In many areas of the world, motorized travel on cars, buses, motorcycles, and other vehicles is the primary way that people move between locations in their home regions. Traveling along the highway, they take in a visual panorama that includes landforms moving through the field of view in an ever-changing display (Cron, 1959, p. 88; Lowenthal, 1978). Indeed, this is one aspect of automobile travel that many motorists find enjoyable. “The view from the road can be a dramatic play of space and motion, of light and texture, all on a new scale,” observed Appleyard et al. in 1964 (pp. 3–4). Even for urban commuters who get no thrill from sitting in traffic, motorized travel is still one of the most common ways to see the natural landscape.

Although there are various sensory ways to learn and know a landscape, such as sounds and smells, the motorist is largely sealed off from these, primarily relying on vision. Scenes from the highway influence the ways that motorists perceive space and orient themselves. Traveling through a place can reduce ignorance of that landscape for passengers who are attentive and traveling during daylight (McKenna et al., 2008). No longer terra incognita, the roadside landscape might even take on an outsized role in motorists' understandings of place. People's mental maps tend to exaggerate the size, prominence, and frequency of features that they have seen or interacted with (Gould and White, 1974, p. 33, p. 130).

That being said, mechanized travel allows only a rapid and relatively limited set of views, viewpoints, and angles compared to those that would be available if the observer could simply roam the landscape, a fact sometimes bemoaned by early rail travelers (Schivelbusch, 1986). The appearances of natural features from the roadway are likewise constrained and further affected by environmental factors such as weather and lighting (Unwin, 1975). Even with the possibility of motorized travel, our cognitive maps sometimes remain sketchy and impressionistic. As our mental maps grow through repeated exposure and experiences, so expands our set of behavioral options, sense of security, and feelings of enjoyment and meaning in the landscape (Bell et al., 1978, pp. 267–269; Chang et al., 2019).

For decades, urban planners and landscape architects have sought to understand how pedestrians and motorists interpret and navigate cities from streets and sidewalks. I propose that some of these inquiries can help learn how people perceive the natural landscape of the broader region. The volume The Image of the City of Lynch (1960) posited that our environmental image

is the product both of immediate sensation and of the memory of past experience, and it is used to interpret information and to guide action. The need to recognize and pattern our surroundings is so crucial, and has such long roots in the past, that this image has wide practical and emotional importance to the individual. (Lynch, 1960, p. 4)

By studying residents' mental maps and navigation habits among three US metropolises, Lynch developed a framework of five elements that contribute to people's image of the city. These are paths, edges, districts, nodes, and landmarks. Paths are channels of movement, such as roads and railways; edges are other linear elements not used as paths, such as shorelines or walls; districts are areal units with a common identifying character, such as neighborhoods; nodes are strategic foci of travel such as stations and junctions; and landmarks are point references not participating in the travel network, such as hilltops or distinctive skyscrapers (Lynch, 1960, pp. 46–48).

The density at which these elements are perceived on the cityscape determines the legibility and imageability of the landscape. For example, participants in Lynch's study had a well-developed image of the city of Boston along the Charles River where edges, paths, and landmarks were abundant and markedly defined; but the details of their understanding declined with distance from the river's edge. Some neighborhoods were even difficult for their own residents to conceptualize due to irregular street matrices and scarcity of landmarks (Lynch, 1960, p. 20).

At the state or provincial scale, features such as roads, ridges, basins, cities, and peaks all find corollaries in Lynch's framework. The degree to which these features actually do fill the roles of paths, edges, districts, nodes, and landmarks is partly based on how visible they are (McKenna et al., 2008). In this context, GIS-based visibility analysis becomes useful for determining which landforms and other natural features might contribute most to the legibility of the landscape.

As computer processing power has improved over the years, some researchers have explored whether Lynch's elements can be derived from spatial databases using algorithms. Computation was viewed as an attractive circumvention of the time and cost associated with finding and interviewing residents about their mental maps. Campagna et al. (2012), for example, experimented with finding prominent paths based on size and topological connectivity of streets, but only after noting that some of Lynch's elements are defined by personal, historical, or cultural meanings that might be harder to calculate.

Other studies introduced visual properties into the computation of Lynchian elements. Dalton and Bafna (2003) used ideas from space syntax research, such as axial lines and isovists (eye-level cross-section polygons of the field of view). The latter were useful for detecting edges, although the authors felt that the “visual elements” of edges and landmarks played only a secondary role of fine-tuning the mental map when compared with the “spatial elements” (nodes, paths, and districts) that the subject could actually traverse. Morello and Ratti (2009) used a digital elevation model (DEM) and employed 3D isovists to calculate Lynchian elements as the subject traveled through urban space. Their work uses cumulative isovists to understand commonly visible surfaces. Filomena et al. (2019) proposed methods for computing all five of Lynch's elements, identifying landmarks by measuring building heights and the longest lines of sight. They also looked at nearby points from historic registries in an attempt to capture some of the socio-cultural meaning associated with the potential landmarks.

Some have questioned how much Lynch's elements are still relevant in the digital era. Park and Evans (2018) note that digital wayfinding tools can elevate alternative routes that might have once been secondary or tertiary in nature (for example, to get around accidents or slowdowns), thereby muddying the clear spatial hierarchy of path structures advocated by Lynch. Hamilton et al. (2014) observe that as algorithms generate maps dynamically, the traveler has less need of a cognitive map or wayfinding skills. Out of Lynch's five elements, this development has the biggest effect on landmarks. Indeed, the definitive landmark in the algorithmic city may actually be the self.

The present article contemplates what Lynch's elements might look like when applied to geomorphological features on a state-level scale and explores ways of identifying possible elements using visibility analysis. Since Lynch's framework was developed in cities, some aspects of it may not translate directly to rural settings; for example, in the countryside, the path network is more limited than in the city. There may only be one reasonable way to get between an origin and destination point. Similarly, nodes as critical junctions between paths may be fewer and farther between. Some elements may not be used directly for route-finding but still contribute to travelers' mental maps and understanding of relative positioning. In the natural landscape setting, the visual elements of edges and landmarks identified by Dalton and Bafna (2003) are useful toward personal orientation and confirming a sense of place. Districts are also possible to derive as polygonal areas that can be seen and comprehended. Thus, the present analysis focuses on identifying landmarks, edges, and districts.

GIS offers numerous approaches for studying the areas that are visible from any particular vantage point. Gridded (raster) data are most common in these analyses, wherein each cell value represents the elevation of the terrain. The software performs geometric calculations on this “digital elevation model” (DEM) to systematically detect whether anything is blocking the view between the observer cell and all possible target cells (Travis et al., 1975; Fisher, 1991). The set of cells visible from the input observer cell is commonly referred to as the viewshed of the input cell. Viewsheds have been deployed in landscape planning (Travis et al., 1975; Fisher, 1996; Sander and Manson, 2007), tourism and recreation studies (Wilson et al., 2008; Jakab and Petluš, 2013), historical analysis (Randle, 2011), and many other fields.

The most accurate method of deriving a viewshed is to calculate the line of sight between the observer cell and all other cells in the study area; however, this approach is time-consuming. Algorithms that make relatively minor sacrifices in accuracy can shorten the processing time considerably by strategically reducing the number of sight lines calculated. Ways of doing this include calculating the lines of sight to the grid edge cells first and using the results to estimate values of inner cells, or working outward from the observer in concentric rings in a way that skips calculations on areas already estimated to be obstructed (Franklin and Ray, 1994; De Floriani and Magillo, 2003; Kaučič and Zalik, 2002; Carver and Washtell, 2012). A different method described by Wang et al. (2000) avoids sightlines and instead uses “reference planes” defined by the heights of the observer cell and two other cells just in front of the target cell. This is the algorithm employed in the free and open-source Geospatial Data Abstraction Library (GDAL) software (Warmerdam, 2008). It was chosen for the present study due to its free and widespread availability, transparent documentation, and reasonable speed.

A viewshed of a single point can be recorded in a Boolean raster format using a value of 1 to denote cells within the viewshed and 0 or “no data” values for all other cells. When viewsheds are calculated from multiple points, the resulting layers can be summed to create a cumulative viewshed wherein the value of any given cell represents the number of observer points that can see that cell. For example, Wheatley (1995) used a cumulative viewshed analysis (CVA) to map how many archeological monuments were visible from any vantage point within an area of interest. The study also examined the cumulative viewshed counts at the monument points themselves to help determine if intervisibility might have been a factor in monument placement.

Determining visibility from polyline features (such as a road network) is carried out in practice by placing points at a fixed interval along the lines and creating a cumulative viewshed from those points. Chamberlain and Meitner (2013) gave an example of this approach to determine scenery visible from a 6 km segment of highway, with the sample points placed about 10 m apart. They described several variations on this technique to account for the speed of the vehicle and the visual magnitude of the feature within the motorist's field of view. Lee and Stucky (1998) used cumulative viewsheds as a cost surface to determine ideal paths for a variety of scenarios such as keeping unsightly features out of view, maximizing scenic vistas, and conducting reconnaissance.

Some probes of novel viewshed methods have been limited by computational capacity, especially when generating many viewsheds over a broad landscape. Most studies involve urban areas or small rural study sites. For example, when calculating visibility from a sample of 220 residential properties within a town, Sander and Manson (2007) mention limited computing time as a barrier to a more comprehensive inquiry. Today's increased computational capacity and data storage capacities can allow for broader CVA studies across states or countries, especially when the viewsheds are generated and summed through automated scripts.

The present study takes advantage of automation to generate and sum many thousands of viewsheds along the highways of Washington State, a study area of approximately 184 000 km2 in the northwestern corner of the contiguous United States. A variation on the analysis weights the viewsheds by traffic counts to get a better understanding of the features visible to the most highway travelers. The results from these cumulative viewsheds are used to construct elements from Lynch's framework, thereby getting a feel for which geographic features might contribute most heavily to motorists' readings of the landscape. I conclude the analysis by discussing different uses of the cumulative viewshed, as well as some of the limitations involved in this approach.

The set of 1 arcsec DEMs covering Washington State was downloaded from the United States Geological Survey (USGS) National Map downloader website (https://apps.nationalmap.gov/downloader/#/, last access: 28 April 2022). The author projected these DEMs into UTM Zone 10 N, mosaicked them, and clipped them to the official state boundary (including water). The cells' spatial resolution of approximately 30 m was fine enough to capture the visibility of major natural features, while being coarse enough to allow for the calculation of thousands of viewshed operations across long distances. For more localized analyses not involving an entire state, a higher-resolution DEM would be preferable.

Highway polylines containing average annual daily traffic (AADT) counts for the year 2019 were obtained from the Washington Geospatial Open Data Portal (https://geo.wa.gov/search, last access: 28 April 2022). This dataset is maintained by the Washington State Department of Transportation and contains all numbered federal and state highways within Washington State, totaling about 11 362 km in length.

The traffic counts were reported as attributes of these polyline segments. Multiple segments made up a single highway, with the counts varying up and down along each route according to how many vehicles per day were estimated to travel the road on average during 2019. More recent counts were not sought, due to the influence of the COVID-19 pandemic on typical traffic patterns.

To prepare for the viewshed generation, the highways were joined by their route numbers, and a set of sample viewpoints was generated at 1 km intervals along each route. Points known to be in tunnels were discarded. The traffic counts from the original highway segments were then spatially joined onto the viewpoints. This created a dataset with 11 225 viewpoints, each containing a traffic count estimate.

The unweighted cumulative viewshed (Fig. 1) shows that the most visible spot of ground from Washington State highways is a location approximately 4298 m high on the northwest flank of Mount Rainier, the highest mountain in Washington State. This pixel is visible from 2104 of the sample points. It might surprise some that the most visible location is not actually the summit of Rainier; however, this is consistent with the Kim et al. (2004) findings that ridges sometimes offer better visibility than peaks.

All sides of Mount Rainier can be seen from state highways. Large sections of the northwest face pointing toward the Seattle area were visible from over 1000 sample points. The only other landforms reaching this threshold were several peaks in the Olympic Mountains, with the most visible being Mount Constance. The high number of viewpoints recorded for these peaks may be due to their visibility from the Seattle and Tacoma metropolitan areas, where there are the most residents and roads. These cities include gentle slopes and expanses of water that afford better views of faraway points.

In the more sparsely populated central part of the state, the Wenatchee Mountains and Rattlesnake Hills are widely seen, as well as long east–west ridges from the Yakima Folds (Kelsey et al., 2017). On the far east side of the state, the Blue Mountains are the most visible. Although the major eastern city of Spokane sits adjacent to several mountain peaks, these are not prominent in the unweighted viewshed, perhaps because of the hilliness of the terrain and edge effects associated with the city being located next to the state boundary.

When the viewsheds are weighted by traffic counts (Fig. 2), the general patterns are similar, although features near metro areas and busy interstate highways are emphasized. These include Mount Spokane, as well as the highlands east of Seattle sometimes locally called the “Issaquah Alps”. In central Washington, the eastern slopes of the Wenatchee Mountains see high values in the weighted cumulative viewshed. These highlands are the first arm of the Cascade Range visible from Interstate 90 as westbound motorists traverse a 110 km straightaway across the Columbia Basin. In fact, these maps show just how much Washingtonians' perceptions of the Cascade Range might be influenced by travel over Snoqualmie Pass on Interstate 90. This is the main artery for personal and commercial vehicle travel between the two sides of the state. The summit sees an average of 34 000 vehicles per day. Figure 3 shows that the viewshed through the pass is generally less than 10 km wide on clear days. On winter days, one is lucky just to see the roadway.

Beyond understanding mental maps, the highway network CVA could be applied in many fields including print and digital cartography, augmented reality development, tourism planning, and toponymic studies.

Although this analysis identified some landforms that may be likely to occupy a place in the mental maps of Washington's residents, it did not verify whether the computationally identified landmarks, edges, and districts do indeed play a significant role in people's mental maps. The statewide sampling and outreach that such a verification would entail were deemed to be out of scope of this paper; however, validating computationally derived Lynchian elements with qualitative surveys or other methods such as text mining from books, articles, or conversations would be an informative exercise in future studies.

In order to scale across a broad area with many thousands of viewsheds, this study built upon Boolean visible and invisible calculations carried out on a uniform DEM. The analysis reveals which features should be visible under ideal conditions, but could yield more nuanced results with additional kinds of methods and ground truthing. Features in both the built and natural environments, such as buildings and trees, can obstruct lines of sight and affect the viewshed shapes and areas. This effect can be substantial in heavily wooded areas such as those in western Washington that inspired the nickname “The Evergreen State”. Models that incorporate the heights of built features and forested areas of land cover would give more accurate results, although without enormous amounts of data, they would also be subject to estimation and imprecision.

A viewshed operation is only as accurate as the DEM it is conducted on. Fisher (1991) lists numerous reasons that the actual elevation of a point may differ from its DEM cell value, including problems with the original survey by field workers or photogrammetrists, mistakes by people digitizing these surveys, and poor interpolation. Limitations with the precision of the data format can also hinder accuracy. For example, elements of highway engineering such as cuts through a hillside might obstruct the motorist's view but are sometimes too small to show up in the DEMs used in this study. Higher-resolution DEMs such as those produced with lidar might yield more accurate viewsheds but could increase calculation time to impractical levels. Approaches that use high-resolution data near the highways and a coarser DEM for everything else could also improve accuracy in future experiments (De Floriani and Magillo, 2003). The downside is that these multi-resolution approaches require more data preparation on the front end.

The cloudy and foggy weather associated with the temperate oceanic climate in western Washington often reduces visibility. Parts of the state on the east side of the Cascade Range are generally much sunnier, with clear visibility most of the year. Future studies could factor in weather and climate when determining the most visible features.

Areas shown as invisible in the CVA should be interpreted with caution, since the analysis is based only on viewsheds taken from sample points spaced by 1 km. Stretches of roadway between the sample points might be able to see areas designated as invisible in this CVA. A denser or different set of sample points would yield a different CVA, although not likely different enough to affect the results at a statewide level.

Only areas within the Washington State boundary were considered in this study. Some viewpoints in Washington can see into other states (and Canada), and some viewpoints from those locations are able to see into Washington. Consequently, the values in the cumulative viewsheds and the calculation of the top 1 % of scenic points are subject to edge effects.

Finally, applying strategic weights or functions to the viewsheds might give a better picture of which landforms people see and think about the most often. For example, Mount Rainier takes up much more of the field of view in the city of Tacoma than it does in Yakima. This is because Tacoma is closer to the mountain, sits at a lower elevation, and has fewer other mountains and ridges to obstruct the vista. Approaches that calculate a “visual magnitude” for each cell based on the viewing angle and distance to the target, such as those described by Chamberlain and Meitner (2013), would help with understanding which features take up the most space in observers' fields of view. Carver et al. (2012) attempt to determine visual impact by using an inverse square distance function and the height of the object. Such approaches are more computationally intensive and more complex to interpret than the one described in this paper; however, they may be useful toward better understanding which visible features have the most influence on a traveler's mental map.

Using automated methods, free and open-source software, and fairly ordinary computing power, this study has demonstrated how a cumulative viewshed can be created from a regional highway network traversing well over 100 000 km2. The resulting layer reveals the landforms most widely visible (and invisible) to motorists along the network. Weighting the contributing viewsheds by traffic counts can give a better feel for which areas are visible to the most people. Further spatial data processing on the cumulative viewshed can assist with deriving landmark, edge, and district elements that contribute to people's mental maps as proposed by Lynch (1960).

Cumulative viewsheds derived from highways can help cartographers prioritize features for labeling, especially areal features such as valleys, basins, and estuaries that are often missed. This applies to both print and electronic maps, as well as augmented reality applications that point out geographic features. Other applications of cumulative viewsheds include siting features for high or low visibility, identifying potential scenic byways, and guiding discussions about place names and perceptions.