Definitions

Open space proximity source: Open space, whose type and quality determine its relative value for beneficiaries.

Open space proximity sink: The presence of highways, which at the neighborhood scale highways can reduce access to and enjoyment of open space.

Open space proximity beneficiaries: Residents who live near and have access to open space.

Open space proximity flow: The movement of people from residences to open space.

Viewshed source: The source of a scenic view, such as mountains, water bodies, or visually significant vegetation types, which is carried across line of sight and affected by the amount of visual interruptions in between.

Viewshed sink: “Visual blight:” landscape features, such as developed land, clearcuts, transmission lines, or mines, which tend to reduce view quality.

Viewshed beneficiaries: Residents who have views of visually significant landscape features, such as mountains, water bodies, or visually significant vegetation types.

Viewshed flow: The flow of aesthetic information along a line of sight from viewers to visually significant objects. View quality can be degraded by the presence of visual blight and decays over long distances.

Model structure and assumptions

Case studies 1. Western Washington State 2. San Pedro River, Arizona 3. Rocky Mountains

Aesthetic proximity source models. Aesthetic proximity values depend foremost on having open space in some form. For the San Pedro, major open space types include desert scrub, grassland, farmland, parks, forests and woodlands, and riparian and wetlands. For Western Washington these include forests, wetlands, beach, riverfront, lakefront, golf courses, cemeteries, farmland, or parks. We use the intermediate variable “Open Space Resource” to aggregate these open space types. Along with the type of open space, its quality matters in determining proximity value. We aggregated several independent measures of open space quality – open space area and formal protection for both models, water quality and crime for Western Washington, and fire threat for the San Pedro – into a single intermediate variable, “Resource Quality,” in order to maintain tractability of conditional probability tables. Anderson and West (2002) found park value to increase with size, though Brander and Koetse (2007) note that open space value on a per hectare basis declines as its size grows. All else being equal, we would generally expect lower per-area value in the vast open landscapes of the rural Southwest than around urban areas. A series of papers from Maryland noted that homeowners more highly value land that is permanently protected over land that may be developed in the future (Irwin and Bockstael 2001, Irwin 2002, Geoghegan 2002, Geoghegan et al. 2003). Troy and Grove (2008) found crime to reduce the value of parks in urban areas in Baltimore, a result that could also potentially apply to older, economically distressed suburbs. We do not include crime in the San Pedro model since the region lacks large urban centers with higher crime rates. Finally, poor water quality could reduce the value of open space due to odors, public health concerns, or reduced recreational opportunities. We did not include water quality in the San Pedro model since, given its rarity, we assume the presence of water of almost any quality to indicate higher quality open space. We added the variable “fire threat” to the San Pedro model. In fire-prone regions of the west, living near fire-prone ecosystems is a risk that may be understood by landowners, leading to lower perceived open space proximity value (Loomis 2004). Finally, we set the top node, “Theoretical Proximity Source” as a function of Open Space Resource and Resource Quality. We derived prior probability distributions for the presence/absence of open space types based on 2001 NLCD and local land use data (i.e., for parks, lakefront, or riverfront) in the San Pedro and Western Washington. The Open Space Resource node uses a NoisyMax node (Pearl 1988), based on the simplifying assumption that the most highly valued land use type will be representative of the total value (i.e., there are no synergistic effects among value components, so a high probability of presence of the most valued nearby landscape component can be taken as the likelihood of a high total potential value). We set the highest values in the contingent probability table for Open Space Resource for beach, parks, riparian, lakefront, and riverfront (which frequently feature public access and open water), the lowest values for farmland (known to provide disamenities like noise and odors), cemeteries and golf courses (which may have limited public access), desert scrub and grasslands (extremely abundant vegetation types in the Southwest) and intermediate values for wetlands and forests. In a global meta-analysis of proximity studies, Brander and Koetse (2007) found parks to be more highly valued than forests, which were more highly valued than farmland. However, these relative values could be adjusted for different parts of the world based on local preferences and hedonic studies indicating relative values of different types. We assume that 25% of the landscape is protected in Western Washington and 60% was protected in Southeast Arizona. We assumed that 10% of parks are located in urban areas in Western Washington where crime may be problematic. We discretized park size by Jenks natural breaks. For Western Washington, we assumed that smaller open space parcels are most abundant, with the abundance of parks in a particular size class declining as park size grows. These assumptions were reversed for Southeast Arizona, since in the rural landscape few small open space parcels and many large open space parcels would be found. We assumed that 85% of open space has no open water, and assume that equal areas meet water quality standards, are waters of concern, or require a TMDL (indicating poor water quality). We assumed that 75% of the landscape is at a high fire threat. We assumed that the highest “Resource Quality” will occur in large, formally protected open space with no water quality or crime problems and low fire risk, and that the lowest value will occur in small, unprotected parcels of open space with crime, water quality problems and/or higher fire frequency. We thus peg the corners of the contingent probability table for Resource Quality and fill in intermediate values (Marcot et al. 2006). We assume that Formal Protection will have the greatest influence on Resource Quality, since unprotected land is potentially much less valuable for its open space quality. We assume the other variables have relatively less influence on Resource Quality. Finally, in defining the contingent probability table for Theoretical Proximity Source, we note that high-value land use-land cover types and high quality (represented through protected status, area, crime, water quality, and fire threat) will produce the highest theoretical proximity source value and vice versa, peg the corners, and interpolate intermediate values.

Aesthetic proximity sink models. If ease of access, privacy, and quiet associated with open space are the attributes that lead to proximity value, highways that prevent access or disturb aesthetic quality would act as sinks. We assume that highways deplete 50% of the potential open space proximity value to users if they are located between a user and potentially valued open space. We use a highways data layer, so no model is required.

Aesthetic proximity use models. For aesthetic proximity use to occur, housing must be located near open space. The use model identifies housing, its value, and urban proximity (e.g., urban, suburban, or rural setting) as a proxy for relative scarcity of open space as determinants of proximity use. Numerous authors have noted that open space is valuable in urban settings where user populations and scarcity are greater and less valuable in rural settings (Brander and Koetse 2007). We discretized housing value and population density, a proxy for urban proximity, using Jenks natural breaks. Based on relevant spatial data, we set priors to reflect 5, 25, and 70% of the landscape in Western Washington and 2.5, 7.5, and 90% in the San Pedro as urban, suburban, and rural settings, respectively. We assume that 75% housing values are most typically at moderate to low levels, with 15% at very low levels and 10% at high or very high levels. Finally, we assumed that 10% of the landscape has housing in Western Washington and that 2% of the landscape has housing in the San Pedro. We set the contingent probability table for “Aesthetic Proximity Use,” the top node by first requiring housing to be present in order to have value. We then set value to decline more quickly moving from urban to rural and less quickly moving from high to lower classes of housing values. Brander and Koetse (2007) found per capita income to be a positive but nonsignificant independent variable in a meta-analysis of proximity values. We thus include housing value in our models, but make its prior influence on proximity use value weaker than the presence of housing or urban proximity. Training the models to real data can be used to reveal the actual weight of the variable in each use case.

Aesthetic proximity flow models. Most studies have found proximity value to decline with distance, as housing directly adjacent to open space would be more highly valued than housing a short walk from open space, which would be more valued than housing a long walk or drive from open space. Most of the studies reviewed by McConnell and Walls (2005) examined housing within a 0.5 to 1-mile radius of open space, and note that open space-related amenity values drop rapidly past that distance. Brander and Koetse’s (2007) meta-analysis used 100 m change in the distance to open space as a dependent variable in their analysis. We thus represent aesthetic proximity value using a walking simulation model. Distance to open space starts off at its full value at the edge of an open space area but drops off quickly with increasing linear distance during the first 0.5 mile and slower decay from 0.5 to 1 mile, with the value reaching zero at a distance of 1 mile from the open space parcel. While Sengupta and Osgood (2003) describe the value of proximity to rivers in the arid Southwest as having a less steep distance decay function, for the time being we use a uniform distance decay function in the proximity flow model. Key outputs from the flow models include: 1. Possible proximate open space: The density of service flow along each walking path between an open space and user, before accounting for highways that limit local access. 2. Accessible open space: Open space providing value when accounting for proximity and the location of homeowners but not highways that limit local access. 3. Open space proximate homeowners: Homeowners benefiting from proximity after accounting for sources of open space and their flow paths, but before accounting for highways that limit local access. 4. Accessible proximity: The density of service flow along each walking path between an open space and user, when accounting for sinks and flow paths. 5. Enjoyed open space: Open space providing proximity when accounting for flow paths, sinks, and the location of beneficiaries. 6. Blocking proximity sink: Highways that actually separate residences from open space. 7. Homeowners with proximate open space: Homeowners benefiting from proximity after accounting for sources of open space, sinks, and flow paths. 8. Homeowners without proximate open space: Homeowners lacking any proximity to open space (typically in urban areas). 9. Blocked proximity: The density of service flow along each walking path between an open space and user that is blocked by highways. 10. Blocked open space: Open space that is blocked by the action of sinks (highways). 11. Homeowners with blocked proximity: Homeowners who would receive benefits from open space proximity but have their access blocked by highways.

Aesthetic view source models. Views should account for local preferences to the degree possible as these preferences are unlikely to be uniform everywhere (Bourassa et al. 2004). For the San Pedro, mountains and certain visually significant landscape types (e.g., riparian, diverse natural vegetation) were preferred landscape elements in viewsheds (Steinitz et al. 2003 based on local viewshed surveys and using the USFS 1995 framework). Mountains and open water are commonly valued natural objects in viewsheds in Western Washington (Benson et al. 1998, Bourassa et al. 2004). We set “Natural Beauty,” the source value for viewsheds, as dependent on the presence of these locally significant visual features. As priors for the San Pedro, we used appropriate LULC data to estimate priors: 1.3% of the landscape was alpine and cliff, 2.1% forest, 6.4% woodland, 1.4% riparian and water, and 88.8% visually neutral or negative landscape features. We estimated that 5% of the landscape was large mountains (>1,800 m), 40% small mountains (1,400-1,800 m), and 55% no mountains (<1,400 m). In the contingent probability table for Natural Beauty, we set instances of alpine and cliff and riparian as the highest potential value (especially when combined with mountain views), woodland and forests intermediate, and other vegetation types as the lowest. For Western Washington, we set priors assuming that 10% of the landscape is ocean, 2% is inland lakes, 2% large mountains (>2,750 m), and 10% small mountains (2,000-2,750 m). For Western Washington, we aggregated these values as Natural Beauty in a contingent probability table by noting that higher values were ascribed to ocean views, lowest values were ascribed to mountain views, and intermediate values were ascribed to lake views for the region (Benson et al. 1998, Bourassa et al. 2004). Although skyline views may be valuable, we do not include them in our analysis since skylines are man-made features and thus do not provide an ecosystem service. For the Rocky Mountains, we designed a more complex model of natural beauty that accounts for vegetation type, landscape and topographic heterogeneity, mountains, and landmarks. The landscape heterogeneity and topographic heterogeniety layers account for the diversity of landcover types and topography (i.e., heterogeneity of the view’s color and texture); data were developed in ArcGIS using the Focal Statistics tool. Valued landcover types include water (most highly valued), followed by coniferous or broadleaf forests. Mountains are denoted using a national land surface forms dataset, and the Geographic Names Information System (GNIS) provided landmark locations.

Aesthetic view sink models. Undesirable visual features, or visual blight, can reduce the quality of views (Benson et al. 1998, Bourassa et al. 2004, Gret-Regamey et al. 2008), acting as a sink in the ARIES modeling framework. In the San Pedro such undesirable features include highways, mines, developed land, and transmission lines (Steinitz et al. 2003). These features are each present on less than 1% of the landscape. In Western Washington, views of lost forest cover, including clearcuts, may also act as a sink, reducing view quality (Wundscher et al. 2008). We assumed that highways or other major roads occupy 2.5% of the landscape, commercial, industrial, or transportation land uses occupy 15%, and clearcuts occupy 2.5% of the landscape for Western Washington. In the Rocky Mountains, we included highways, developed land, and various types of mining or energy infrastructure (e.g., wind turbines, mines, transmission lines, or well pads) and forest disturbance (clearcuts, bark beetle kill areas, or burned areas). We aggregated the types of “Visual Blight” using a NoisyMax node, assuming that the greatest source of blight will override lesser sources of blight. For the San Pedro, we assume that mines have the greatest visual impact, followed by transmission lines and developed land, with highways having the least visual impact. For Western Washington, we assume that clearcuts reduce view quality less than highways, commercial, industrial, or transportation land uses. Although not currently included in the models, dust, air pollution, or persistent cloudy or foggy conditions also reduce views, and could act as sinks at variable temporal scales. These conditions can be simulated in the flow models by changing the decay rates for views.

Aesthetic view use models. The use model for aesthetic views is quite similar to that for proximity, with the exception that we do not use the “Urban Proximity” node. This is because views are potentially equally valuable in urban, suburban, or rural settings. The use model thus simply identifies housing and its value as determinants of use. We assumed the same priors as for the aesthetic proximity use model. The contingent probability table for “View Use” simply states that in order to have value, housing must be present, and that the added value from aesthetic viewsheds is greater for higher-value housing.

Aesthetic view flow models. View flows are simply accounted for through a line-of sight or ray casting model, which is dependent on a digital elevation model. The DEM accounts for cases where topography blocks views. Using top surface LIDAR data instead of elevation would account for the presence of trees and buildings and could more accurately represent obstructions to viewsheds. Since LIDAR data are not always available across the entire study landscape and are often at very high spatial resolution (slowing processing time), we currently rely on DEMs to run the viewshed flow model. The relative view quality of desirable objects in the landscape is projected toward their viewers, as are views of undesirable landscape features. When high-quality views pass through a sink (visual blight) before reaching a beneficiary (housing), view quality is depleted. Steinitz et al. (2003) note that for southeast Arizona, the view of another residential property depletes view quality only within a 0.5-mile radius of the viewer’s perspective (i.e., the effect drops off relatively quickly). Thus, we use a steep decay function to model the effects of sinks (visual blight). Key outputs from the flow models include: 1. Possible views: The flow of aesthetic information (views) from natural areas toward homeowners, when not accounting for sinks. 2. Visible natural beauty: Open space providing views when accounting for lines of sight and the location of homeowners but not visual blight. 3. Homeowners with possible views: Homeowners benefiting from views when sources of high-quality views and their flow paths are accounted for, but visual blight is not. 4. Actual views: The actual flow of aesthetic information (views) from natural areas toward homeowners, when accounting for sinks and flow paths. 5. Enjoyed views: Open space providing views when accounting for flow paths, sinks, and the location of beneficiaries. 6. Relevant visual blight: Areas of visual blight located between visually valuable views and beneficiaries, that actually degrades high quality views. 7. Homeowners with views: Homeowners benefiting from views when accounting for sources of views, sinks, and flow paths. 8. Homeowners without views: Homeowners lacking any views due to their lack of flow connections (i.e., living in areas too flat or distant from high quality views). 9. Blocked views: Flows of aesthetic information (views) toward homeowners that are blocked by visual blight. 10. Degraded natural beauty: Sources of views that are blocked by the presence of visual blight. 11. Homeowners with degraded views: Homeowners who would receive benefits from views but have their views degraded by visual blight.

Spatial data

Acknowldegements and additional contributors

Dave Batker, Jim Pittman, and Paula Swedeen provided data and model review for the Western Washington case study. An expert review panel including individuals from the U.S. Geological Survey, University of Arizona, Bureau of Land Management, and other organizations provided data and model review for the San Pedro case study. Initial ARIES data and models for the Rocky Mountains were developed by students participating in a graduate level ecosystem services modeling course taught in the University of Denver’s Department of Geography in the fall of 2011; James Reed, Darius Semmens, and Todd Hawbaker assisted with further data and model refinement.