A multiple spatial scales water use simulation for capturing its spatial heterogeneity through cellular automata model

Modeling urban growth using spatially heterogeneous cellular automata models: Comparison of spatial lag, spatial error and GWR

Cellular automata (CA) is a bottom-up self-organizing modeling tool for simulating contagion-like phenomena such as complex land-use change and urban growth. It is not known how CA modeling responds to changes in spatial observation scale when a larger-scale study area is partitioned into subregions, each with its own CA model. We examined the impact of changing observation scale on a model of urban growth at UA-Shanghai (a region within a one-hour high-speed rail distance from Shanghai) using particle swarm optimization-based CA (PSO-CA) modeling. Our models were calibrated with data from 1995 to 2005 and validated with data from 2005 to 2015 on spatial scales: (1) Regional-scale: UA-Shanghai was considered as a single study area; (2) meso-scale: UA-Shanghai was partitioned into three terrain-based subregions; and (3) city-scale: UA-Shanghai was partitioned into six cities based on administrative boundaries. All three scales yielded simulations averaging about 87% accuracy with an average Figure-of-Merit (FOM) of about 32%. Overall accuracy was reduced from calibration and validation. The regional-scale model yielded less accurate simulations as compared with the meso- and city-scales for both calibration and validation. Simulation success in different subregions is independent at the city-scale, when compared with regional- and meso-scale. Our observations indicate that observation scale is important in CA modeling and that smaller scales probably lead to more accurate simulations. We suggest smaller partitions, smaller observation scales and the construction of one CA model for each subregion to better reflect spatial variability and to produce more reliable simulations. This approach should be especially useful for large-scale areas such as huge urban agglomerations and entire nations.

A size-adaptive strategy to characterize spatially heterogeneous neighborhood effects in cellular automata simulation of urban growth

Natural disturbances affect spatial and temporal heterogeneity in plant communities, but effects vary depending on type of disturbance and scale of analysis. In this study, we examined the effects of fire frequency (1-, 4-, and 20-yr intervals) and grazing by bison on spatial and temporal heterogeneity in species composition in tallgrass prairie plant communities. Compositional heterogeneity was estimated at 10-, 50-, and 200-m2 scales. For each measurement scale, we used the average Euclidean Distance (ED) between samples within a year (2000) to measure spatial heterogeneity and between all time steps (1993-2000) for each sample to measure temporal heterogeneity. The main effects of fire and grazing were scale independent. Spatial and temporal heterogeneity were lowest on annually burned sites and highest on infrequently burned (20-yr) sites at all scales. Grazing reduced spatial heterogeneity and increased temporal heterogeneity at all scales. The rate of community change over time decreased as fire frequency increased at all scales, whereas grazing had no effect on rate of community change over time at any spatial scale. The interactive effects of fire and grazing on spatial and temporal heterogeneity differed with scale. At the 10-m2 scale, grazing increased spatial heterogeneity in annually burned grassland but decreased heterogeneity in less frequently burned areas. At the 50-m2 scale, grazing decreased spatial heterogeneity on 4-yr burns but had no effect at other fire frequencies. At the 10-m scale, grazing increased temporal heterogeneity only on 1- and 20-yr burn sites. Our results show that the individual effects of fire and grazing on spatial and temporal heterogeneity in mesic prairie are scale independent, but the interactive effects of these disturbances on community heterogeneity change with scale of measurement. These patterns reflect the homogenizing impact of fire at all spatial scales, and the different frequency, intensity, and scale of patch grazing by bison in frequently burned vs. infrequently burned areas.

Patterns of benthic community structure are driven by a range of biological and physical processes that act over multiple spatial and temporal scales. Settlement panels were deployed in relatively ‘pristine’ subtidal habitats off southwest Australia, to examine spatial variability in assemblage structure at multiple spatial scales, from centimetres to 100s of kilometres. Panel assemblages were harvested after 3, 9 and 14 months of maturation, to test the following hypotheses: (i) that the magnitude of variability at large spatial scales increases with assemblage development time, (ii) that variability at the smallest spatial scales is consistently high regardless of assemblage development time, and (iii) that patterns of spatio-temporal variability differ between taxa. No clear trends in the magnitude of variability at each spatial scale examined, in relation to assemblage development time, were recorded. Sessile assemblages were highly variable at all spatial scales examined, and variability at the smallest-spatial scale (cms) was consistently high. As predicted, the magnitude of variability at the largest spatial scales (i.e. between locations 100s of km apart) was lowest for immature assemblages, but overall patterns of large-scale variability did not alter predictably with maturation time. Subtidal sessile assemblages in southwest Australia, like elsewhere, are structured by a complex, interacting suite of biological and physical processes that vary in their relative importance throughout assemblage maturation. As such, understanding variability patterns is challenging, and requires greater appreciation of variability in physical processes across multiple spatial and temporal scales and improved knowledge of the life histories and population structures of key taxa.

Cellular automata (CA) models are used to analyze and simulate the global phenomenon of urban growth. However, these models are characterized by ignoring spatially heterogeneous transition rules and asynchronous evolving rates, which make it difficult to improve urban growth simulations. In this paper, a partitioned and asynchronous cellular automata (PACA) model was developed by implementing the spatial heterogeneity of both transition rules and evolving rates in urban growth simulations. After dividing the study area into several subregions by k-means and knn-cluster algorithms, a C5.0 decision tree algorithm was employed to identify the transition rules in each subregion. The evolving rates for cells in each regularly divided grid were calculated by the rate of changed cells. The proposed PACA model was implemented to simulate urban growth in Wuhan, a large city in central China. The results showed that PACA performed better than traditional CA models in both a cell-to-cell accuracy assessment and a shape dimension accuracy assessment. Figure of merit of PACA is 0.368 in this research, which is significantly higher than that of partitioned CA (0.327) and traditional CA (0.247). As for the shape dimension accuracy, PACA has a fractal dimension of 1.542, which is the closest to that of the actual land use (1.535). However, fractal dimension of traditional CA (1.548) is closer to that of the actual land use than that of partitioned CA (1.285). It indicates that partitioned transition rules play an important role in the cell-to-cell accuracy of CA models, whereas the combination of partitioned transition rules and asynchronous evolving rates results in improved cell-to-cell accuracy and shape dimension accuracy. Thus, implementing partitioned transition rules and asynchronous evolving rates yields better CA model performance in urban growth simulations due to its accordance with actual urban growth processes.

We developed a hybrid cellular automata (CA) modelling approach to explore the dynamics of a key predator–prey interaction in a marine system; our study is motivated by the quest for better understanding of the scale and heterogeneity-related effects on the arrowtooth flounder (Atheresthes stomias) and walleye pollock (Theragra chalcogramma) dynamics during the summer feeding season in the eastern Bering Sea (EBS), but can be readily extended to other systems. The spatially explicit and probabilistic CA model incorporates individual behaviours and strategies and local interactions among species, as well as spatial and temporal heterogeneity due to geographical and (or) environmental changes in the physical environment. The model is hybridized, with an individual-based model (IBM) approach for increasing its capacity and continuum and for balancing between computational efficiency and model validity, which makes it suitable for simulating predator–prey dynamics in a large, complex ecological environment. We focus on the functional and aggregative responses of predators to prey density at different spatial scales, the effects of individual behaviours, and the impacts of systematic heterogeneity. Simulations from the model with suitable parameter values share qualitatively similar features found in field observations, e.g., local aggregations around hydrographical features. Spatial heterogeneity is an important aspect of whether local-scale functional and aggregative responses reflect those operating over large, or global, scales.

Calibrating and assessing uncertainty in coastal numerical models

Despite the many models developed for phosphorus concentration prediction at differing spatial and temporal scales, there has been little effort to quantify uncertainty in their predictions. Model prediction uncertainty quantification is desirable, for informed decision-making in river-systems management. An uncertainty analysis of the process-based model, integrated catchment model of phosphorus (INCA-P), within the generalised likelihood uncertainty estimation (GLUE) framework is presented. The framework is applied to the Lugg catchment (1,077 km2), a River Wye tributary, on the England–Wales border. Daily discharge and monthly phosphorus (total reactive and total), for a limited number of reaches, are used to initially assess uncertainty and sensitivity of 44 model parameters, identified as being most important for discharge and phosphorus predictions. This study demonstrates that parameter homogeneity assumptions (spatial heterogeneity is treated as land use type fractional areas) can achieve higher model fits, than a previous expertly calibrated parameter set. The model is capable of reproducing the hydrology, but a threshold Nash-Sutcliffe co-efficient of determination (E or R 2) of 0.3 is not achieved when simulating observed total phosphorus (TP) data in the upland reaches or total reactive phosphorus (TRP) in any reach. Despite this, the model reproduces the general dynamics of TP and TRP, in point source dominated lower reaches. This paper discusses why this application of INCA-P fails to find any parameter sets, which simultaneously describe all observed data acceptably. The discussion focuses on uncertainty of readily available input data, and whether such process-based models should be used when there isn’t sufficient data to support the many parameters.

Sensitivity analysis in simulating oil slick using CA model

Landscape heterogeneity, namely the variation of a landscape property across space and time, can influence the distribution of a species and its abundance. Quantifying landscape heterogeneity is important for the management of semi‐natural areas through predicting species response to landscape changes, such as habitat fragmentation. In this paper, we tested whether the change in spatial heterogeneity of the vegetation cover due to farming expansion affected the distribution of the African elephant in the Tarangire‐Manyara ecosystem, northern Tanzania. Spatial heterogeneity (based on the normalized difference vegetation index) was characterized at multiple spatial scales using the wavelet transform and the intensity‐dominant scale method. Elephant distribution was estimated from time‐series aerial surveys using a kernel density function. The intensity, which relates to the contrast in vegetation cover, quantified the maximum variation in NDVI across multiple spatial scales, whereas the dominant scale, which represents the scale at which this maximum variation occurs, identified the dominant inter‐patches distance, i.e. the size of dominant landscape features. We related the dominant scale of spatial heterogeneity to the probability of elephant occurrence in order to identify: 1) the scale that maximizes elephant occurrence, and 2) its change between 1988 and 2001. Neither the dominant scale and intensity of spatial heterogeneity, nor the probability of the elephant occurrence changed significantly between 1988 and 2001. The spatial scale maximizing elephant occurrence remained constant at 7000 to 8000 m during each wet season. Compared to the findings of a recent, similar study in Zimbabwe, our results suggest that the change in the dominant scale was relatively small in Tarangire‐Manyara ecosystem and well within the critical threshold for elephant persistence. The method is a useful tool for monitoring ecosystems and their properties.

Accurate prediction of crop phenological stage is essential for evaluating management strategies and assessing crop responses to environmental changes. In this work, we modified Non-dominated Sorting Genetic Algorithm with the core algorithm of PEST (MNSGA-II) and compared it to two other algorithms of Generalized Likelihood Uncertainty Estimation (GLUE) and Differential Evolution (DE) to calibrate the cultivar-specific parameters (CSPs) of CROPGRO-Soybean phenological model (CSPM) so as to exactly simulate the soybean phenology using the multi-source datasets of multi-site, multi-year, and multi-cultivar. Independent experimental data are used to validate the CSPM with the optimized parameters. The root means square error (RMSE), the mean absolute error (MAE), and coefficient of determination (R2) are used to evaluate the effects of different algorithms on calibrating the CSPs. The RMSEs (MAEs, R2) between all observed data and simulated data based on MNSGA-II, GLUE and DE are 4.28 (3.53, 0.9445) days, 4.76 (4.05, 0.9438) days and 5.17 (4.85, 0.9336) days, respectively, with little difference among the three algorithms. MNSGA-II has a certain advantage in calibration effect, and GLUE is the most stable during the repetition of each calibration. The MNSGA-II can be considered as a relatively ideal algorithm for estimating the crop model parameter. Which algorithm should be selected to calibrate the parameters of crop model according to the actual requirements. These results provide a reference to choose the suitable algorithm for estimating crop model parameter.

A key component of cellular automata (CA) models is the transition rules that determine the transformation of cells at each iteration. However, most previous studies use a single set of transition rules across the entire study region, and therefore do not fully account for spatial heterogeneity. In this research, a vector CA model has been implemented that calibrates transition rules by taking the entire study region and partitioned sub‐regions into consideration. The changes in residential areas were modelled for the city of Ipswich, Queensland, Australia, from 1999 to 2016. The results confirm that the spatially partitioned rules can generate more accurate and stable results compared to calibrated rules using the whole study area, with an increase of mean producer's spatial accuracy of 72.07 and 75.59% in two sub‐regions (2‐2 and 2‐3). The implementation of CA models with partitioned transition rules enables a better understanding of spatial heterogeneity in land use change.

Questions: What is the observed relationship between plant species diversity and spatial environmental heterogeneity? Does the relationship scale predictably with sample plot size? What are the relative contributions to diversity patterns of variables linked to productivity or available energy compared to those corresponding to spatial heterogeneity?Methods: Observational and experimental studies that quantified relationships between plant species richness and within‐sample spatial environmental heterogeneity were reviewed. Effect size in experimental studies was quantified as the standardized mean difference between control (homogeneous) and heterogeneous treatments. For observational studies, effect sizes in individual studies were examined graphically across a gradient of plot size (focal scale). Relative contributions of variables representing spatial heterogeneity were compared to those representing available energy using a response ratio.Results: Forty‐one observational and 11 experimental studies quantified plant species diversity and spatial environmental heterogeneity. Observational studies reported positive species diversity‐spatial heterogeneity correlations at all points across a plot size gradient from ∼1.0 × 10−1 to ∼1.0 × 1011 m2, although many studies reported spatial heterogeneity variables with no significant relationships to species diversity. The cross‐study effect size in experimental studies was not significantly different from zero. Available energy variables explained consistently more of the variance in species richness than spatial heterogeneity variables, especially at the smallest and largest plot sizes.Main conclusions: Species diversity was not related to spatial heterogeneity in a way predictable by plot size. Positive heterogeneity‐diversity relationships were common, confirming the importance of niche differentiation in species diversity patterns, but future studies examining a range of spatial scales in the same system are required to determine the role of dispersal and available energy in these patterns.

Most experimental work is done at small spatial scales due to scientific, logistical, and financial constraints. Unfortunately, ecologists (and society) require answers to problems about dynamics that arise at larger scales than often can be studied experimentally. Thus, it is imperative to develop empirical and theoretical methods for scaling up the results of small-scale studies to predictions at larger scales. These methods should also identify the limits to scaling up: i.e., clarify when results from small-scale experiments cannot be extrapolated to larger scales. In this special topic, we identify three important hurdles associated with scaling up in population biology and methods of addressing these problems: (1) increased spatial heterogeneity with increasing spatial scale, (2) changes to species pools and species identities with changes in spatial scale, and (3) behaviors and trait-mediated indirect effects that emerge at larger scales, but are absent in small, relatively homogeneous experimental settings. Larger spatial scales will usually incorporate greater abiotic and biotic heterogeneity than small scales, including greater genetic or phenotypic variation among individuals. Simple extrapolations that assume linear scaling relationships will not provide good predictions when there are both spatial heterogeneities and nonlinear interactions among species or between species and abiotic resources. Thus it may be troubling that spatial heterogeneity is ubiquitous and many ecological interactions are known to be non-linear. Fortunately, if both the degree of nonlinearity and the amount of spatial heterogeneity at different scales were quantified, available methods may allow integrating large-scale observational studies with small-scale experiments to account for the influence of heterogeneities on the outcome of nonlinear interactions. Alternatively, models or experiments can be used to directly examine the effects of changing levels of variance and to determine the importance of different sources of heterogeneity in different systems. Three of the contributions illustrate ways to account for effects of increasing heterogeneity and non-linearities. Melbourne and Chesson use scale-transition theory to develop an expression for regional population dynamics that accounts for non-linear local density dependence and spatial heterogeneity in resources. Incorporating spatial variances and covariances, they predict the regional responses of caddisfly populations to riffle disturbance regimes. Inouye describes data collected at two nested spatial scales on the variances and covariances of distributions of competitors in a patchy and ephemeral habitat. These data are used to parameterize a model for the regional population dynamics of these competitors that includes spatial heterogeneity at both spatial scales. Helms and Hunter show that using observed spatial variation in local population growth parameters can produce regional population dynamics that are different from those obtained using average parameter values. A second hurdle in scaling up is that at larger scales, one is likely to encounter additional species or habitats within the domain of the study. In moving from studying a single species or pair of species interacting within a microcosm to studying the same species and interaction embedded in a landscape, the indirect effects of additional species may swamp whatever direct effects were measured in the microcosm. To address these problems, we need to include information on how species pools change as the spatial scales of studies increases. Srivastava addresses the relative roles of local biotic interactions and regional abiotic influences in aquatic treehole communities across a range of spatial scales and levels of diversity. Although local treehole communities are similarly structured around the world, communities Communicated by Craig W. Osenberg