Optimizing nature-based solutions by combining social equity, hydro-environmental eﬃciency, and economic costs through a novel Gini coeﬃcient

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Introduction
Nature-based solutions (NBS) describe a collection of sustainable management approaches that emulate natural processes to address hydro-environmental hazards while simultaneously providing social and ecosystem benefits. NBSs have evolved within the literature to encompass the urban drainage concepts of green infrastructure (GI), low-impact development (LID), best management practices (BMPs), sustainable urban drainage systems (SuDs), water-sensitive urban design (WSUD), and blue-green infrastructure (BGI) (Ruangpan et al., 2020). As such, the predominant modeling schemes used for NBS planning have typically highlighted hydrological efficiency with less attention to social characteristics (K. Zhang & Chui, 2018). However, we know that the location of human settlements can influence several social factors that have been linked to NBS co-benefits, such as improvements in communal well-being, mental health, recreation, and physical health (Alves et al., 2019;Fenner, 2017;Li et al., 2017). By providing enhanced greenspaces and social gathering places, NBSs have been linked to a reduction in cardiovascular disease, diabetes, cancer, mental disorders, and chronic respiratory diseases, which are disproportionately higher among racial and ethnic minorities and the socioeconomically disadvantaged (Astell-Burt & Feng, 2021;Brown et al., 2016;Fuertes et al., 2014;Gascon et al., 2016;Maas et al., 2009;Mitchell & Popham, 2008;Ray & Jakubec, 2014). As such, we must integrate hydro-environmental and social characteristics to realize the full benefits of NBSs.
At the local scale (i.e., laboratory-, plot-, neighborhood-scale), NBS technologies have shown great promise in addressing both stormwater abatement goals and socio-environmental cobenefits (Jato-Espino et al., 2016;Kabisch et al., 2016;Loperfido et al., 2014). At the regional scale, however, widespread use of NBS technologies has been limited due to a lack of understanding the complex interactions between physical characteristics and social conditions (Lim & Welty, 2017;K. Zhang & Chui, 2018). When planning for NBS systems, there will exist inherent tradeoffs between spatial priority and functionality that must be considered. The optimal spatial configuration of an NBS system is a function of overlapping rainfall patterns, watershed properties, equity factors, environmental triggers, ecological considerations, socio-demographics, risk and vulnerability, and other underlying principles that have not been fully elucidated (Perez-Pedini et al., 2005). Traditionally, NBS optimization schemes have continued to prioritize drainage characteristics in lieu of social functionality throughout space, while assuming such co-benefits will somehow propagate naturally throughout the system (Ruangpan et al., 2020;K. Zhang & Non-peer reviewed EarthArXiv preprint. Under review by Water Resources Research Chui, 2018). In this way, NBS multi-functionalities are not included as an explicit representation of their full locational benefits, thus limiting the maximum potential of NBSs to mitigate crosscutting issues within the urban fabric. A right first step toward fully encompassing NBS multifunctionalities is to represent disparate phenomena as functions of space and to quantify their tradeoffs through the lens of overlapping disciplines.
In the age of the Anthropocene, where hydrologic, environmental, and social processes are being influenced and altered by human patterns, we are starting to study Earth systems outside of the traditionally-fixed vacuum of ideal physical boundary conditions. Researchers are beginning to couple biophysical processes with societal influences through the flourishing fields of sociohydrology, coupled human and natural systems (CHANS), socio-ecology, and others (Blair & Buytaert, 2016). The hydrological community is suggesting that we address socio-environmental justices by integrating transdisciplinary variables into watershed modeling frameworks. Much of the recent progress in socio-hydrology has evolved from a combination of exploratory frameworks (i.e. feedbacks, causal relationships, patterns) with water balance models and system dynamics (Kuil et al., 2016;Pande & Sivapalan, 2017). While such couplings have been widely noted within the literature, they are seldom quantitated and considered holistically in NBS management frameworks (Ruangpan et al., 2020).
NBS systems are instead typically planned with either simplified data-overlay methods for defining hot-spots of vulnerable locations or complex hydro-dynamic programs that prioritize stormwater volume abatement over social functionalities (Madureira & Andresen, 2014;K. Zhang & Chui, 2018), with the latter being limited in their scale of analysis due to large data requirements and computational difficulties (Barco et al., 2009). By relying on complex modeling tools (i.e., SWMM, MIKE-URBAN), most NBS studies have tended to neglect the social dimension altogether in favor of earth-system processes, thereby lacking optimal configurations for capturing holistic co-benefits (Kandakoglu et al., 2019). For these reasons, widespread adoption of green infrastructure has generally remained stunted, despite the ongoing evidence that NBSs provide efficient stormwater mitigation, lower costs in comparison to traditional grey infrastructure, and numerous social benefits (Golden & Hoghooghi, 2018;Madureira & Andresen, 2014). A recent state-of-the-art review described how consideration of multiple co-benefits has been increasingly valued as a desirable goal throughout the NBS literature, yet the majority of NBS planning has continued to prioritize stormwater abatement, due in part to a lack of integrated socio-hydrological Non-peer reviewed EarthArXiv preprint. Under review by Water Resources Research frameworks (Ruangpan et al., 2020). We thereby have substantial knowledge gaps regarding informed NBS optimization (Golden & Hoghooghi, 2018;Kabisch et al., 2016), as interactions between NBS phenomena and the social conditions with which they aim to address are poorly represented in our existing frameworks (Lim & Welty, 2017). As such, explicit representation of the social co-benefits of NBS systems is one of the most critical barriers to overcome for widespread success in this field (Adib & Wu, 2020).
In addition to a lack of robust representation of social characteristics within NBS optimization frameworks, the decision to implement NBS within a given locale is also highly dependent on stakeholder buy-in (Van de Meene et al., 2011;Wihlborg et al., 2019). NBSs are unlike traditional stormwater infrastructure due to regular human interaction with greenspace, which impacts social well-being. Many NBS technologies, such as roof gardens or rainwater harvesting systems, function as an optimal unit when implementation occurs on both public and private properties. In this respect, local community buy-in is essential for achieving widespread NBS adoption. Studies have demonstrated how NBS implementation continues to be limited due to the inability for decision-makers to visualize overlapping co-benefits at the local scale (Adib & Wu, 2020;L. Liu & Jensen, 2018;Van de Meene et al., 2011;S. E. Sarabi et al., 2019;Wamsler et al., 2020;Wihlborg et al., 2019). Studies have also shown that attitudes regarding NBSs are improved when stakeholders can readily identify how NBS solutions will benefit their locale in a manner that extends beyond stormwater performance (L. Liu & Jensen, 2018;S. Sarabi et al., 2020;Wamsler et al., 2020). In other words, robust NBS implementation will not occur until city planners are able to identify and prioritize the multiple co-benefits involved in the NBS system.
As such, in order to fully capture the multi-functionalities of NBS systems and improve implementation, we necessitate innovative optimization frameworks encompassing the variety of physical and social functionalities associated with NBSs.
Current stormwater management within the study area (Houston, Texas, USA) is based on a 'worst-first' framework (Despart, 2019), where hydrological improvements are prioritized according to flood risk reduction and the number of persons benefited, irrespective of their socioeconomic conditions. Such frameworks do not address inherent vulnerabilities within the populations served to consider human aspects, such as ability to recover from a storm or the reinforcing impacts of hydro-environmental hazards on socio-economics. This study re-shapes the NBS planning process by transcending beyond flood risk to also include components of social Non-peer reviewed EarthArXiv preprint. Under review by Water Resources Research characteristics as a policy-making mechanism. Here, a novel equity-based indexing framework is proposed to better understand how we might optimize social and physical functionalities of NBS systems as a function of trans-disciplinary characteristics. Specifically, this study explores the spatial tradeoffs associated with NBS allocation by first optimizing a local watershed-scale model according to traditional metrics of efficiency (e.g., cost efficiency, hydrological runoff reduction, and pollutant load reduction). The statistical dispersion of social vulnerability is then identified using the Area Deprivation Index (ADI), which is a spatial account of neighborhood disadvantage according to United States census characteristics. The ADI is incorporated into the optimization scheme using a novel area Gini coefficient and Lorenz curve. This framework is intended to spur the positive connection of social and physical influences within robust NBS planning.

Area Deprivation Index
The ADI was introduced in 2016 as a proxy indicator of socio-economic status from census results that have been curated to reflect the highest risk factors associated with long-term health (Knighton et al., 2016). The ADI is primarily used within the medical literature to measure social determinants that have been shown to influence public health issues, such as cancer rates (Kurani et al., 2020), hospital admissions (Hirshberg et al., 2019;Ingraham et al., 2021), asthma (Nkoy et al., 2018), obesity (Ludwig et al., 2011), diabetes (Addala et al., 2021), mental health (Martikainen et al., 2004), and mortality (Chamberlain et al., 2020;Singh, 2003), each of which are impacted by NBS systems (van den Bosch & Ode Sang, 2017). The ADI merges characteristics of income, employment, education, and housing from the United States census to represent social disadvantage (Kind & Buckingham, 2018), which have been shown collectively to influence communal health (Link & Phelan, 1995).
An advantage of using the ADI for NBS planning, as opposed to other social indices, involves its highly-granular geospatial scale. The ADI provides a unique measurement of social deprivation for each census block group within the United States. Other standard metrics of social vulnerability, such as the Center for Disease Control (CDC) Social Vulnerability Index (SVI) (Flanagan et al., 2020), are delineated at the census tract-scale, thereby lacking spatial heterogeneity to assess key differences between neighborhoods.

Hydrological Modeling
The basin model for the WOB watershed was initialized using the HMS-PrePro tool, which rapidly delineates a watershed into subcatchments according to the local terrain, connects hydrological topology in a format consistent with standard hydrological modeling software, and estimates common hydrological parameters to represent basin infiltration, runoff, and channelized routing of flow (Castro & Maidment, 2020). The Green-Ampt method was used to represent The time of concentration for each subcatchment was calculated using the TR-55 methodology for curve estimates a frequency of occurrence for extreme precipitation events, which is commonly used to design urban stormwater infrastructure (Koutsoyiannis et al., 1998).

Pollutant Load Modeling
The event mean concentration (EMC) method was used to estimate non-point water pollution within each subcatchment according to where is the event mean concentration, is the standard concentration of a target pollutant, and is the runoff volume for each subcatchment, , changing over simulation time, .
Local stormwater monitoring data was obtained from the National Stormwater Quality Database (NSQD), which contains public water quality meta-data from over 9,000 runoff events for approximately 200 municipalities in the United States, including 41 monitoring stations within Harris County, Texas (Pitt et al., 2015). Since the GreenPlan-IT algorithm searches for the most cost-effective solution according to an individual pollutant type (further described in Section 2.3), total suspended solids (TSS) were chosen as the criteria pollutant due to the strong adsorption effects of TSS on other contaminants (Yang Liu et al., 2019;Rossi et al., 2006). Pooled values of TSS concentrations were obtained for each land use type within the NSQD, as summarized in  not been shown to pose a significant impact on the resulting model outcomes, particularly when the purpose of analysis is for comparison between scenarios (Lin, 2004;M. White et al., 2015).
The land use values in the WOB basin model were obtained from the 2016 National Land Cover Database (NLCD), which contains 16 unique land classifications based on the modified Anderson Level II scheme (Yang et al., 2018). The NLCD land uses were re-classified to correspond with the five land use types used in the NSQD, as shown in  (2015)).

NBS Water Balance Modeling
EPA's SWMM engine calculates the water balance for NBS-driven systems using a nonlinear reservoir model (Chen & Shubinski, 1971)   The water fluxes are defined by: and where 1 is the depth of ponded water on the surface zone with outflow 1 (cfs), 2 is the depth of the soil zone with moisture content , 3 is the depth of the storage zone with outflow 3 (cfs), 0 describes the inflow to each NBS cell (cfs), 1 and 2 represent the evapotranspiration from the surface zone and the soil zone, respectively, 1 describes infiltration between the surface and soil zone, p is percolation between the soil and storage zone, and 3 is infiltration from the storage zone to the underdrain layer.
The flux terms ( , , ) are functions of the water content within each layer and subcatchment site conditions. The set of equations is solved at each runoff time step, according to the Green-Ampt method, to calculate how the inflow hydrograph to the NBS unit is converted to a runoff hydrograph, further described by Rossman (2014).
Within NBS systems, the surface zone represents the ground surface, which stores excess inflow and generates outflow either overland or to an adjacent drainage system. The soil zone is comprised of an engineered soil mixture that allows water to percolate into the underlying zone, which consists of rock and gravel for additional storage. The underdrain system conveys water out of the storage layer and into an engineered outlet. The three NBS features used in this case study (bioretention cells, porous pavement, and tree boxes) are described in Table S.2 as a function of the representative water balance layers modeled in PCSWMM. In the WOB case study, tree boxes were modeled as bioretention cells with no outflow drain.
Various input parameters are also required within a SWMM model to describe the engineered design of local NBS features (e.g., conductivity rate, vegetation volume, clogging properties, surface roughness, etc.), which were obtained from the City of Houston design guidelines for low impact development (COH, 2019a), as summarized in Table S.4.

Calibration & Validation
The hydrological basin parameters were calibrated to observed streamflow measurements from United States Geological Survey (USGS) stream gauges #08074020 and #08074500 (USGS, Non-peer reviewed EarthArXiv preprint. Under review by Water Resources Research 2021a, 2021b). One year of daily precipitation values were obtained from the Harris County Flood Warning System (HCFWS) precipitation gauges #530, #535, #550, #555, #560, #570, #582, #590, and #595 (HCFCD, 2021), encompassing the totality of the White Oak Bayou watershed. The first six-months of precipitation data (October 2, 2020 -March 2, 2021) were used to calibrate the model, while the latter six-months of data (March 3, 2021 -August 2, 2021) were used to validate the model. The PCSWMM sensitivity-based radio tuning calibration (SRTC) tool was used to aid in identifying the most sensitive parameters within the model, according to user-identified uncertainty, and for calibrating the model to match observed streamflow (CHI, 2015). The annual set of hydrographs for the basin model was disaggregated for wet weather conditions with a criterion of at least 500 cfs flow for a minimum of 4 consecutive hours, resulting in ten unique storm events for calibration and eight unique storm events for validation. The wet weather flow hydrographs were calibrated using the PCSWMM SRTC tool by selecting uncertainties for control parameters based on their data source and sensitivity gradient, per guidelines proposed by Choi and Ball (2002) and James (2003). The basin model was then simulated with the calibrated parameters and compared to observed streamflow and resulting error metrics to measure goodnessof-fit.
The error metric employed in this study was the integrate square error (ISE), which amalgamates differences between observed and calibrated values according to overall storm runoff volume, peak flow, mean flow, and the hydrograph time to peak (James, 2003). The ISE is advantageous over the traditional Nash-Sutcliffe efficiency (NSE) or coefficient of determination (R 2 ) because these latter error metrics are both sensitive to outliers and tend to converge on one measure of hydrological efficiency (i.e., total runoff or peak flow or average runoff) (CHI, 2020).
The ISE is recommended for large-scale watershed planning due to its capability to assess goodness-of-fit over a range of historical rain events and hydrograph parameters, rather than potentially biasing the model to one specific event or metric of performance (CHI, 2015).
Moreover, the ISE is beneficial in urban watersheds that are modeled without sub-surface flow because sewer system hydraulics may be indirectly calibrated using the ISE, whereas the NSE is dominated solely by overland flow conditions (Sarma et al., 1973).

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The ISE is expressed as where is the observed value, and is the computed value for the -th observation. Then, the rating of the resulting ISE error metric may be defined on a qualitative scale, as defined by Sarma et al. (1973), such that ISE ≤ 3 = Excellent, 3 < ISE ≤ 6 = Very Good, 6 < ISE ≤ 10 = Good,  Table S.5 -Table S.6), respectively.

Spatial Allocation Optimization
A decision support tool, called GreenPlan-IT, was used to optimize the fully-calibrated to identify the optimal spatial allocation of NBS features, including: 1. GIS-based Site Locator Tool (SLT): Merges spatial characteristics of NBS types with regional geospatial information to identify all possible NBS locations within the study area.
2. EPA SWMM Basin Model: Establishes baseline conditions for runoff and pollutant loading prior to NBS optimization.
3. GreenPlan-IT Optimization Tool (GPOT): An executable file that runs through the user's command prompt to identify optimal combinations of NBS types within each catchment area according to a cost-benefit analysis (where costs are defined by the user, and benefits are calculated using SWMM to assess the reduction in stormwater runoff and pollutant loads for many simulations).
The GIS-based SLT was used to identify all potential locations of NBS features within the   The NSGA-II algorithm, originally presented by (Deb et al., 2002), searches for the optimal solution among numerous possible scenarios by first modeling a random set of NBS placements and comparing their outputs for non-dominance. Non-dominance occurs when a solution performs no worse than any other solution for all objectives (e.g., cost, runoff, and pollutant load efficiency) and also performs better than all other solutions within the cohort for at least one objective. This cohort (known as a generation), then sorts each of the sub-routines within the series (known as populations) for non-dominance. Another generation is run using the previous generation's non-

Multi-objective Gini Index
The Gini coefficient, which was originally identified by Gini (1912), is a statistical representation of inequality across a population. The Gini coefficient is based on the Lorenz curve, depicted in Figure 3, which describes the cumulative proportion of values along the x-axis compared with the cumulative proportion of values along the y-axis. Within the social sciences, the Gini-based approach is commonly used to assess the degree of matching between population (x-axis) and income/wealth (y-axis) for economic purposes to quickly compare and rank disparate geographic entities (Giorgi & Gigliarano, 2017).
In a perfectly-equal scenario, the distribution of income matches the distribution of the population, shown as the diagonal line in Figure 3. In a more realistic scenario, the normalized Non-peer reviewed EarthArXiv preprint. Under review by Water Resources Research percentage of population to percentage of household income typically follows an exponential distribution, known as the Lorenz curve, which delineates state spaces A (e.g., the inequality gap) and B (e.g., the actual income distribution) in Figure 3.
where represents the total area between the line of equality and the Lorenz curve distribution, and represents the area between the Lorenz curve and the base axes.
A numerical form of the Gini coefficient ( ) is given by where is the cumulative percentage of the variable on the x-axis, and is the cumulative percentage of the variable on the y-axis, for data point , from =1 to = total data points.
Gini coefficient values range from 0 to 1, where 0 indicates absolute equality, and 1 represents absolute inequality. Due to the popularity of the Gini coefficient to quickly identify statistical differences in equality, studies have begun applying this economic concept to issues of energy allocation (Jacobson et al., 2005;Saboohi, 2001), environmental inequity ( Many of the recent applications of the Gini concept to issues of environmental concern utilize the area-based Gini coefficient. The area-based Gini ("AR-Gini") compares a social metric, calculated on an area basis, to a distributed social good, calculated on a resource basis (Druckman & Jackson, 2008). The AR-Gini may be used to compare spatial patterns of space-based resources and population-based social metrics to reveal internal relationships, improve planning frameworks, and identify useful cross-disciplinary spatial indicators. An example of using the AR-Gini coefficient beyond the traditional scope of economic wealth disparity is given by Sun et al. (2010) where wastewater discharge permitting is optimized using the Gini index and a multi-criteria assessment of land, population, income, and environmental capacity. In the AR-Gini study, the conflict between wastewater efficiency and social equality is bridged by balancing tradeoffs between various policy-making goals amidst limited resources (Sun et al., 2010).
The method presented here uses a novel representation of the AR-Gini to advance sustainability planning by combining hydrological, environmental, and social efficiencies within NBS spatial allocation optimization. The cumulative area of NBS allocation as a proportion of each subcatchment area is plotted on the y-axis, normalized on a scale from 0-100. Unique evaluation indicators (i.e., stormwater runoff, stormwater quality, and social equity) are then plotted on the x-axis, such that each potential optimization model contains three different Gini coefficients. Hydrological efficiency is represented as the percent difference of stormwater runoff volume between baseline and optimized conditions as a function of cost. Environmental efficiency is described as the percent difference of pollutant load abatement between baseline and optimized conditions according to cost. Social equity is a function of the average neighborhood disadvantage over the weighted area of NBS allocation within each subcatchment. By minimizing the sum of these multi-objective Gini coefficients, this novel approach reveals the state space of optimal hydrological efficiency and distribution of NBSs in socially-vulnerable locations.
Minimizing the Gini coefficient as a function of hydrological efficiency and social justice provides the novel framework for allocating NBSs according to both their hydrological functionality and also the social characteristics of persons that would be influenced by varying spatial arrangements. A high Gini coefficient would reveal that the distribution of NBSs using only GreenPlan-IT tool are calculated using the multi-functional Gini calculations, described below, to better understand the trade-offs between hydro-environmental/economic efficiency and spatial equality when planning watershed-scale NBS solutions. The first objective is to maximize the economic benefit efficiency of hydro-environmental spatial optimization. The second objective is to maximize social equity using a composite AR-Gini coefficient. In doing so, a hypothesis is generated from robust hydro-dynamic modeling, which is then tested against the spatial representation of social deprivation to elicit a numerical hypothesis of holistic NBS conditions that are optimally distributed to maximize urban greening in areas of highest social vulnerability. The following equations are applied in deriving the multi-objective Gini coefficient: where is the allocation of NBS area per subcatchment , is number of unique NBS feature types = bioretention cells, porous pavements, or tree boxes, is the number NBSs per subcatchment, is the area of each NBS feature type ( : bioretention cells = 500 SF, porous pavements = 5,000 SF, tree boxes = 60 SF), where is the percent efficiency of hydro-environmental improvement between the baseline model, , and the optimized model, for each subcatchment as a function of the cost for each NBS feature, ( = $6.07/SF, $8.68/SF, $9.46/SF for =bioretention cells, porous pavements, and tree boxes, respective); and represent the total stormwater runoff volume (VR, in million gallons) for hydrologic efficiency and the total pollutant load runoff (TSS, in lbs) for environmental efficiency, from SWMM modeling.
where µ is the percent of social inequality addressed by the optimized model according to the total NBS allocated area within each subcatchment, , for all subcatchments , and the social where ̃ is the normalized value of each = hydrologic efficiency ( ), environmental efficiency ( ), and social equity (µ ).
Consequently, the sum of the normalization series for each Lorenz curve axis is 100. The Gini coefficient is then calculated by: where is the y-axis value on the Lorenz curve, is the x-axis value on the Lorenz curve, is the area of each subcatchment , with total subcatchments , and is the Gini coefficient corresponding to the evaluation index = runoff volume efficiency, pollutant load efficiency, or social equity distribution. and are plotted on the Lorenz curve by sorting in ascending order, where 0 and 0 each equal 0.
Finally, the composite optimization objective is represented by where is the multi-functional Gini coefficient for each indicator, .
In summary, the following steps are applied to calculate the composite Gini index for amalgamating a series of NBS efficiency indicators according to both social deprivation and hydro-environmental risk: 1. Select a set of potential NBS allocation scenarios according to hydroenvironmental SWMM-based optimization modeling, 4. Aggregate the objective functions and compare Lorenz curves according to the multi-criteria Gini coefficient, Eq. 16, 5. Identify the greatest distribution of social equality and hydro-environmental efficiency by minimizing the objective function in Eq. 16.

Hydro-environmental Pareto Front Curve
The As such, hydrologic versus environmental efficiency goals may be compared and contrasted between scenarios as a function of cost distribution and intensity of design storm metrics (SFEI, 2020). For example, if decision-makers had a goal of reducing the 100-YR storm flow by 5% (equating to a total cost of $1,187M on the hydrologic cost-effectiveness curve), stakeholders could quickly visualize the flow reduction efficiency for additional design storms and the tradeoffs associated with pollutant load abatement at this cost point. To demonstrate how such optimization outputs may be combined with the multi-objective Gini coefficient described in Section 2.4, the 5-YR storm event with $1,000M NBS expenditure was chosen for further analysis.
In this scenario, Generation 97, Population 117 produced the most optimal NBS allocation scenario according to hydro-environmental efficiency. In comparing the spatial distribution of NBSs from this model with the areas of highest social deprivation in the WOB watershed (reference Figureab), we may note how sole reliance upon hydrological characteristics for NBS planning could result in a missed opportunity to address potential social benefits from enhanced urban greening. As such, the multi-objective Gini is explored to further refine the NBS optimization results. A sample set of outputs from the GreenPlan-IT tool was selected from the 5-YR storm event, each resulting in a total NBS implementation cost of ~$1,000M, to assess how the optimal allocation scheme may shift when the multi-objective Gini coefficient is applied. As shown in Figure6 and summarized in Table 1  to changes in spatial scale. In other words, the Gini index provides a transparent measurement tool of the summary of impact fractions for optimal planning (Lee, 1997).     Population 246. The primary reason for this disparity is that areas highly prone to flooding or environmental quality issues are not always spatially proportional to areas of high social deprivation. As such, reliance upon a "worst-first" approach to NBS planning through the lens of hydro-dynamics may result in non-optimal allocation for addressing the many societal benefits provided by NBS solutions.

Conclusions
As resilience and sustainability goals have become increasingly linked, many governmental agencies are seeking the prioritization of NBS capital improvement projects using an equity-based or benefits-based prioritization metric to help guide equitable investments rather than focusing in a one dimensional benefit (Marchese et al., 2018). To amalgamate such interwoven goals, decision-makers seek the ability to identify priority planning areas according to the culmination of socio-enviro-hydro processes, which interact within NBS systems to simultaneously enhance both environmental challenges and social health vulnerabilities.
Interventions and policies that acclaim to provide social health benefits, but which do not explicitly consider the spatial distribution of social health characteristics within their planning paradigms may be ineffective.
NBS design is a function of rapid urban development, quality of life goals, and a scarcity of resources for addressing hydro-meteorological challenges. As such, proper co-development of NBS plans can and should account for the multifunctional components involved in all of these processes, and we must do so in a coherent fashion for optimal impact in the coming era of water science. In this light, strategic NBS planning requires real-world empirical datasets to aid in clarifying causality amongst disparate social and physical domains in a manner that is understandable and usable by diverse parties to inform interventions for long-term resilience (Frantzeskaki et al., 2019).
By solely relying on hydro-environmental modeling, the relative benefits addressed by NBS solutions are limited and are not able to be optimized according to unique exposures of socioeconomic and health-related conditions. Improving resiliency begins with valuing the entangled nature of social well-being and water dynamics. The framework presented here converts hydroenvironmental risk and social disparity into a common unit for comparison to adequately capture variation across spatial domains. The Gini index and Lorenz curve are presented as an alternative fundamental approach for optimal NBS planning. This study demonstrates how NBS strategies may be optimized holistically by assessing unique scenarios and minimizing the Gini coefficient across three disparate, but equally important, domains of NBS systems using existing tools and methods in a novel way. As we continue to have increased access to high-resolution spatial datasets, the composite Gini coefficient maximizes our understanding of regional risks and benefits to answer challenging questions associated with multi-functional planning. We demonstrate here how real-world social and hydro-environmental complexities may be amalgamated using a novel application of the area Gini coefficient for actionable science. This case study investigates how social equity and watershed dynamics propagate throughout the NBS system, which is fundamental to planning for an equitable environment. We harmonize risk-based planning by facilitating an explicit integration of social determinants within the framework of natural-planning using data-driven science. This research transitions beyond the standard focus of watershed physiological characteristics to investigate the complex associations relating social patterns and watershed efficiency. By constructing models with inter-disciplinary elements, we strengthen the foundation for novel research regarding how NBSs function in diverse geographical locations, each with unique properties.
The vision for the future is that we will approach these issues with a systems mindset and transition from our dependency on linear thinking. In the era of the Anthropocene, change is occurring rapidly, and we must better understand complex socio-hydrological systems as necessary for addressing variability in climate and human patterns. Instead of attempting to superimpose human dynamics on the results of physical models, or as a pre-existing boundary condition, we are transitioning toward coupled modeling frameworks that integrate human characteristics as a stimulus that interacts with the environment (Bouziotas & Ertsen, 2017). While coupled social and physical models have proliferated within the general realm of water security (e.g., droughts, water use, hydro-meteorological hazards, migration, agriculture, etc.), the foundation of such a framework has been hitherto lacking within the NBS scientific literature. In considering the rising popularity of urban green infrastructure, we are presented with an opportunity to re-cast how decision-making operates in order to maximize the numerous co-benefits associated with NBSs.
The practical implications of this research will enhance the user-friendliness of NBS spatial planning in a flexible manner while merging well-established hydrological methodologies with a NBS social functionalities (Kuller et al., 2017). When we are better able to select the optimal location of NBSs at a large-scale, the specific typologies and precise placement may be analyzed using the numerous platforms that currently operate through small-scale physical modeling. To date, there has been very little research on NBS optimization at the catchment-scale and even less progress in combining numerical modeling with comprehensive social benefits and human impacts. This study successfully integrates various types of NBS co-benefits into one inter-related framework that combines stormwater abatement, pollutant load modeling, cost-efficiency, and Non-peer reviewed EarthArXiv preprint. Under review by Water Resources Research social equity-based decision-making for robust spatial optimization of NBS systems at the catchment-scale.
By constructing models with inter-disciplinary elements, the foundation for novel research regarding how NBSs function in diverse geographical locations is strengthened. Coupled humanearth models allow for an improved understanding of how social characteristics correlate with environmental processes as a socio-technological system. In a world with increasing socioenvironmental stressors and finite resources, this research will improve public policy interventions by providing the knowledge necessary for identifying, quantifying, and linking complex interactions of NBS functions for sound decision-making. Nature-based solutions are expected to become a central tool for climate change adaptation, and we necessitate enhanced approaches to synchronize resiliency goals associated with societal well-being, environmental justice, and natural hazard mitigation through the informed use of NBSs.