## 2 Materials and Methods
### Analysis of Stream Burial Patterns across the PRB, in Relation to Slope and Catchment Area  
The completed stream burial probability layer was imported into a GIS [41], and stream burial predictions were evaluated in the context of urbanization intensity (total impervious surface area in the 8-pixel neighborhood), catchment area (FAC; flow accumulation area), and local topographic slope. Counties and independent cities, the jurisdictional level where most development decisions are made, were used to represent the largest analysis units. Urban development across the PRB largely began in and around Washington, DC, and has since radiated outward in concentric rings from the urban center [42]. A series of 16 counties and independent cities were selected to capture the full development gradient, from rural to densely urban (Figure 2), and their boundaries (National Boundary Dataset 2014; [[http://nationalmap.gov/boundaries.html](http://nationalmap.gov/boundaries.html)]([http://nationalmap.gov/boundaries.html](http://nationalmap.gov/boundaries.html))) used to quantify the extent of predicted burial and total impervious cover [36] within each. For the purposes of comparison, counties were assigned to one of four \"development tiers\", based on a combination of their level of total impervious cover (%) as of 2006 [36] and relative distance from Washington, DC (Figure 2). Mean values of impervious cover area for development tiers 1-4, were 32.9%, 13.9%, 3.0%, and 2.4%, respectively. Flow direction and flow accumulation (FAC) were calculated for each county from 10-m National Elevation Data [43] using the TauDEM [44] suite of tools. Values for FAC represent the areal sum of all 100 m\({}^{2}\) pixels upstream from each stream pixel. Slope values for each stream pixel were derived directly from the DEM using the average landscape gradient (rise/run) in a nine-cell window surrounding and including each stream pixel. Data for county-level burial rates, catchment area, and slope were examined to determine the relationship between burial and each of the two other variables. For comparisons with predicted stream burial, catchment area and slope were each individually treated as the independent variable. To summarize the large variability in predicted stream burial rates, stream reaches were grouped into 'bins' of equally spaced catchment area and the mean stream burial was calculated for streams in each bin. Mean predicted stream burial was then plotted against catchment area and slope and the resulting  
Figure 2: The sixteen study counties and independent cities colored by development “tier”, as determined by the total amount of impervious cover, and relative distance from the Washington, DC, urban center. relationships were analyzed. To understand collinearity in the independent variables (catchment area and slope), we also analyzed slope against binned catchment area. Initial examination of the plotted relationships revealed a consistent pattern between average predicted burial rates and catchment area, with burial exhibiting a characteristic \"hump-shaped\" distribution (e.g., Figure 3). For each county, a local burial'maximum' is evident in the mid-range of catchment area, with a characteristic 'ascending limb' and 'descending limb' in the burial distribution to either side. To analyze how the shape of the distribution of values on either side of this maximum changed with the level of development, we subset the data, and ran separate regressions for each limb. High rates of collinearity between slope and catchment area across all levels of development precluded reliable analysis of the interaction between the two, so separate analyses were run to determine the relationship between predicted burial rates and the two independent variables individually within each limb. Due to similarities in development history and resulting patterns in burial predictions, and to ensure sample sizes for analysis across catchment area bins, the 5 independent cities of Virginia were analyzed as a single unit.