Jonathan B. Thayn

Accounting for Spatial Autocorrelation in Linear Regression Models Using Spatial Filtering with Eigenvectors

Ordinary least squares linear regression models are frequently used to analyze and model spatial phenomena. These models are useful and easily interpreted, and the assumptions, strengths, and weaknesses of these models are well studied and understood. Regression models applied to spatial data frequently contain spatially autocorrelated residuals, however, indicating a misspecification error. This problem is limited to spatial data (although similar problems occur with time series data), so it has received less attention than more frequently encountered problems. A method called spatial filtering with eigenvectors has been proposed to account for this problem. We apply this method to ten real-world data sets and a series of simulated data sets to begin to understand the conditions under which the method can be most usefully applied. We find that spatial filtering with eigenvectors reduces spatial misspecification errors, increases the strength of the model fit, frequently increases the normality of model residuals, and can increase the homoscedasticity of model residuals. We provide a sample script showing how to apply the method in the R statistical environment. Spatial filtering with eigenvectors is a powerful geographic method that should be applied to many regression models that use geographic data.

Julian dates and introduced temporal error in remote sensing vegetation phenology studies

Remote‐sensing‐based vegetation phenology studies are commonly used to study agriculture, forestry, species distributions, and the effect of climate change on vegetation. These studies utilize annual time series of NDVI data to characterize seasonal growth patterns. The NDVI data for most of these studies have been pre‐processed using a maximum value compositing process to minimize contamination from clouds. A side effect of this process is a degradation of temporal data, since NDVI values are assigned to multiday periods rather than the specific date of image capture. In this study, the compositing process is examined to determine if there is a reliable pattern to pixel selection. Also, the magnitude of the introduced error is estimated by comparing vegetation phenology metrics calculated using the temporally degraded data and metrics calculated using the actual date of each pixel. The root mean square errors between these datasets ranged from 9.4 to 10.9 days, much larger than is acceptable for most phenology studies. We conclude that vegetation phenology studies must make use of accurate temporal data to characterize changes in vegetation seasonality.

Assessing vegetation cover on the date of satellite-derived start of spring

Time series of satellite imagery are commonly used to study and model phenology. To use these models, their results must be compared with time series of areal field data, and vegetation condition must be assessed relative to model predictions. Field data and Moderate Resolution Imaging Spectroradiometer (MODIS) data for corn fields in Illinois, USA, were collected throughout the growing season, including vegetation cover fraction (VCF) derived from kite aerial photography (KAP). The mean height of corn on the estimated start of spring (SOS) date was just over 2 cm and the mean VCF on SOS was nearly 10%, indicating that satellite models of phenology lag behind field-based measures of phenology like crop emergence. The relationships between MODIS Normalized Difference Vegetation Index (NDVI) and both KAP NDVI (coefficient of determination (R 2) = 0.918, p < 0.000) and KAP VCF (R 2 = 0.920, p < 0.000) were strong, highlighting the importance of areal field data in phenology studies.

Locating Amazonian Dark Earths (ADE) using vegetation vigour as a surrogate for soil type

Amazonian Dark Earths (ADE) are patches of archaeological soils scattered throughout the Amazon Basin. These soils are a mixture of charcoal, nutrient vegetable matter and the underlying Oxisol soil. ADE are extremely fertile in comparison to the surrounding soils and they are sought after by local residents for agricultural food production. Research is being conducted to learn how ADE were created and to explore the possibility of replicating them to sequester carbon and to reclaim depleted soils in the Amazon Basin. A factor limiting the success of this research is our current inability to locate ADE sites hidden beneath the tropical forest canopy. We use annual time-series Moderate Resolution Imaging Spectroradiometer (MODIS) Enhanced Vegetation Index (EVI) satellite imagery from 2001 to 2005 and harmonic analysis (HA) to examine the spectral differences between forest vegetation growing on ADE and forest vegetation growing on non-ADE. There is a significant difference between the reflectances of vegetation growing on the two soil types, due primarily to lower EVI values over ADE during the dry season (multiple analysis of variance (MANOVA) p-value = 0.040). A logistic model is used to create a predictive map of ADE location.

Satellite-based metrics of rangeland complexity and cattle stocking rates in Kansas

Abstract We examine relationships between landscape scale measurements of rangeland complexity and cattle stocking rates in Kansas. Rangeland complexity was characterized using Advanced Very High Resolution Radiometer (AVHRR) satellite imagery and the USGS National Land Cover Dataset (NLCD). Satellite Normalized Difference Vegetation Index (NDVI) values were summed over the 2002 growing-season and then summarized by county. FRAGSTATS spatial pattern analysis software was used to derive 43 metrics of landscape complexity for each county. The metrics used were of two types: spatial pattern metrics, which quantify the shape and distribution of rangeland patches in each county; and spectral diversity metrics, which take advantage of variation in NDVI values to quantify complexity within each rangeland patch. A principle components analysis step-wise regression model revealed a strong correlation between rangeland complexity and cattle stocking rates (r2 = 0.53, p =0.000). This suggests that, from a rangeland grazing perspective, intact blocks of rangeland are more desirable than fragmented rangelands. The model indicates that spatial pattern metrics are better predictors of rangeland stocking rates than spectral diversity metrics. This study also demonstrates the utility of satellite remote sensing for monitoring rangeland condition at a landscape scale.

GEOGRAPHIC INFORMATION SYSTEM MODELING OF DE SOTO'S ROUTE FROM JOARA TO CHIAHA: ARCHAEOLOGY AND ANTHROPOLOGY OF SOUTHEASTERN ROAD NETWORKS IN THE SIXTEENTH CENTURY

Abstract This research revisits the question of the most likely paths traveled during the 1540 entrada of Hernando de Soto and colonizing efforts of Juan Pardo about 20 years later by utilizing the spatial modeling method of geographic information system (GIS) analysis to evaluate the favorability of different paths and place them within the context of recent archaeological and ethnohistoric research. Analysis results make the larger anthropological point that GIS route modeling should explicitly take into account the size of the party traveling. Routes for small parties are not the same as optimal routes for large armies such as de Soto’s, which included hundreds of people, pieces of equipment, and livestock. The GIS-modeled routes correlate with the distribution of contact-period archaeological sites and attested eighteenth-century routes. More accurate estimation of Spanish routes allows us to better model the Native American social, economic, and political nexus of this period, showing that the residents in far eastern Tennessee were probably part of a dynamic borderlands between the chiefdom of Coosa to the west and the ancestral Cherokee heartland to the east. This anthropological refinement in GIS modeling will be useful in investigating ancient paths of interaction in many parts of the world.

The effects of spatial patterns of neighborhood risk factors on adverse birth outcomes

Abstract Neighborhood environments play an important role in shaping health. But how do the conditions of surrounding neighborhoods affect health? Specifically, how do the spatial patterns of neighborhood characteristics shape birth outcomes? Using Census and health data from Wyandotte County, Kansas, we analyze the relationship between spatial patterns of socio-demographic risk factors and incidence of low weight births in neighboring block groups. Using spatial filtering with eigenvectors we identify significant socio-demographic patterns and use them as predictors of low-weight births in a regression model. We identify several patterns that predict significant variability in birth outcomes and find that while some factors, like unemployment, have strong internal neighborhood effects on birth weight they may not have strong external neighborhood effects. We argue spatial filtering methods may improve our understanding of persistent inequalities in health by helping to identify the differential effects of proximate social conditions and spatial interdependencies.

Locating Amazonian Dark Earths (ADE) Using Satellite Remote Sensing – A Possible Approach

Amazonian Dark Earths (ADE) are the result of preColumbian humans’ occupation of the Amazon Basin and are related to the need for fertile soils for growing crops (e.g. Glaser and Woods 2004). ADE soils contain highly elevated levels of organic matter, mostly in the form of very slowly decomposing charcoal, which retains water and nutrients, and makes ADE some of the most fertile soils in the world (Kern et al. 2003; Lehmann et al. 2003). When productivity of plants grown on ADE soil was contrasted with typical Amazonian soils, Major et al. (2005) found that maize yields were as much as 63 times greater, weed cover was 45 times greater, and plant species diversity was up to 11 times greater than for adjacent typical Amazonian soils. ADE soils contain up to 70 times more SOM than typical Amazonian soils (Mann 2002). Woods and McCann (1999) have shown that nutrient transfers from outside of ADE sites are necessary to explain current nutrient levels in ADE soils, suggesting that the formation of these soils ultimately became an intentional effort on the part of prehistoric Amerindian populations to improve the quality of their farmland. These nutrient sources may have been plant and animal food wastes, fish bones and other un-used fish matter, or human excrement, as well as a host plant materials used for fuel and construction. The presence of algae in ADE from c.1150 BP and later suggests that silt from riverbanks was incorporated into the ADE soils in at least one location (Mora et al. 1991). In addition to opening a window to the past, ADE soils may hold a key to the future. The most readily observed characteristic of ADE soils is their high concentration of charcoal, which gives them the distinctive dark brown-to-black coloration. Glaser et al. (2001) found 64 times more charcoal in ADE soils than in the surrounding soils. To meet the challenges of possible global climate change caused by greenhouse gases, atmospheric carbon concentrations must be reduced. Vegetation actively withdraws carbon from the atmosphere and stores it as organic matter. Biochar is created when organic matter is heated without oxygen and it contains twice the carbon content of ordinary biomass (Lehmann 2007). Biochar is much more resistant to decay and can store carbon for centennial timescales (Lehmann et al. 2006). The addition of biochar to the soil was part of the creation

Refining Hernando de Soto's Route Using Electric Circuit Theory and CircuitScape

A least-cost path (LCP) analysis and a circuit theory analysis were used to estimate the path followed by Hernando de Soto as he crossed the Appalachian Mountains between Tennessee and North Carolina in 1540. The analyses were performed on the slope of the terrain and on a function of the slope that estimates hiking speed. The analyses were performed on data sets with 90-m and 180-m spatial resolutions. Three potential routes were found and compared. The most novel element of the work was the use of CircuitScape software, which returned the likelihood that each cell in the raster data was a part of de Sotos route. This clearly illuminated areas where the estimated routes were more constrained and areas where de Soto would have been free to take alternate paths without increasing travel time. The two analysis methods, LCP and circuit theory, corroborate one another and provide insight into de Sotos journey.

Monitoring fire recovery in a tallgrass prairie using a weighted disturbance index

The recently proposed Disturbance Index (DI) has been repeatedly shown to accurately detect stand-replacing disturbances. We assess the utility of the DI for monitoring more subtle disturbances using a weighting scheme that increases its sensitivity to specific disturbances. The weights were derived separately for each Landsat image in a dense time-series using linear discriminate analysis based on training data collected during a year of recovery after controlled prairie burns in the Tallgrass Prairie National Preserve in Kansas. The weights drew closer to zero as recovery progressed and the spectral differences between unburned and recovering sites diminished. The initial classification accuracy was very high, nearly 94%, but the accuracy decreased as recovery advanced. By about 100 days after the initial fire, the classification accuracy was not statistically better than what might be achieved by chance. The results clearly highlight the value of statistically fitting the DI to specific disturbances and local conditions using derived weights.