Public Benefits Valuation of Dynamic Green Roof Stormwater Retention

Abstract

This study evaluates the public benefits associated with different green roof systems to manage stormwater runoff in Milwaukee, Wisconsin. An internet-based stated-preference conjoint choice experiment was administered to residents of Milwaukee to ascertain the public benefits value of different potential green roof infrastructure programs. This study contributes to the literature on the public benefits of green roofs in two ways. First, this study examined the perceived value of dynamic stormwater retention facilitated using “smart” green roofs with access to real-time weather data versus traditional extensive green roofs. Second, a wider range of public benefits associated with green roofs, including improved water quality, air quality, biodiversity, and urban heat island effects, were estimated. Estimation of these public benefits allows for determination of the optimal public policy for supporting green roofs as a component of decentralized stormwater management in municipalities.

1. Introduction

The creation of impermeable surfaces accelerated by the increasing urbanization of cities alters the natural water cycle by preventing rain from infiltrating the soil. This increases the volume of runoff in urban centers and makes peak runoff events difficult to control with centralized grey infrastructure approaches. The traditional approach is expensive, and it is increasingly difficult to keep up with the growing needs of municipalities, particularly in urban centers with combined sewer systems that manage both waste effluent and stormwater within the same infrastructure. This often leads to overflow events when the stormwater flow is too heavy and inflicts externalized costs to all users of the affected watershed.

Decentralized, low-impact development controls using green infrastructure offer an integrated approach to comprehensive environmental management, and green roofs play a dynamic role within these alternatives [1]. These systems mimic predevelopment ground infiltration wherever possible and the inherent flexibility of these decentralized controls makes them ideal for a whole-system approach to urban stormwater management [2]. Green roofs contribute to solving stormwater management issues by retaining water and delaying runoff, thereby limiting peak flow. In addition to stormwater management, green roof systems contribute to broader social welfare by providing additional public benefits, such as reducing urban heat island effects, improving air quality, and creating urban green space and habitat for wildlife.

The primary public benefit that green roofs provide is reducing combined sewer overflows (CSOs) and improving water quality. Combined sewer systems are relatively common in urban areas and are designed to convey sewage as well as a limited amount of stormwater. When rain falls on bare roofs, streets, and parking lots, the water cannot soak into the ground and is drained through these sewer systems. Increased impervious surface area, which results from increased urbanization, drastically increases the amount of runoff from storms. Stormwater that would have previously been able to soak into the ground, evaporate, or become absorbed by plants becomes runoff water when areas become urbanized. When the sewer system is overwhelmed and overflows, the stormwater is sent to nearby lakes and rivers, carrying trash, bacteria, heavy metals, and waste [3]. CSOs lower the quality of the water where the pollutants are discharged, resulting in external costs being imposed on residents of the area, and are estimated to be a leading cause of pollution in rivers and lakes in the United States [4]. By retaining stormwater, green roofs can delay the runoff, which can prevent sewer systems from overflowing [5,6,7] and can conservatively reduce CSOs by 26% [4].

A second public benefit that green roofs provide is improving air quality. Urban areas are affected by air pollution, which is linked to health issues including coughing, difficulty breathing, and aggravated asthma, as well as increased risk of heart attack and premature death in people with heart or lung disease. Green roofs’ ability to provide cooling and insulation to buildings leads to a reduction in energy consumption, which results in reductions in emissions of nitric oxide (NO_x), sulfur dioxide (SO₂), and carbon dioxide (CO₂). Reductions in these types of emissions can lead to reductions in healthcare costs that come from air pollution [8]. Plants grown on green roofs can also reduce air pollution by absorbing pollutants such as CO₂ as well as generating oxygen and reducing pollutants through the uptake of ozone, NO_2, and SO₂ [9,10].

A third public benefit green roofs provide is reducing the urban heat island (UHI) effect. Urban areas have higher surface and air temperatures because of the use of materials that trap heat and reduce shade. The process of evapotranspiration from the vegetation in green roofs leads to the absorption of heat, and the higher heat capacity compared to conventional surfaces can reduce urban temperatures and reduce the UHI effect. Increased temperatures pose health problems for vulnerable populations, such as the young and elderly, as well as result in increased energy use and greater discomfort outdoors. Standard roofs can have surface temperatures more than 72°F higher than green roofs at midday during the summer months [11,12]. On a hot sunny day, the surface immediately above a standard roof can exceed ambient air temperatures by 90°F or more, with much of that heat transmitted into the building below [3]. Green roofs can decrease the surface temperature of the roof by 86°F to 140°F, thereby decreasing the UHI effect in urban areas [13]. For example, previous literature suggested that replacing 50% of an urban city’s rooftops with green roofs could result in a citywide decrease in ambient temperature from 1.4°F to 3.8°F, depending on whether the green roof is irrigated or not [11].

A fourth public benefit that green roofs provide is the creation of urban “green space”. A lack of natural green habitats creates two known problems in urban areas. First, it contributes to the habitat loss of species such as birds, bats, and bees. These species provide beneficial services, acting as natural insecticides and pollinators, which are then lost. Second, a lack of green space can also increase stress, depression, and anxiety in individuals. Visible green roofs create a more natural environment in urban areas, which can help to improve the physical and mental health of residents [14,15]. Green roof infrastructure can positively impact both problems by simultaneously creating natural wildlife habitats and visible green spaces, which improve well-being.

Estimating the value of these public benefits is increasingly important due to the high costs associated with comprehensive stormwater management and prevention of CSOs. The public costs associated with a green roof program would include installation, building retrofit (if needed), and ongoing maintenance as part of any municipality-level program. Depending on the location and scale of implementation, the costs for public green roof implementation could be substantial. As such, it is critical to estimate and understand individuals’ willingness to pay for the public benefits of green roofs, to assess whether utilizing green roofs as part of a stormwater management program makes sense. Given that grey infrastructure investments located and implemented for similar purposes of eliminating CSOs are also substantial, understanding the value of and individuals’ willingness to pay for the public benefits that a green roof program can provide is important. The difference between a traditional grey infrastructure CSO response (and cost) versus a green roof program CSO response is that the green roof program can potentially generate significant additional public benefits that the grey infrastructure does not, and valuing this difference can allow for a more effective policy assessment [16].

Previous studies have generally estimated the value of public benefits attributable to green roofs using one of two methods. The first method relies on utilizing the value of statistical life and linking changes in pollutants to changes in mortality and morbidity risk. Assuming a statistical life has a certain dollar value (or falls within a range of values), a corresponding dollar value can be determined by reducing the risk of mortality and morbidity for a statistical life. Given that green roofs have the potential to significantly reduce a range of pollutants harmful to human health, this type of method provides a straightforward strategy to assign a dollar value to the human health-related components of the types of public benefits outlined above.

For example, using the value of statistical-life method, improved air quality benefits within the literature have been estimated between $0.00 and $0.59 per meter squared of installed green roof [17,18]. Niu et al. (2010) estimated the CO₂ removal benefits of green roofs to average $3.80 per mg of CO₂ on the low end and $33.70 per mg of CO₂ on the high end [19]. The city of Chicago estimated that the economic benefits of greening only 10% of the city’s roofs could remove 17,400 mg of NO_x per year, potentially avoiding public health costs of $29.2 to $111 million annually [11]. Similarly evaluating only NO_x removal, Mullen et al. (2013) found the overall public health benefit of greening a 2000-m squared roof was between $890 and $3390 per year [8]. One study quantifying the UHI value of green roofs found it to range from $0.0083 to $0.017 per meter squared of installed green roof, while the habitat creation generated from green roofs was estimated to provide a benefit ranging from $0.00–$10.20 per meter squared [18]. The limitation of most of these previous studies was that they often focused on a single benefit (e.g., pollutant reduction) at a time, thereby limiting the economic assessment of public benefit.

The second method relies on stated-preference techniques to estimate the value of these public benefits. This method relies on presenting survey respondents with carefully constructed hypothetical scenarios that are designed to mirror real-world contexts. Survey respondents evaluate the hypothetical scenario and are asked to consider the situation as if it were real. Oftentimes, a change in policy is proposed (e.g., a potential green roof program) and is then presented in a referendum format for which respondents must vote (in favor or against). The policy change not only presents specific potential benefits for respondents but also entails a required cost that respondents must incur to gain those benefits. In these scenarios, respondents are trading off between environmental improvements and the proposed cost (in dollars) of the improvements. Only if the environmental benefits outweigh the costs would the respondent rationally support the program, and from this information, a dollar value can be estimated for the environmental benefits.

Several studies have employed stated-preference methods to value the public benefits associated with green roofs. For example, Zhang et al. (2019), using the contingent-valuation method, estimated Beijing, China, residents’ value for a reduction in the UHI effect (ignoring all other public benefits) and found that citizens were willing to pay $22 per household per year. Kim et al. (2016), using choice experiments, found that respondents in South Korea were willing to pay between $56.68 and $76.59 for every 1m² increase in urban forest, which decreases the UHI effect [20,21]. Vanstockem et al. (2018) found that the appearance and vegetation of a green roof habitat influenced individuals’ perceptions and preferences [22]. More recently, Netusil et al. (2022) used a stated-preference conjoint choice experiment to evaluate multiple public benefits more comprehensively [23]. The benefits examined included CSO, UHI, and biodiversity improvements associated with traditional, extensive green roof implementation in the city of Portland, Oregon. They found that households’ willingness to pay for a new green roof program ranged between $202 and $442, employing a 1-year increase in sewer and stormwater fees. This aggregates at the city level (population ~635,000 in 2022) to a total value of $54.4 to $116.8 million dollars.

This study contributes to the literature on the public benefits of green roofs in two ways. First, the value of dynamic stormwater retention facilitated using “smart” green roofs with access to real-time weather data versus traditional extensive green roofs was estimated in the large urban MSA of Milwaukee, Wisconsin. This builds on the existing literature by examining how individuals’ willingness to pay changes depending on the levels of water retention available through different types of green roofs. Second, a wider range of public benefits associated with green roofs, including improved water retention, air quality, biodiversity, urban heat islands, and water quality, were estimated than in previous studies. Depending on program characteristics, we found that households’ willingness to pay for a new green roof program through an increase in water/sewer fees ranged from $145 to $232 per year on average. This aggregates to values of $138 to $221 million for the entire Milwaukee, MSA.

The remainder of the article is organized as follows: Section 2 discusses the methods employed, specifically the survey design and administration, as well as the conjoint choice experiment used to establish preferences and the theoretical and econometric framework of the model; Section 3 presents the empirical results and welfare analysis; Section 4 discusses these results; and Section 5 concludes.

2. Methods

2.1. Study Area

The Milwaukee MSA provides a unique location for green roof implementation. It is 241.10 square miles in size and contains a population of 951,448 individuals in 381,715 households. The watershed has significant water quality impairments due to nonpoint urban runoff and combined sewer overflows. The Milwaukee area experiences an average of nine days per year of unhealthy air quality for at-risk groups, such as the young, elderly, or those with respiratory conditions. In addition, the Milwaukee area experiences air quality health warnings an average of ten days per year. Biodiversity and green space within the downtown portion of the MSA are limited and on average, residents of the Milwaukee area describe four of their last thirty days as being “poor mental health days”. Lastly, there exists significant potential for green roof implementation in the downtown area. These factors combine to meet many of the conditions that would make green roof implementation on a widespread scale attractive. Figure 1 shows the Milwaukee MSA area, as well as outlines the sewer district planning boundary (purple line) and CSO area (dark red area).

2.2. Data

To establish public preferences regarding any publicly supported green roof program, a stated preference survey was designed and administered to an internet-based panel of Milwaukee MSA residents in 2016 within the sewer-district planning boundaries. The survey was administered in collaboration with Survey Sampling International (SSI). They provided a sample of respondents who were drawn from their internet panel who lived in the Milwaukee MSA and met the study requirements. The survey was coded May 2016 in Qualtrics Survey Software and distributed to the panel of respondents via SSI, who tracked progress participation and incentivized completion. A total of 542 responses were obtained through the internet survey sample from 643 individuals who were asked to participate (yielding an 84.3% effective response rate).

Sample and population statistics are presented in

Table 1. Socio-demographic Characteristics.

Variable	Sample Mean	Population Mean
Age (Median)	40.7	34.2
Income (Household)	$63,797	$43,873
Gender (Female)	68%	51.7%
Race  (White)  (Indian)  (Black)  (Asian)  (Hawaiian)  (Latino)	84.9% 0.9% 7.7% 2.6% 0.6% 3.2%	65.1% 1.0% 27.1% 4.2% <0.5% 14.5%
Education  (HS<)  (BS<)	99% 41%	86.5% 29.1%
Homeowner	58.5%	49.9%

. In the Milwaukee population, 51.7% of individuals were female, with a mean age of 34.2 years. Of the population, 86.5% had completed a high school education or higher, with 29.1% having completed a bachelor’s degree or higher. The median income was $43,873. Of the population, 61.5% were white and 49.9% were homeowners. In the sample, 68% of the respondents were female, with a median age of 40.8 years. Of the respondents, 99% had completed a high school education or higher, with 41% having completed a bachelor’s degree or higher. The median household income was $63,797. Of the respondents, 84.9% were white and 58.5% were homeowners. As can be seen, the panel was more educated, wealthy, white, female, and older than the overall population. These results likely come from the sample being derived from SSI’s internet-based online panel. Although designed to mimic the MSA population characteristics, the nature of the outreach (through an online panel) likely resulted in a wealthier, more educated panel of respondents. As such, the results in terms of generalizability to the overall population should be interpreted cautiously.

To get the survey respondents to begin thinking about green roof infrastructure and to gauge their experience regarding water-related topics, they were asked several lead-in questions. Only 4.5% of the sample respondents lived in a flood plain, but 23.5% of the respondents had experienced issues with flooding at their residence in the last 5 years. Of the respondents, 36% had knowledge of green infrastructure prior to taking the survey and 86% thought that the use of green infrastructure was very or somewhat important for helping with issues of water management. Of the respondents, 27% believed that combined sewer overflows are currently the greatest threat to local water quality, while 39.8% thought the greatest threat is polluted stormwater runoff. Of the respondents, 87.6% believed that everyone has a role to play in maintaining or improving water quality, while 4% believed it is the government’s responsibility, and 2.4% believed that they have no impact. The mean and median water/sewer payments were $57.84 and $100.00 per month, respectively.

2.3. Conjoint Choice Experiment

To ascertain residents’ preferences on the public benefits generated by green roof installations as well as their willingness to support public investment, a conjoint choice experiment was administered as part of the survey. A series of choice scenarios were designed to estimate trade-offs between the attributes describing different green roofs and the public benefits that would be generated from their installation. To obtain the benefits presented, these roofs would need to be installed on a sufficient surface area of roofs (estimated at 30%) in Milwaukee (focused in the urban downtown on commercial buildings) and would result in increased water/sewer fees. A “choice scenario” consisted of three alternatives, two of which represent different potential green roof programs and a third “opt-out” alternative for simply maintaining the current status quo outcomes associated with bare roofs. The alternatives were defined over six attributes: water retention, air quality, temperature effect, biodiversity, water quality, and payment. The possible levels these attributes can take on are summarized in

Table 2. Choice Experiment Attributes and Levels.

Attribute	Levels
Water Retention	99% water retention 95% water retention 73% water retention 4% water retention
Air Quality	3-Day reduction in unhealthy air days/year 2-Day reduction in unhealthy air days/year 1-Day reduction in unhealthy air days/year No change in number of unhealthy air days
Temperature (Urban Heat Island)	6°F reduction in average ambient air temp. 4°F reduction in average ambient air temp. 2°F reduction in average ambient air temp. No change in average ambient air temp.
Biodiversity	Restores habitat and provides visible greenery No change in habitat or visible greenery
Water Quality	Highest quality (blue) Higher quality (green) Lower quality (yellow) Lowest quality (red)
Payment	$0, $12, $18, $24, $30, $60, $90 or $120 per year

.

The first attribute, water retention, took on four levels: 4%, 73%, 95%, and 99%. These levels were chosen to correspond to actual bare and green roof water retention values. A standard (bare) roof is made of shingles, tile, concrete, or steel and retains virtually no water (4%) when it rains. A traditional, extensive green roof retains 73% of water falling on the roof when it rains. Another higher performance, extensive green roof has a larger water storage layer, where 95% of water falling on the roof is captured when it rains. Lastly, a “smart” extensive green roof has a computer control mechanism for water release, where 99% of water falling on the roof is retained when it rains, and this roof uses weather predictions to decide when to release water. When rain is predicted, the roof releases water from its storage layer before it rains to maximize storage for upcoming rain. Virtually no water is sent to the sewer system when it rains. All retained water is stored and used to irrigate the plants. This most advanced green roof can dynamically respond to changing weather conditions, thereby maximizing its ability to mitigate or avoid CSOs and improve water quality.

The second attribute was air quality, which also took on four levels. This attribute described the green roofs’ ability to reduce the number of days with air quality classified as “Unhealthy for Sensitive Groups” by an average of no days, 1 day, 2 days, or 3 days per year.

The third attribute presented was the temperature effect and was defined over four levels. This attribute described the green roofs’ ability to reduce the average ambient air temperature in the Milwaukee area by 0° (no change), 2°, 4° or 6° Fahrenheit (F).

The fourth attribute, biodiversity, took on two levels. The first level indicated the green roofs’ ability to improve biodiversity and aesthetics by restoring habitats for birds and other species and adding visible green space. The second level indicated the status quo that no change in biodiversity or visible greenery may occur.

The fifth attribute, water quality, also took on four values: lowest, lower, higher, and highest quality. The lowest water quality level described water that was very murky and where algae had spread, contained no fish that could survive, and contained few birds; the water was not safe for swimming, fishing, boating, or pets, and water contact could be hazardous to human and animal health. Lower water quality levels contained water that was murky and slightly green, with some algae, no game fish and a few coarse fish, but was a habitat for common, local birds; the water was not safe for swimming, but was safe for fishing, boating, and pets. Higher water quality levels contained water that was less clear but contained no algae, a few game fish, and abundant coarse fish, was a habitat for local birds, and was safe for boating, fishing, swimming, and pets. The highest level of water quality had water that was clear, with healthy plants and no algae, contained game and coarse fish, and was a habitat for common, local birds; it was again safe for boating, fishing, swimming, and pets.

Lastly, the payment attribute was defined over eight levels. The values were determined based on a small (1.7%) to large (17%) percentage change of the current mean payment following best practices in the environmental valuation literature. Respondents were informed that an increase in water/sewer fees would be necessary to install, operate, support, and/or maintain green roofs to receive the benefits. Depending on the program, the increase in their monthly payment could be $1, $1.5, $2, $2.5, $5, $7.5 or $10. These amounts would correspond to an annual increase in water/sewer fees of $12, $18, $24, $30, $60, $90 or $120, respectively. Alternatively, the status quo would maintain water/sewer fees at current levels and as such, there would be no change ($0) in the current payment.

The conjoint choice experiment was conducted to elicit residents’ relative preferences regarding these different attributes that make up the change in public benefits associated with green roof implementation. By observing residents’ choices among the alternatives, the preference relationship regarding each attribute could be established. In an ideal setting, each respondent would face all possible choices between alternatives described by the attributes in Table 2. Unfortunately, a 4 × 4 × 4 × 4 × 2 × 8 experimental design would result in 4096 possible combinations of attributes to describe different possible green roof programs. A survey representing all combinations was practically impossible to administer and presented a cognitively challenging task for respondents. The well-established experimental design literature was used to simplify the experiment, without loss of information. The experimental design related the designated attributes and their various levels using a systematic and planned process through which the attributes and their levels were pre-defined without measurement error, and then varied to create choice alternatives [24]. Each resulting choice alternative represented a different potential green roof program.

A C-optimal design was constructed using the Ngene 1.1.2 software to maximize the recovery of willingness-to-pay estimates [25]. C-optimality resulted in a set of choices for residents that would be dissimilar enough, and non-overlapping, so respondents could more easily decide which program they would prefer. Some trade-offs were made between orthogonality and statistical efficiency to maximize the information obtained in each choice scenario and prevent duplicate or dominated alternatives from occurring. The inclusion of a “baseline” scenario was another necessary trade-off that allowed individuals to have an “opt-out” or “no-change” option within the choice set. The status quo alternative fitted the current profile for variables in the Milwaukee MSA. The variables were as follows: bare roof, no change in number of unhealthy air days, no change in average ambient air temperature, no change in habitat or visible greenery, and lowest water quality rating (red), with no resulting change in water/sewer payment. This was important for maintaining unbiased parameter estimates [26].

The experimental design results in twenty-four choice scenarios, which is still too large to expect any individual resident to be able to complete consistently. As such, the design was divided into six blocks with each block containing four choice scenarios. Each respondent was then presented with one of the six blocks containing that block’s four selected choice scenarios from the twenty-four available. This was a reasonable number of choice scenarios for a single individual to complete, based on the survey and experimental design literatures and still allowed for population-level parameters to be estimated [27,28]. An example of a choice question format is seen in Figure 2.

2.4. Statistical Model

Residents’ responses to the questions in the choice experiment yielded the preference structure for the attributes. The choice between alternatives was assumed to be driven by respondents’ underlying utility. The utility function had two components (deterministic $\overline{V}\left(x_{ij} , \beta \right)$ and stochastic ${\epsilon }_{ij}$) and was therefore embedded in a standard random-utility framework [29] denoted by (1),

$$U_{ij}=\overline{V}\left(x_{ij} , \beta \right)+{\epsilon }_{ij}$$

(1)

where subscript i denotes the individual, subscript j denotes the alternative, x is the vector of attributes that vary across alternatives, and ${\epsilon }_{ij}$ is a stochastic error term capturing individual and alternative specific factors influencing utility unobservable by the researcher. The model was further formalized by assuming that the deterministic portion of utility could be approximated as a linear function of attributes, was additive over individuals, and can be represented by (2),

$$U_{ij}={\beta }_0+x_{ij}{\beta }_l+\left(M_i+p_{ij}\right){\beta }_M+{\epsilon }_{ij}$$

(2)

where $M_i$ is individual i’s income and $p_{ij}$ is the payment faced by respondent i under the alternative profile j. The coefficient on the residual income, ${\beta }_M$, is the marginal utility of income. The marginal price for a specific attribute was derived solely with respect to a change in that attribute. After estimating the common utility function, the marginal price for attribute l was obtained by normalizing the marginal utility estimate of attribute l by the negative inverse of the marginal utility of income to yield,

$${MP}_l=-\frac{{\widehat{\beta }}_l}{{\widehat{\beta }}_M}$$

(3)

where MP_l represents marginal price of attribute l, ${\widehat{\beta }}_l$ is the estimated coefficient on attribute l, and ${\widehat{\beta }}_M$ is the estimated marginal utility of income.

The probability, P_ij, of a respondent, i, choosing an alternative, j, was given by U_ij > U_ik and can be denoted as,

$$P_{ij}={Pr\left(V_{ij}+{\epsilon }_{ij}>V_{ik}+{\epsilon }_{ik}\right)=Pr\left({\epsilon }_{ij}-{\epsilon }_{ik}>V_{ik}-V_{ij}\right)}_{ }$$

(4)

Statistical analysis of the choice experiment proceeded by estimating the utility difference model using the random parameters logit estimator. The random parameter logit model assumed stochastic variation in the preference structure, so that each individual, i, had a unique ${\beta }_i$ for one, some, or all the attributes, and these parameters were distributed in accordance with certain conditions in the population. When the generalized extreme value distribution is assumed to be the probability distribution of the error term, and f(β|θ) is the density function for a given distribution of β with parameter θ (i.e., means and distributions) the choice probability can be expressed as,

$$P_{ij}=\int \frac{\exp V_{ij}}{\sum \exp V_{ik}}(\mathsf{\beta })\mathrm{f}(\mathsf{\beta }|\mathsf{\theta })d\mathsf{\beta }$$

(5)

A continuous distribution, such as the normal, is assumed for f(β). The selection probability becomes P^* using simulated maximum likelihood procedures. R represents the number of draws with β^r representing the r^th draw from the density function. This results in a simulated probability of,

$${P^{\ast }}_{ij}=\frac{1}{R} {\sum }_r{P}_{ij}\left({\beta }^r\right)$$

(6)

which is used to estimate the simulated log likelihood function (LL^*) and the parameter θ which defines the distribution that maximizes this function. Given d_ij is a dummy variable representing respondents’ choices and is set to 1 when alternative j is chosen, the simulated log likelihood is estimated as,

$${\mathrm{LL}}^{\ast }={\sum }_i{\sum }_j{d}_{ij}\ln \left(P_{ij}^{*}\right)$$

(7)

The distribution function, which quantifies the variability in preferences found between respondents, could be derived from these calculations [29]. Since the random parameters logit did not guarantee global concavity, multiple starting values were evaluated to determine whether the final estimated coefficients were true maximums.

To establish the willingness-to-pay (WTP) for residents to choose a green roof program over the status quo, the indirect utility function described in (2) was calculated for different potential programs and then equated to the indirect utility associated with the status quo option of no program (with attribute values denoted as x₀) and solved for WTP in (8).

$$x_j{\widehat{\beta }}_l+\left(M-{WTP}_j\right){\widehat{\beta }}_M=x_0{\widehat{\beta }}_l+\left(M\right){\widehat{\beta }}_M$$

(8)

Here, x_j represents the vector of attribute values describing the listed green roof programs, $\widehat{\beta }$_l is the vector of estimated attribute parameters, and ${\widehat{\beta }}_M$ is the estimated marginal utility of income. Solving for WTP_j yields (9), where Δx is the difference between the proposed green roof program and status-quo attribute levels.

$${\mathrm{WTP}}_{\mathrm{j}}=\frac{{(\Delta x)\widehat{\beta }}_l}{{\widehat{\beta }}_M}$$

(9)

3. Results

Given each of the 542 respondents faced four choice scenarios, a maximum of 2168 choice scenarios could be recovered. After cleaning the data and eliminating scenarios where a respondent failed to make a choice, 1994 complete choice scenarios comparing 5982 alternatives remained.

The conjoint choice experiment provided important insight into which attributes were relevant to residents’ decision-making regarding green roofs and their associated public benefits. All the variables had well-defined expectations regarding signs. Respondents were expected to prefer higher levels of water retention (indicating an expected positive sign on water retention). Respondents were expected to prefer greater reductions in poor air days (indicating an expected positive sign on air quality). Respondents were expected to prefer greater reductions in ambient temperature (indicating an expected positive sign on temperature). Respondents were expected to prefer more biodiversity and visible greenery (indicating an expected positive sign on biodiversity). Respondents were expected to prefer higher levels of water quality (indicating an expected positive sign on water quality). Lastly, respondents were expected to prefer lower payment levels (indicating an expected negative sign on payment).

The results of three random parameters logit estimators are presented in

Table 3. Random Parameters Logit Estimates.

Variables	Model 1	Model 2	Model 3
Water Retention	0.008 ***	0.008 ***
(base:4%)	(0.001)	(0.001)
73%			0.669 ***
			(0.151)
95%			0.979 ***
			(0.157)
99%			0.801 ***
			(0.128)
Air Quality	0.077 ***	0.066 **	0.045
(base: no change)	(0.026)	(0.027)	(0.030)
Biodiversity	0.259 ***	0.229 ***	0.201 **
(base: no change)	(0.050)	(0.055)	(0.061)
Water Quality	0.306 ***
(base: lowest quality)	(0.026)
Lower Quality		0.464 ***	0.352 ***
		(0.103)	(0.116)
Higher Quality		0.848 ***	0.826 ***
		(0.114)	(0.114)
Highest Quality		0.905 ***	0.836 ***
		(0.080)	(0.089)
TemperatureR	0.002	−0.001	−0.008
(base: no change)	(0.014)	(0.014)	(0.014)
Payment	−0.009 ***	−0.009 ***	−0.009 ***
(base: $0)	(0.001)	(0.001)	(0.002)
N	5982	5982	5982
Likelihood Ratio Test	0.00	0.00	0.00
Log-Likelihood	−1942.90	−1940.09	−1937.59

(a) The alternative specific constant on the status quo was tested and was not significant. (b) Coefficients are the marginal effects with standard errors in parentheses below. (c) Significant at the 95% level (**) and 99% level (***). (d) “R” indicates that the variable was specified as a random parameter.

below. Well-known limitations to conditional logit estimators (such as the IIA property) often necessitate the use of more flexible models, including the random parameters logit, which relaxes restrictions on the error term imposed by the conditional logit. Model 1 is the base model with all attributes included in a simple linear fashion. Model 2 introduces non-linearity in the water quality estimates, while Model 3 adds non-linearity in both the water quality and retention estimates.

Results across all model specifications were generally consistent and conformed to expectations—with one exception. Improvements in water retention, water quality, and biodiversity were uniformly positive, and statistically significant at the 99% level, regardless of the model specification. These results indicate that respondents have strong preferences for improvements in water retention (CSO reduction) and water quality in the region, as well as improvements in biodiversity and green space. Air quality was also positive and statistically significant across the first two model specifications (although it is insignificant in the third). The temperature attribute was statistically insignificant across all model specifications. This indicates that respondents did not value the temperature reduction benefits and were not concerned with UHI effects in the Milwaukee MSA. These results provided evidence that residents preferred improvements in all categories of public benefits except the UHI effect. The payment attribute was negative and statistically significant across all specifications, indicating that residents preferred lower payment levels.

The non-linear changes in water retention demonstrated the public benefits value of additional retention provided by “smart” green roofs relative to traditional extensive green roofs. The “smart” green roof provides the best water retention of all extensive green roof options and respondents did, on average, have a positive willingness-to-pay for this greater retention capacity relative to the baseline retention level of 4%. However, individuals also have a positive willingness-to-pay for both traditional extensive green roofs with 73% as well as 95% retention capacity. Individuals placed a marginal price of $74 for 73% retention, $109 for 95% retention, and $89 for 99% retention (holding constant the impact the water retention capacity had on other associated public benefits such as biodiversity, air quality, or water quality). This indicates that the added retention capacity provided by “smart” green roofs relative to traditional green roofs with deep reservoirs was not viewed as providing significant additional benefit, although it did offer more benefit than a green roof with a standard reservoir capacity. This indicates that the value individuals place on increased retention increases, but at a decreasing rate over these levels of retention, and then declines. This is informative because if “smart” green roofs with their inherent technological requirements led to higher installation, operation, and maintenance costs, these results showed that the marginal increase in water retention was not valued as strongly by respondents over a traditional green roof program with expanded reservoir capacity (ceteris paribus).

The non-linear changes in water quality were also interesting to examine to see how much more individuals were willing to pay for higher levels of quality, and whether this willingness to pay diminished at the highest margins. For example, the value of moving from lowest to lower quality was different than the value of moving from lowest to higher quality. Additionally, the value of moving from lower quality to higher quality, or higher quality to highest quality, was also different. Utilizing a single parameter caused the effect to be averaged, so moving from lowest quality to lower quality to higher quality to highest quality had the same value. The results of Models 2 and 3 both showed for water quality that moving from lowest to lower quality had a much higher value compared to moving from lower to higher and higher to highest quality (where both qualities were good). These results are as expected—individuals are willing to pay a larger amount to move from lowest to lower or lowest to higher quality but are not willing to pay as much for the smaller improvement of moving from higher to highest quality.

The WTP in dollars for the implementation of programs are listed in

Table 4. Willingness-To-Pay.

Attribute	Est. Coef.	Marginal Price ($)	Program A	Program B	Program C
Water Retention	0.008	0.89 (per % improved)	99% (95% improvement)	95% (91% improvement)	73% (69% improvement)
Air Quality	0.066	7.33 (per day reduced)	3-day reduction	2-day reduction	1-day reduction
Biodiversity	0.229	25.44	Improved	Improved	Improved
Water Quality
:lower	0.464	51.56			Lower quality
:higher	0.848	94.22		Higher quality
:highest	0.905	100.56	Highest Quality
Payment	−0.009
Average WTP/Per Person/Per Year:			$232.44	$215.22	$145.67
Total Benefits (Population = 951,448):			$221,158,801	$204,772,752	$138,594,258

using the parameter estimates from Model 2 in Table 3. The coefficient estimates from Models 1 or 3 could also be used to perform these calculations and both the marginal price and aggregate WTP results were quantitatively similar. These values indicated the average resident’s WTP, in dollars, to support the implementation of the indicated green roof program when it resulted in the stated benefits. WTP for each green roof type (relative to the status quo) was explored. Temperature was excluded, as no value or preference was attached to the attribute. Each green roof type and corresponding program resulted in distinct levels of improvement in the public benefits attributes because of its underlying properties, as described earlier in the paper. The average WTP per person per year, as well as the average population benefits, are also included in Table 4.

The marginal price of water retention was estimated at $0.89 indicating that Milwaukee residents valued each additional percentage point of water retention increase beyond the status quo (4% retention) at $0.89 (on average). The marginal price of air quality was estimated at $7.33 for every additional day of improved air quality per year (i.e., days of bad air quality reduced) beyond the status quo (no change in air quality days). Since the coefficient on temperature was insignificant, the marginal price could not be determined and was excluded; Milwaukee residents did not find value in having a reduction in the UHI effect (ceteris paribus). The marginal price of biodiversity was estimated at $25.44, which was the value that Milwaukee residents placed on having an increase in biodiversity (versus no increase, the status quo). The marginal price of increasing from the status quo (lowest) quality of water to the lower quality of water was valued at $51.56; increases from the status quo to higher quality of water were valued at $94.22; and increases from the status quo to the highest quality of water was valued at $100.56. These results show us that individuals did have a higher willingness to pay for bigger improvements in water quality; however, the value that residents placed on these improvements diminished as higher levels of water quality were achieved. This reinforces that the results are reliable, and respondents appear to have answered the survey questions rationally.

Considering all these public benefits, the average WTP per person per year for the traditional, extensive green roof program was $145.67 with a total population benefit estimated to exceed $138 million. For the expanded water retention program, the average WTP per person per year increased to $215.22, which equates to a total population benefit per year exceeding $204 million. Lastly, the average willingness-to-pay per person per year for the advanced water retention program increased to $232.44 in our sample. This would extrapolate to a total population benefit exceeding $221 million per year. Given the sample differences from the total population, these aggregate benefits should be interpreted cautiously. Given the higher average income of the sample, it is possible that these figures may overestimate the true WTP in the population. In addition, the total population benefits are the gross benefits if the Milwaukee MSA achieved the public benefits presented through the implementation of the proposed green roof infrastructure program. To determine feasibility, the public cost of these water retention programs would also need to be examined to assess the net benefit of implementation.

4. Discussion

These results provide important insights into the value of the public benefits provided by green roofs. The results clearly demonstrated that the associated public benefits of green roofs were highly valued by the public (particularly water quality improvements). Utilizing green roofs in urban areas with a substantial amount of flat roof space, as well as significant issues with CSOs may provide not only improvements to CSO avoidance and water quality, but additional benefits in terms of cleaner air and creation of urban green space and wildlife habitat. This implementation could potentially be done as an alternative to large-scale, expensive grey infrastructure investments.

The cost of a green roof program is still an important consideration. This study focuses solely on the value of public benefits provided by green roofs. Public benefits associated with green roofs are only one component of the overall equation that may determine the net social benefit of a comprehensive green roof public policy. Important considerations must also be given to public costs associated with program implementation. To determine the full net social benefit, a comprehensive cost and risk assessment associated with installation, building retrofit (if needed), and maintenance needs to be performed. Estimation of these costs provides an important future research opportunity and is essential for determining whether it makes sense from a social perspective to proceed with a comprehensive green roof program in the Milwaukee MSA. However, the difference between a traditional grey infrastructure CSO response (and cost) versus a green roof program CSO response is that the green roof program can potentially generate significant public benefits. These results demonstrate the importance of these benefits to the public, and their provision as part of a broader public policy program may allow that program to pass a social cost-benefit test where a comparably priced grey infrastructure program does not.

5. Conclusions

This study provides empirical estimates of the value placed on the most important public benefits associated with green roof implementation. Specifically examined here are the potential gains in water retention available with different extensive green roof types relative to each other and traditional grey infrastructure. According to the value associated with the public benefits that come with green roofs found in this study, green roofs should be given priority relative to grey infrastructure investments which achieve the same CSO reduction and have the same construction cost. With both green and grey infrastructure investment, the cost of any program implementation would need to be seen as acceptable relative to the benefits produced.

The public benefits associated with green roofs make them an attractive low-impact development option to replace grey infrastructure to reduce combined sewer overflows and improve water quality ceteris paribus. The results provide evidence that Milwaukee MSA residents prefer improvements in all these categories of public benefits, except impacts to the UHI effect. Improvements in water retention (which reduces CSOs) and water quality are valued most highly, followed by biodiversity and air quality. The WTP estimates arrived at can provide useful policy information to municipal governments and water utilities. These insights can help in setting subsidies for private green roof installation and/or creating a program to embark on public installation and maintenance of green roofs in urban downtown areas [30].

Decentralized approaches to stormwater management, such as green roofs, do generate valuable public benefits as highlighted in this study. There are factors that slow down or prevent such low-impact development options, including the costs of construction, training personnel, changing local business codes, construction on private property, monitoring and enforcement changes, and fear that these solutions will provide insufficient protection during extreme storms. Future research should prioritize the study of these factors and their impacts on implementation. In addition, further investigation across different contexts and green roof performances should be undertaken to demonstrate their value and potential for implementation as a more sustainable stormwater management practice.