Methods

The data set examined was the USGS National Hydrography Dataset (retrieved January 2012, http://nhd.usgs.gov). This combines multiple surveys through time, using the resulting high-resolution USGS topographical maps to delineate aquatic boundaries (Simley and Carswell, 2009). While a variety of resolutions are available, only 1 : 24 000 was used in this analysis. The data set covers the area of all 48 U.S. contiguous states, including Washington D.C. Because they are not completely contained within the U.S., we chose to exclude the Laurentian Great Lakes for this analysis.We extracted all lake, reservoir and pond polygons from the GIS data set. Because the data set does not distinguish between artificial or natural lakes and ponds, no distinction was made for this analysis, and all waterbodies hereafter are collectively referred to as lakes. The elevation component of these polygons was removed using ArcGIS (ESRI ArcGIS v10.1; ESRI, Redlands, CA, U.S.A). For simplicity, all island data were excluded from the results presented here, although we discuss the small resulting bias. Duplicate polygons were identified and removed using the permanent identifier field included with the data. All calculations were completed using the MathWorks Mapping Toolbox (v2010b; MathWorks, Natick, MA, U.S.A), which adds geographical information functionality to MATLAB. A single-point location for each lake was defined as the centroid of the lake boundary polygon.To examine perimeter while considering the issue of a fractal lake perimeter, we estimated perimeter using two complexity-insensitive and repeatable techniques. First, a theoretical minimum perimeter (Pmin) was established by calculating the perimeter of a circle with the same area as each lake using: Pmin = 2(pi(A))^(1/2) where A is the total area of the individual lake (Kalff, 2001). This represents the absolute minimum perimeter, on a flat plane, required to encompass a given area (spherical coordinates could reduce Pmin further, though for the size scale of lakes examined here, the difference is negligible). Second, a resolution-specific perimeter was calculated using a simple yardstick method based on Mandelbrot (1979). With this method, a fixed-length line segment was progressively "walked" along the polygon until reaching the start point. This simulated a perimeter estimate at specific and adjustable mapping resolutions. The yardstick length was varied across a range of values (25–1600 m) to examine the sensitivity of the perimeter estimate to measurement resolution. To compare the sensitivity of perimeter estimate with previous studies, the slope of the relationship between logperimeter and log-yardstick length was calculated using least-squares regression, based on Kent and Wong (1982). Lastly, we calculated the maximum-observed perimeter of each polygon (Pobs) using the full-resolution data and summing the lengths of each polygon segment. Shoreline development factor (SDF) was calculated using the equation: SDF = P / (2((A)pi)^1/2) where A is area and P is perimeter. The perimeter measurement technique used in SDF calculations (Pobs or the yardstick method) is indicated where discussed. Calculations of perimeters, area and centroid were fast for any single polygon, but because of the high number of lakes and high polygon resolution, calculations became computationally intensive. This and other geostatistical calculations were accelerated using a computer cluster. HTCondor software (Thain, Tannenbaum and Livny, 2005) was used to distribute this task.The extents of stream and river shorelines were calculated from the National Hydrography Dataset using the same technique as the fractal-naive perimeter (Pobs). Only features classified with a type of stream/river (USGS Feature no. 460) were included. This feature type includes intermittent, ephemeral and perennial streams and rivers, but excludes features such as underground streams and canals. The shoreline length of small streams, represented in the data set by polyline objects, was estimated as the length of the lines doubled to account for both sides of the stream. The shoreline of larger rivers, which are stored in the data set as polygons, was calculated directly as the observed perimeter of the polygons (Pobs) on the WGS84 datum.Maps of lake abundance (number km^-2), area (per cent cover) and shoreline density (m km^-2) were created by dividing the area of the U.S. into equal-area cells (cell size: 50 km^2). Each lake’s attributes were assigned to a cell based on its unique single-point location, and statistics were calculated for lake density and per cent cover in each cell. Where a lake’s area exceeded that of a single cell, the full lake shape was split into overlapping cells based on the amount of overlapping area. Cumulative distributions of lake number, area and perimeter as a function of lake area were used to evaluate general attributes of the entire U.S. lake population.To aid future work in this area, we have released useful derived data sets on the Web. While the data are freely available from the USGS, the National Hydrography Dataset’s large size makes analyses challenging. To encourage additional research in this area, we have released the extracted perimeter data set. It is available at the data repository hosted by the North Temperate Lakes Long-Term Ecological Research website at http://lter.limnology.wisc.edu

Methods

Overview: Hard copy historical plat maps of Dane County in four year intervals from 1962to 2005 were digitized and converted to a GIS format using a process known as rectification, wherebycontrol points are set such that a point placed on the scanned image takes on the coordinates of thepoint chosen from the earliest GIS dataset, which for Dane County is from 2005. After a number ofcontrol points are set, the map is assigned the coordinates of the 2005 GIS dataset. In this way,the scanned plat map is now an image file with a distinct spatial location. Since the scanned platmaps do not have any attributes associated with the parcels, the third step is to assign attributesby working backwards from the 2005 GIS dataset. This process begins by making a copy of the 2005 GISdataset, then overlaying this new layer with the rectified scanned image. A subdivision choice isidentified where the parcel lines on the GIS layer are not in agreement with the scanned plat maps.The last step is to modify the copy of the 2005 GIS layer so that it matches the underlying plat map- in effect creating a historical GIS layer corresponding to the year of the plat map. When thelines that delineate a parcel appear in the GIS file but not the plat map, the multiple smallparcels in the 2005 GIS layer are merged together to represent the pre-subdivision parcel. Thisprocess is repeated for each historical year that plat maps are available. In the end, each timeperiod-1974 through 2000 in 4 year intervals-has a GIS file with all of the spatial attributes ofthe parcels.Land Atlas - Plat Books: The Land Atlas plat books were obtained for Dane County from theMadison Public Library, Stoughton Public Library and Robinson Map Library. With these materials onloan the pages were scanned at 150ppi in grayscale format; this process took place at the RobinsonMap Library. Once scanned, these images were georeferenced based on the 2000 digital parcel map.This process of rectification was done in Russell Labs using ESRI ArcMap 9.3. Control points such asroad intersections, were chosen to accurately georeference the 1997 scanned parcel map (1973 wasdone in this way as well). This process was done using a specific ArcGIS tool(View/Toolbars/Georeferencing). For the other years the scanned images were georeferenced based offthe four corners of the 1997 georeferenced scanned images. Georeferencing off the 1997 rectifiedimage allows for easier and quicker rectification but also facilitated detection of differencesbetween the scanned plats. The scanned image of the land ownership could be turned on and off foreasy comparison to the previous time set; these differences are the changes which were made on thedigital ownership map. We scanned and digitized the following years:Scanned plats: 1958, 1962, 1968, 1973, 1978, 1981, 1985, 1989, 1993, 1997, 2001, 2005Digitized plats: 1962, 1968, 1973, 1978, 1981, 1985, 1989, 1993, 1997, 2001, 2005Prepping the parcel Map: Digital parcel shapefiles for the years 2000 and 2005 wereprovided by the Dane County Land Information Office(http://www.countyofdane.com/lio/metadata/Parcels.htm) and were used as the starting reference.These datasets needed to be prepared for use. Many single parcels were represented by multiplecontiguous polygons. These were dissolved. (Multi-part, or non-contiguous polygons were notdissolved.) Here is the process to dissolve by NAME_CONT (contact name): Many polygons do not have acontact name. The majority of Madison and other towns do not have NAME_CONT, but most large parcelsdo. In order not to dissolve all of the parcels for which NAME_CONT is blank we did the following:Open the digital parcel shapefile and go to Selection/Select by Attributes. In this window choose thecorrect layer, chose method create new selection , scroll and double click NAME_CONT, then in thebottom both make sure it says [ "NAME_CONT" <>; ] (without brackets). This will select allpolygons which do not have an empty Name Contact attribute (empty value). From those polygonsselected they were aggregated based on the Name Contact field (parcels with the same NameContact were combined), where borders were contiguous. To do this the dissolve tool in DataManagement Tool/Generalization/Dissolve was used. Dissolve on field NAME_CONT and enter everyother field into the statistical fields menu. This was done without the multipart feature optionchecked, resulting in parcels only being combined when they share border. Keep these dissolvedpolygons highlighted. Once the dissolve process is complete use select by attributes tool again butthis time choose method of Add to Current Selection and say [ "NAME_CONT" = ]. This will provide adigital layer of polygons aggregated by name as well as nameless polygons to be manuallymanipulated.Parcel Map Manipulation: The goal from here was to, as accurately as possible, recreate adigital replica of the scanned parcel map, and aggregate up parcels with the same owner. This goalof replication is in regards to the linework as opposed to the owner name or any other informationin order to accurately capture the correct area as parcel size changed. This process of movingboundaries was independent of merging parcels. If individual scanned parcel boundaries are differentfrom the overlayed digital parcel shapefile, then the digital parcel linework must be changed. Asthis project utilizes both parcel shape and area, the parcels must be accurate. When mergingparcels, parcels with the same owner name, same owner connected on the plat map with an arrow, sameowner but separated by a road, or same owner and share a same point (two lots share a single pointat the corner) were merged to create a multi-part feature. Parcels with the same owner separated byanother parcel of a different owner with no points touching where not merged. This process ofreverse digitization was done using ArcMap. The already dissolved shapefile was copied to create onefile that was a historical record and one file to be edited to become the previous year (the nextyear back in time). With the digital parcel shapefile loaded, the rectified scanned plat maps werethen added. Once open, turn on the Editor Toolbar and Start Editing . The tools to use are thesketch tool and the merge tool. Quick keys where used (editor tool bar\customize) to speed thisprocess. To edit, zoom to a comfortable level (1:12,000) and slowly move across the townships in apattern which allows no areas to be missed (easiest to go township by township). When polygonsneeded to be reconstructed (the process of redrawing the parcel boundary linework), this was doneusing the sketch tool with either the create new polygon option or cut polygon option in theeditor toolbar. Using the sketch tool, with area highlighted, you can redraw the boundaries bycutting the polygons. Areas can be merged then recut to depict the underlying parcel map. If, forexample, a new development has gone in, many small parcels can be merged together to create a bigparcel, and then that large parcel can be broken into the parcels that were originally combined toform the subdivision. We can do this because the names in the attribute are not being preserved.This is a key note: THE OWNER NAME IS NOT A VARIABLE WE ARE CREATING, PRESERVING, OR OTHERWISEREPRESENTING. Once you merge the parcels, they will only maintain one of the names (and which nameis maintained is pretty much random). After the entire county is complete, go through again to checkthe new parcel shapefile, there will be mistakes. Snake through, going across the bottom one row ofsquares at a time. Examples of mistakes include primarily multi-part features that were exploded tochange one part, where the other parts would need to be re-merged. Another common correction arosebecause we typically worked on one township at a time, whereas ownership often crossed townships, soduring this second pass, we corrected cross-township ownership at the edges of the two scannedparcel maps. Finally, some roads which had been built into parcels (driveways) needed to be removedand these were not always caught during the first pass. Once the second run through is complete copythis shapefile so that it also has a back up.