine parts

Problem. The development of automotive technology for various purposes and the improvement of existing car models, requires a fast and flexible design process. Spatial models of details and nodes are the starting points for design, and the necessary design documentation is performed on their basis. When manufacturing parts on CNC machines, it is necessary to quickly obtain a control program that will increase the accuracy of the product by ensuring the optimal trajectory of the mutual movement of the part and the tool. Therefore, the creation of a comprehensive methodology for the design of car parts, their basic inspection and obtaining design documentation is an important technical task. Goal. The main goal of the work is to determine the rational sequence and basic principles of computer-aided design, research and manufacturing of car and engine parts, and the development of mathematical spatial models of surfaces in order to optimize control programs for CNC machines. Methodology. The approaches adopted in the work for solving the set goal are based on general design principles. The methods of conducting static and dynamic calculations, as well as spatial mathematical modeling of the processes of manufacturing parts were also used. Results. A comprehensive methodology for designing parts of engines and cars has been developed. The main principles of creating spatial models have been determined in order to achieve their flexibility and simple editing. Methods of automating the development of drawings and design documentation are described. The software options for the primary verification of static strength and frequency analysis are considered. A calculation program has been developed for constructing transient and amplitude-phase-frequency characteristics. The mathematical spatial modeling of typical surfaces of the camshaft is provided with the aim of further research and optimization of the development of a control program for processing on a CNC machine tool. Originality. The defined basic principles of designing parts of engines and cars provide an opportunity to create a flexible spatial model and more fully automate the process of drawing up technical documentation. The developed mathematical spatial models of the supporting and working surfaces of the camshaft make it possible to write a control program with the determination of the optimal trajectory of the mutual movement of the part and the tool. Practical value. The obtained results can be recommended when designing car parts and assemblies.

Estimating the abundance of a group‐living species using multi‐latent spatial models

AbstractStatistical models use observations of animals to make inferences about the abundance and distribution of species. However, the spatial distribution of animals is a complex function of many factors, including landscape and environmental features, and intra‐ and interspecific interactions. Modelling approaches often have to make significant simplifying assumptions about these factors, which can result in poor model performance and inaccurate predictions.Here, we explore the implications of complex spatial structure for modelling the abundance of the Serengeti wildebeest, a gregarious migratory species. The social behaviour of wildebeest leads to a highly aggregated distribution, and we examine the consequences of omitting this spatial complexity when modelling species abundance. To account for this distribution, we introduce a multi‐latent framework that uses two random fields to capture the clustered distribution of wildebeest.Our results show that simplifying assumptions that are often made in spatial models can dramatically impair performance. However, by allowing for mixtures of spatial models accurate predictions can be made. Furthermore, there can be a non‐monotonic relationship between model complexity and model performance; complex, flexible models that rely on unfounded assumptions can potentially make highly inaccurate predictions, whereas simpler more traditional approaches involve fewer assumptions and are less sensitive to these issues.We demonstrate how to develop flexible spatial models that can accommodate the complex processes driving animal distributions. Our findings highlight the importance of robust model checking protocols, and we illustrate how realistic assumptions can be incorporated into models using random fields.

Hierarchical Transformed Scale Mixtures for Flexible Modeling of Spatial Extremes on Datasets With Many Locations

–Flexible spatial models that allow transitions between tail dependence classes have recently appeared in the literature. However, inference for these models is computationally prohibitive, even in moderate dimensions, due to the necessity of repeatedly evaluating the multivariate Gaussian distribution function. In this work, we attempt to achieve truly high-dimensional inference for extremes of spatial processes, while retaining the desirable flexibility in the tail dependence structure, by modifying an established class of models based on scale mixtures Gaussian processes. We show that the desired extremal dependence properties from the original models are preserved under the modification, and demonstrate that the corresponding Bayesian hierarchical model does not involve the expensive computation of the multivariate Gaussian distribution function. We fit our model to exceedances of a high threshold, and perform coverage analyses and cross-model checks to validate its ability to capture different types of tail characteristics. We use a standard adaptive Metropolis algorithm for model fitting, and further accelerate the computation via parallelization and Rcpp. Lastly, we apply the model to a dataset of a fire threat index on the Great Plains region of the United States, which is vulnerable to massively destructive wildfires. We find that the joint tail of the fire threat index exhibits a decaying dependence structure that cannot be captured by limiting extreme value models. Supplementary materials for this article are available online.

A Nonstationary Geostatistical Framework for Soil Moisture Prediction in the Presence of Surface Heterogeneity

AbstractSoil moisture is spatially variable due to complex interactions between geologic, topographic, vegetation, and atmospheric variables. Correct representation of subgrid soil moisture variability is crucial in improving land surface modeling schemes and remote sensing retrievals. In addition to the mean structure, the variance and correlation of soil moisture are affected by the underlying land surface heterogeneity. This often violates the underlying assumption of stationarity/isotropy made by classical geostatistical models. The present study proposes a geostatistical framework to predict and upscale soil moisture in a nonstationary setting using a flexible spatial model whose variance/correlation structure varies with changing land surface characteristics. The proposed framework is applied to model soil moisture distribution using in situ data in the Red River watershed in Southern Manitoba, Canada. It is seen that both the variance and correlation structure exhibits spatial nonstationarity for the given surface heterogeneity driven primarily by vegetation and soil texture. At the beginning of the crop season, soil texture plays a critical role in the drying cycle by decreasing variance and increasing correlation as the soil becomes drier. Once the crops begin to mature, vegetation becomes the dominant driver, promoting spatial correlation and reducing SM variance. We upscale our point scale soil moisture predictions to the airborne extent (∼1.5 km) and find that the upscaled soil moisture agrees well with the observed airborne data with root‐mean‐square error values ranging from 0.04 to 0.08 (v/v). The proposed framework can be used to predict and upscale soil moisture in heterogeneous environments.

Combining satellite data and appropriate objective functions for improved spatial pattern performance of a distributed hydrologic model

Abstract. Satellite-based earth observations offer great opportunities to improve spatial model predictions by means of spatial-pattern-oriented model evaluations. In this study, observed spatial patterns of actual evapotranspiration (AET) are utilised for spatial model calibration tailored to target the pattern performance of the model. The proposed calibration framework combines temporally aggregated observed spatial patterns with a new spatial performance metric and a flexible spatial parameterisation scheme. The mesoscale hydrologic model (mHM) is used to simulate streamflow and AET and has been selected due to its soil parameter distribution approach based on pedo-transfer functions and the build in multi-scale parameter regionalisation. In addition two new spatial parameter distribution options have been incorporated in the model in order to increase the flexibility of root fraction coefficient and potential evapotranspiration correction parameterisations, based on soil type and vegetation density. These parameterisations are utilised as they are most relevant for simulated AET patterns from the hydrologic model. Due to the fundamental challenges encountered when evaluating spatial pattern performance using standard metrics, we developed a simple but highly discriminative spatial metric, i.e. one comprised of three easily interpretable components measuring co-location, variation and distribution of the spatial data. The study shows that with flexible spatial model parameterisation used in combination with the appropriate objective functions, the simulated spatial patterns of actual evapotranspiration become substantially more similar to the satellite-based estimates. Overall 26 parameters are identified for calibration through a sequential screening approach based on a combination of streamflow and spatial pattern metrics. The robustness of the calibrations is tested using an ensemble of nine calibrations based on different seed numbers using the shuffled complex evolution optimiser. The calibration results reveal a limited trade-off between streamflow dynamics and spatial patterns illustrating the benefit of combining separate observation types and objective functions. At the same time, the simulated spatial patterns of AET significantly improved when an objective function based on observed AET patterns and a novel spatial performance metric compared to traditional streamflow-only calibration were included. Since the overall water balance is usually a crucial goal in hydrologic modelling, spatial-pattern-oriented optimisation should always be accompanied by traditional discharge measurements. In such a multi-objective framework, the current study promotes the use of a novel bias-insensitive spatial pattern metric, which exploits the key information contained in the observed patterns while allowing the water balance to be informed by discharge observations.

The role of visual and spatial working memory in forming mental models derived from survey and route descriptions.

This study examines the involvement of spatial and visual working memory (WM) in the construction of flexible spatial models derived from survey and route descriptions. Sixty young adults listened to environment descriptions, 30 from a survey perspective and the other 30 from a route perspective, while they performed spatial (spatial tapping [ST]) and visual (dynamic visual noise [DVN]) secondary tasks - believed to overload the spatial and visual working memory (WM) components, respectively - or no secondary task (control, C). Their mental representations of the environment were tested by free recall and a verification test with both route and survey statements. Results showed that, for both recall tasks, accuracy was worse in the ST than in the C or DVN conditions. In the verification test, the effect of both ST and DVN was a decreasing accuracy for sentences testing spatial relations from the opposite perspective to the one learnt than if the perspective was the same; only ST had a stronger interference effect than the C condition for sentences from the opposite perspective from the one learnt. Overall, these findings indicate that both visual and spatial WM, and especially the latter, are involved in the construction of perspective-flexible spatial models.

On the effect of preferential sampling in spatial prediction

The choice of the sampling locations in a spatial network is often guided by practical demands. In particular, many locations are preferentially chosen to capture high values of a response, for example, air pollution levels in environmental monitoring. Then, model estimation and prediction of the exposure surface become biased due to the selective sampling. Since prediction is often the main utility of the modeling, we suggest that the effect of preferential sampling lies more importantly in the resulting predictive surface than in parameter estimation. Our contribution is to offer a direct simulation-based approach to assessing the effects of preferential sampling. We compare two predictive surfaces over the study region, one originating from the notion of an 'operating' intensity driving the selection of monitoring sites, the other under complete spatial randomness. We can consider a range of response models. They may reflect the operating intensity, introduce alternative informative covariates, or just propose a flexible spatial model. Then, we can generate data under the given model. Upon fitting the model and interpolating (kriging), we will obtain two predictive surfaces to compare. It is important to note that we need suitable metrics to compare the surfaces and that the predictive surfaces are random, so we need to make expected comparisons.

Flexible Spatial Models for Kriging and Cokriging Using Moving Averages and the Fast Fourier Transform (FFT)

Models for spatial autocorrelation and cross-correlation depend on the distance and direction separating two locations, and are constrained so that for all possible sets of locations, the covariance matrices implied from the models remain nonnegative-definite. Based on spatial correlation, optimal linear predictors can be constructed that yield complete maps of spatial fields from incomplete and noisy spatial data. This methodology is called kriging if the data are of only one variable type, and it is called cokriging if it is of two or more variable types. Historically, to satisfy the nonnegative-definite condition, cokriging has used coregionalization models for cross-variograms, even though this class of models is not very flexible. Recent research has shown that moving-average functions may be used to generate a large class of valid, flexible variogram models, and that they can also be used to generate valid cross-variograms that are compatible with component variograms. There are several problems with the moving-average approach, including large numbers of parameters and difficulties with integration. This article shows how the fast Fourier Transform (FFT) solves these problems. The flexible moving-average function that we consider is composed of many small rectangles, which eliminates the integration problem. The FFT allows us to compute the cross-variogram on a set of discrete lags; we show how to interpolate the cross-variogram for any continuous lag, which allows us to fit flexible models using standard minimization routines. Simulation examples are given to demonstrate the methods.