Network Analysis: Modeling Overland Paths Using a Least-cost Path Model to Track Migrations of the Wolpertinger of Bavarian Folklore in Redwood National Park, Northern California Natalie Cabrera GSP 370 Assignment 5.5 March 1, 2018
Abstract Few studies have been done on the elusive wolpertinger. But this unique species is gaining attention as it draws interested new visitors to its habitat range within Redwood National Park in coastal northern California. The goal of this study was to employ a least-cost path model in a GIS to estimate potential paths traveled by the animals between their mountain dens across the National Park, to the town of Orick, during its fall migration in October. Data for known den locations were collected in one summer field season by Humboldt State University students. Other field observations revealed preferred modes of travel to favor higher elevations, steep slopes where its predators are less able to travel, dense canopy to hide, and not to cross water bodies or rivers and streams. These factors were used to build the model upon raster data from a digital elevation model, percent tree canopy, and hydrography. The landscape factors with the strongest influence on potential routes were, in descending order, elevation, slope, hydrography and canopy cover. Routes often paralleled ridges, or stream valleys along the steepest slopes, or trended perpendicular to ridges and valleys favoring the steepest route straight up or down and crossing streams at the narrowest point until a steep traverse to higher elevation could be found. The longest path was 26 miles, and the shortest was 8.4 miles. The routes were convergent with one another, eventually sharing a single route on approach within about 3.1 miles north of Orick. Total path costs increased with distance from dens to Orick with little variation. The results of this study can be valuable for focusing future field efforts, which should be done to further verify accuracy of the predicted paths. With better knowledge of the behaviors of this newly studied species, management efforts can be targeted with the goal of increasing its protection and conservation within the National Park. Introduction The mysterious and seldom seen wolpertinger is a creature that dwells in the dark, remote, wild redwood forests of northern California s Redwood National Park, shown in Figure 1. What little is known has revealed the wolpertinger to be of about rabbit shape and size, covered in fur with wings and antlers. Though it has received scant attention, greater knowledge could be of great benefit to this unique species by enabling land managers to identify areas requiring protection for habitat and forage. Further benefits gained could be increased visitation to Redwood National Park as a result of new public awareness. In an effort to learn more about its behavior, a group of Humboldt State University students spent one summer tracking the animals and taking data to describe wolpertinger modes and preferences of travel, and its den locations. From tracking evidence, a strong pattern was observed for a mass migration at the end of the season around October, out of the mountains, and toward the town of Orick situated near the south end of the National Park (Figure 1). However, data were not specific enough to locate actual migration routes. An overland least-cost path model was used in a Geographic Information System (GIS) to predict a single possible route for each mapped den location to Orick based upon observed preferences for travel. Wolpertinger prefer higher elevations and ridgelines, steep slopes where its predators are less able to travel, dense canopy to hide, and not to cross water bodies or rivers and streams. Natalie Cabrera GSP 370 Assignment 5.5 Page 2 of 7
Figure 1. Location of project area in northern California. Orick lies north of Eureka at the south end of Redwood National Park. Park boundary data from National Park Service (2017). County data from US Census Bureau (2016). Methods The analysis was conducted in ArcMap. All spatial data layers were projected into the common spatial reference for the project of NAD83 UTM Zone 10 North. Data layers used were den locations, the post office in Orick, a digital elevation model (DEM), canopy cover density, and hydrography. Locations for ten dens were collected in the field as GPS points whose latitude and longitude coordinates were plotted in ArcMap from a csv file, then exported to shapefile. Coordinates for the town of Orick were found using geolocation in Google maps, then converted in a shapefile using the same method as the dens. The dens and Orick were merged and the resulting shapefile buffered by 10 miles into a dissolved, single polygon for use in clipping the raster data. The DEMs, canopy cover density, and hydrography data were downloaded through the United States Geological Survey (USGS) National Map website (USGS, 2018). The two DEM images were added to a single mosaic file, projected into NAD83 UTM Zone 10 N using the cubic sampling method to ensure lack of artifacts in later derived products, and clipped with the den and Orick buffered area. A slope layer was derived from the DEM using the Slope tool in Spatial Analyst. The canopy cover density was clipped. The hydrography data consisted of three separate shapefiles; line features for flowlines, and two polygon features for water bodies, and ocean. The geoprocessing environment was set to the extent of the clipped DEM. Natalie Cabrera GSP 370 Assignment 5.5 Page 3 of 7
In an overland least-cost paths model, each raster data type represents a range of costs to travel that would be encountered by the migrating wolpertinger, or a cost surface. For example, because the wolpertinger prefers high elevations, high elevations on the DEM are a low cost, and lower elevations represent high cost. The model required the input of a single raster from which to evaluate possible paths between the source points, dens, and the destination, Orick. But because the different raster data types had different scales for their ranges of data, the scales of each layer were converted into a single relative cost scale. The new relative scale required reclassification of the original range of values into a scale with discreet values between 1 and 10 that could then be compared equally to each of the other layers. More importantly, the individual cost surfaces could then be combined into the single cost surface needed by the model. The breakpoints between classes used to reclassify each raster to the new 1 through 10 scale were determined based on a factors unique to each raster type as observed through the field research. Table 1 shows the classes for each factor. Each layer was reclassified using a remap table file. Table 1. Classes for each layer used to reclassify each layer type to a relative cost scale. Relative Cost Elevation Slope Canopy Water Features 1 >1000 >35 >90 No water 2 >800 to 1000 >30 to 35 >80 to 90 3 >600 to 800 >60 to 80 4 >400 to 600 >25 to 30 5 >200 to 400 >40 to 60 6 >100 to 200 >20 to 25 7 >1 to 100 >20 to 40 8 >10 to 20 9 >5 to 10 10 >-1 to 1 0 to 5 0 to 20 Water The three hydrography features were first each converted to cost surface models, then each reclassified into a relative cost surface using a 1 or 10 (Table 1), then combined into one that could be used in the total coast surface. They each were first converted to cost surface rasters using the Features To Raster conversion tool, then reclassified to change NoData pixels to a value of 1, and water data to a value of 10. The three cost surface layers were then multiplied with the Raster Calculator resulting in values of 1, 10, 100, and NoData. Areas with a value of 1 represented no water, 10 represented locations with water derived from only one water type, and 100 represented locations where two water types overlapped. This final raster was reclassified so that any water was a 10, and no water was a 1. To create the total cost surface model, the four cost surface rasters (slope, elevation, water, and canopy cover) were multiplied with the Raster Calculator. To determine the easiest possible paths that each wolpertinger could navigate through the terrain and landscape between its particular den and Orick, or its least-cost path, a three-step method was used. First, two cost-distance surface models were created; one with Orick as the origin, and another with the dens as the origin. Second, a migration corridor raster was created to show general areas by low to high difficulty for travel. Third, a least-cost path was derived for each den. Each cost-distance surface model was created from the total cost layer using the Path Distance tool in Spatial Analyst. Along with the cost-distance surface, which assigns a cumulative cost value to each pixel as distance increases away from the source, a backlink raster was also created that assigns a direction value to each pixel from 0 to 8 based on which direction has the least cost from a given pixel to each of its neighbors. The migration corridor raster was generated by adding together the two cost-distance rasters using the Corridor tool in Spatial Analyst. The result was a raster with pixels valued on a spectrum from easiest to most difficult for Natalie Cabrera GSP 370 Assignment 5.5 Page 4 of 7
travel according to the combined four factors of elevation, slope, canopy cover and water. This raster is presented in Figure 2 and is symbolized from blue to pink to white as difficulty of travel increase from low to moderate to high. The least-cost paths were created one at a time for each route. For each repetition of the following steps, a definition query was performed on the dens point file to display only one den. To create each least-cost path, the Cost Path tool was used with each den location as the destination, and the Orick cost distance and backlink rasters as the other inputs. The result for each was a raster that coded the least-cost path pixels with a value of 1, and an attribute table in which the total cumulative cost for all the pixels with a value of 1 was recorded. The total cumulative costs for each least-cost path are shown in Table 2. The result were exactly the same if the dens were used as the source, and the dens cost distance, and den backlink rasters were used as the other inputs. When the least-cost path raster was viewed, the pixels with a value of 1 were adjacent to one another to form a meandering line. For mapping purposes this single pixel line was very difficult to see, so the least-cost path for each den was converted to a polyline shapefile for better display. Upon close visual inspection, there was no difference between the raster and vector versions of the least-cost paths. Results Table 2 compares the differences between path costs for each den, and Figure 2 maps the least-cost paths for each den. It followed logically that the furthest den, A, had the longest path at 26 miles, and highest path cost of 1,869,200, and the nearest den, B, had the shortest length at 8.4 miles and the lowest path cost of 997,425. The other paths generally had lower path costs as they were closer to Orick ranging between 1,154,120 and 1,177,440. Dens D, H, and E were clustered at roughly the second furthest away after Den G, and Dens C, F, I, and J clustered together at roughly all second nearest to Orick. The path for Den J was the only one out of pattern with the second highest path cost of 177,440. Separated by two canyons from the other points, its path was forced to stay high and meander before it could find a route similar to the other routes. Finally, it is no surprise the paths all eventually converge and overlap as they approach Orick. They each trended along the undulating, southwest oriented ridge to cross Highway 101 and meet path B before being forced to cross a few valleys along their final 3.1 mile approach to Orick. In general, where a continuous ridge was not available, the paths would dip down into valleys, but when they did so, crossed perpendicular and climbed immediately again. Table 2. Total Least-Cost Path Results from Each Den to Orick. Den ID Path Cost A 1,869,200 B 997,425 C 1,247,330 D 1,327,770 E 1,269,850 F 1,182,210 G 1,375,240 H 1,257,500 I 1,154,120 J 1,177,440 Natalie Cabrera GSP 370 Assignment 5.5 Page 5 of 7
Figure 2. Map showing least-cost paths from each den to Orick based on the total cost surface raster also shown here over the DEM. Natalie Cabrera GSP 370 Assignment 5.5 Page 6 of 7
Conclusion Though this scenario generally had lower total path costs and shorter path lengths with closer distance to the origin, it is not always true that the least-cost path is the shortest possible route. Had any of the four landscape factors been classified differently to favorably weight a larger portion of its values very high on the relative cost scale, then it could have swayed the results to favor different, potentially longer paths. This may have been the case with the canopy cover density. By viewing the four input rasters individually in relation to the least-cost paths, some light can be shed on which factors may have had the most influence. Canopy cover likely had the least influence as the majority of area is densely covered. There was some variation in canopy cover however that had some influence. Elevation and slope appeared to have the strongest influences. While elevation was favored, it was not strictly ridgetops traveled. Because the wolpertinger also favors steep slopes, the routes did parallel ridges where possible, but would favor the steepest faces along the ridge, which was often very near ridge. Where it was not possible for a path to travel parallel a ridge, routes seemed to either parallel stream valleys along the steepest slopes and cross streams at their narrowest sections until a path to a higher elevation could be found, or would go perpendicular to streams and valleys seeking the steepest route straight up or down until a steep traverse across contour could be found to climb to the common ridge found by all of the paths. More study of wolpertinger migrations are needed to verify the accuracy of the least-cost paths. These results can be a valuable guide for prioritizing future field efforts. Once field surveys are available, actual migration data can be combined with the modeled paths, as other researches have demonstrated (Davidson et al., 2013), to derive the most likely, actual migrations paths. With better knowledge of the behaviors of this newly studied species, management efforts can be targeted with the goal of increasing its protection and conservation within Redwood National Park. References Davidson, A., Carmel, Y. Bar-David, S. (2013). Characterizing wild ass pathways using a non-invasive approach: applying least-cost path modeling to guide field surveys and a model selection analysis. Landscape Ecol, 28, 1465-1478. doi:10.1007/s10980-013-9915-8 United States Census Bureau. (2016). Tiger Line US Counties, 1:500,000. Retrieved from https://www.census.gov/geo/maps-data/data/cbf/cbf_counties.html National Park Service. (2017). Administrative Boundaries of National Park System Units 12/31/2017 - National Geospatial Data Asset (NGDA). NPS National Parks Dataset. NPS - Land Resources Division. Retrieved from https://irma.nps.gov/datastore/reference/profile/2224545?lnv=true United States Geological Survey. (2018). National Geospatial Program, 20180205, USGS National Hydrography Dataset (NHD) Best Resolution HU4-8 20180205 for HU-4 Subregion Shapefile Model Version 2.2.1. Retrieved from http://viewer.nationalmap.gov/viewer/ United States Geological Survey. (2013). NLCD 2011 Percent Tree Canopy, by State: NLCD2011_CAN_California. Retrieved from http://viewer.nationalmap.gov/viewer/ United States Geological Survey. (2013). USGS NED n42w124 1/3 arc-second 2013 1 x 1 degree ArcGrid. Retrieved from http://viewer.nationalmap.gov/viewer/ Natalie Cabrera GSP 370 Assignment 5.5 Page 7 of 7