To explore the relationship between reflectivity and luminance, data were averaged in both study periods to the geography of the 100m2 radar pixel, with the results plotted in Figure 8. The first statistical test run on the joined data was an ordinary least squares (OLS) regression, relating the independent variable of the log of luminance to the dependent variable reflectivity. The OLS regression for fall and spring yielded adjusted R2 values of 0.0008 and 0.004 respectively, meaning that either season's model explains little of the variation of the data. The correlation coefficients for fall and spring are -0.011 and -0.02, along with a p-values of 0.21 and 0.02, indicating that for either model there is neither a particularly positive nor negative relationship between to the two variables. This finding was also found to be statistically insignificant in the fall, assuming a significance of p < 0.05.
However, because the use of linear regression relies on the assumption that the variables exhibit no spatial autocorrelation, a Global Moran's I was run on both reflectivity and building lumination to determine the extent of autocorrelation (Poole, 1971). For reflectivity, a Moran's I of 0.74 and 0.72 was found for Fall and Spring, along with a Moran's I of 0.21 and 0.19 for logged lumination. With p-values all below 0.01 for these spatial autocorrelation tests, both lumination and especially reflectivity were found to exhibit spatial autocorrelation. These findings mean local variation will need to be accounted for in a regression, so a spatial lag model was introduced, creating local regressions of reflectivity against lumination for each point based on a weights matrix of 3rd order and lower queen contiguity. The spatial lag model returned R-squared values of 0.8 and 0.79 for Fall and Spring, correlation coefficients of 0.001 and -0.008, and p-values of 0.6 and 0.03. Based on these results, the spatial lag model shows that there is high local variation between reflectivity and lumination, but in aggregate there is neither a positive or negative relationship between the two, so a closer investigation into the temporal components of the data will be needed to better understand the relationship.
Time Series Analysis
To first get a sense of these variables over time, dBZ is plotted over time along with building lumination estimates. Figure 9 shows a trend of average brightness decreasing overnight, while reflectivity increases later in the night and into the morning, suggesting night time migratory trends. When compared with Audubon collected data in Figure 7, there do not appear to be similar patterns in reflectivity and dead birds found, although given the limited spatial scope of the bird walks, this relationship remains inconclusive.