Designing Nature-Based Solutions for Sediment Control in Impaired Humid Subtropical Forests: An Approach Based on the Environmental Benefits Assessment

Abstract

Land-use changes cause disturbance to sediment dynamics, increasing downstream sediment loads discharged into ecosystems and provoking impacts on stream quality and damage to current stormwater infrastructures. Wastewater nature-based solutions (NBSWT) are bioretention techniques that alleviate downstream degradation caused by runoff sediment accumulation and are projected as an off-line street device that enhances treatment of runoff contaminant loads. This research assesses the economic, social, and environmental benefits from sediment load reduction in runoff by designing a new NBSWT in a selected urban area of the Mantiqueira Mountain Range (São Paulo, Brazil), considered an irreplaceable protected area for biodiversity and urban water supply. To achieve this quantification, the shadow prices methodology has been used. The results obtained here show the adaptive capacity that NBSWT have according to the territory and its climatic particularities, quantified at USD 40,475,255. This value demonstrates that the retention of runoff sediment generates a direct environmental benefit related to the ecosystem improvement of the river system located downstream, preserving its environmental and social importance. Hence, this study demonstrates the potential of using shadow prices methodology as a management tool for quantifying the environmental benefit of removing runoff solids by using NBSWT in developing urban areas.

1. Introduction

Alteration of hydrographs due to urban growth makes urban areas increasingly susceptible to disruption of key city features and may adversely impact the economy, as well as the health of the environment [1,2]. Urbanisation causes increasing difficulties in accessing satisfactory non-contaminated water sources, especially in developing areas with a lack of regulatory basis in sustainable urban planning [3]. This leads to environmental issues with water quality and compromises the safety of new and existing neighbourhoods [4,5]. Protected ecoregions of humid subtropical and tropical areas are particularly sensitive to land-use changes. In these cases, deforestation, together with the increase in impervious surfaces, affects sediment dynamics, with increased pollution causing impairment of aquatic systems and becoming a main factor in undermining living conditions, locally and regionally. Sediment pollution is one of the most common pollutants in water basins caused by stormwater runoff that drains directly into nearby aquatic systems, such as fluvial ecosystems and free-surface flow bodies, without any management and treatment [6]. The main problem caused by sediment load increase in aquatic ecosystems is the loss of water quality due to the following: (i) sediments fill up natural drainage systems, increasing flood risk and reducing normal water volume available for organisms; (ii) sediments hamper light transport in water, provoking changes in organisms’ feeding; and (iii) nutrients transported in sediments cause eutrophication. This situation is made worse by depth modifications of the sedimentation of particles [7,8].

This trend affects Brazilian biomes, with the Atlantic Forest being the most degraded due to anthropic occupation [9,10]. The study area is located in the Mantiqueira Mountain Range, an Atlantic Rainforest at a high altitude in Southeast Brazil. Considered one of the few irreplaceable protected areas for biodiversity and water conservation worldwide [9], the Mantiqueira Mountain Range provides mineral water resources that drain to the largest water reservoir of the state of São Paulo, the Cantareira system. Land-use changes lead to disturbances in water quality and quantity of local Mantiqueira streams that affect these larger water supply facilities [11]. The São Paulo metropolitan region has limited access to continuous drinking water caused by climate change and the increase in urban water demand. Urban water supply depends on healthy watersheds where the water supply comes from, known as source watersheds. The health of these watersheds influences water security for urban drinking and other uses, which requires sustainable water management strategies. Anthropogenic activities and diffuse pollution washed off urban streets increase the sediment and pollutant level in receiving water bodies. In the Mantiqueira area, pollutants come from agriculture and pastureland uses upstream from the watershed. In the form of phosphates and nitrates, these pollutants negatively impact the integrity of local fluvial systems.

Wastewater nature-based solutions (NBSWT) are technologies based on bioretention techniques considered to be nature-based solutions that integrate with conventional stormwater infrastructures to reinstate pre-development hydrological features through retention, infiltration, and treatment of polluted runoff [3]. Bioretention is an effective form of NBSWT designed in a decentralised manner for built-up areas to provide a first-flush control at the source. The implementation of NBSWT for runoff control and treatment is a recommended strategy for the regulation of water quality in urbanised areas worldwide [12,13,14]. However, urban regions of this study’s selected ecoregion lack economic evaluation studies. To support the implementation of these systems, economic benefits from NBSWT need to be assessed. Lack of knowledge and experience in NBSWT benefits for controlling runoff sediment and pollutants limits public awareness and the future uptake of these technologies in urban planning actions, in the definition of standards, and in water management regulations, both locally and beyond. Economic assessment methods, developed in conjunction with design and sizing criteria for NBSWT, help to estimate the monetary benefits of these systems. These kinds of studies nurture strategic planning processes and decision-making for government and local municipalities in many regions of the world [15].

Assessing externalities associated with runoff sediment and pollutant inputs is a fundamental part of planning for impaired watersheds. Further, pollution and sediment inputs in local streams are a negative environmental externality that needs to be managed in future projects and policies for watershed protection and restoration [16]. This study assesses the environmental benefits associated with sediment removal by NBSWT, implemented in urban developments in a high-altitude humid subtropical region. NBSWT are planned and sized to reduce runoff sediment in the study area, and the sediment retained by the system is estimated for the evaluation of the associated economic benefits. Thus, the study combines methods for planning, sizing, and evaluating the economic benefits of these technologies that perform as a source control of sediment load washed off from built-up areas, providing evidence of their effectiveness in the form of bioretention devices.

From an environmental and social point of view, the dragging of solids by runoff has a negative impact on water ecosystems. This negative impact modifies the socio-economic dynamic of populations, forcing decision-makers to design and implement preventive and corrective measures to ensure the quality of water bodies. However, correction of these impacts entails a cost for administrations that must be considered during the design, implementation, and maintenance processes. Regarding these costs, international agencies aim to encourage the consideration of all aspects that influence the design, construction, and performance of the infrastructures of the hydrological cycle to achieve their efficiency and effectiveness [17]. As part of the scope of these measures, the inclusion of environmental externalities in economic feasibility studies should be encouraged. Currently, the inclusion of the environmental externalities is carried out through monetary valuation methodologies as a tool to express their environmental importance. This type of methodology is important because in most cases the environmental externalities lack market value that can be used as a reference price [18]. Furthermore, values obtained by implementing these methodologies are considered as the environmental benefit of improving the quality of ecosystems.

To obtain the environmental benefit of removing the runoff solids using NBSWT in São Paulo’s state rural regions, this work proposes the implementation of the shadow prices methodology. The implementation of shadow prices has been previously used in the published literature to obtain the environmental benefit of removing different pollutants in the urban water cycle [19]. These works are focused on wastewater treatment plants, which are considered both as infrastructures receiving wastewater pollution and, at the same time, as infrastructures capable of removing these pollutants from wastewater and obtaining treated water that can be reused for environmental and agricultural purposes. The novelty and innovation of the approach proposed in this study is the implementation of shadow prices in NBSWT to obtain the environmental benefit of their performance: retaining runoff solids to reduce the sediment load that arrives at water bodies. Specifically, this research combines both the social and environmental assessment and the design and sizing tools of NBSWT, implemented in a specific study area of Brazil, to assess the environmental benefit of NBSWT solutions for water management in developed urban areas. Through this innovative approach, the importance of NBSWT as water management solutions has been highlighted. At the same time, the proposed approach allows the assessment of prevention and reduction of pollutant discharges, and the hydrological impacts generated by urbanisation processes in terms of economic feasibility assessment models [20]. Results obtained show the environmental and social benefit of reducing sediment runoff by using NBSWT that increase the ecological value of the study area.

2. Materials and Methods

This section includes information about the study area (Section 2.1), NBSWT planning and sizing (Section 2.2), the inputs and outputs obtained for the monetary valuation assessment (Section 2.3), and the shadow prices methodology description (Section 2.4) to obtain the environmental benefit of reducing sediment volume of runoff. The description and the approach proposed in this study (according to the sections aforementioned) are included in Figure 1.

2.1. Study Area

This work is focused on the Mantiqueira Mountain Range, an Atlantic Rainforest at a high altitude in Southeast Brazil, within a large watershed region of 24,757.65 hectares. The climate of this region, according to the Köppen–Geiger climate classification system (1928), is Cwb, named a humid temperate climate with dry winters and temperate summers, having at least 3 to 4 months of frequent medium-to-intense storm events and a dry season with occasional rainfalls [9]. This climate enhances the existence of a high diversity of flora and fauna species, and it has been identified as one of the world’s most irreplaceable Protected Areas (PAs) for conservation of biodiversity [10]. At the same time, it plays a crucial role as a source watershed for other metropolitan areas. In fact, it is positioned between the metropolitan areas of São Paulo (21.6 million inhabitants) and Rio de Janeiro (11.9 million inhabitants) and is part of the largest and most important mountain chains of Southeast Brazil [9].

The area has been monitored in previous studies to assess deforestation pressures by anthropic actions [9]. Following these studies, urban areas have grown by nearly 120% between 1985 and 2017, and 85% of the region has been identified as under high or very high pressure for biodiversity and water quality resources conservation. Population increases, estimated at 67% in the number of inhabitants from 1985 to 2015, together with land-use conversion, lead to anthropogenic alterations as main drivers of loss of biodiversity in the area, and increased sedimentation and pollution of existing water bodies, limiting its potential role in the water distribution system at a regional scale. Taking this into consideration, a network of public and private conservation units was created by the Brazilian Ministry of the Environment to enhance biological conservation and local sustainability of this mountain range. However, there has been a lack of implementation of most conservation units, as well as effective and efficient strategic municipal planning for water quality and biodiversity protection in the local urban areas. Currently under serious threats, associated with land-use changes and urban sites, the Mantiqueira Mountain Range watersheds require environmental assessment and sustainable management implementation actions to preserve water security locally and regionally [9].

2.2. NBSWT Planning and Sizing

Topographical curves, generated using Google Earth Pro, and downloaded as shapefile using the GPS Visualizer free online software, were imported to ArcMap software (10.3.1 version). Raster DEM was created using an interpolation tool from Analyst Tools in ArcToolBox; contour lines were extracted from DEM with Surface-Contour tool from ArcToolBox. Flow direction and flow accumulation grid was created from the previous DEM grid. Stream order was performed in the sequence and then Stream by feature with input Stream order and Flow direction was generated. This allowed the modelling of main runoff paths across the study area, with layer properties modified using the Query builder. The basin tool from the Hydrology Toolbox was used, using the Flow directions as the input layer, and the Raster to polygon from Conversion tools was used to save the files with the generated data in a shapefile format. Saved data were imported to Google Earth Pro to facilitate visualization with satellite view for delineation of NBSWT. The NBSWT were drawn manually in Google Earth Pro based on available street space and simulated water flows, within each watershed boundary. NBSWT elements were numbered and classified, and the attribute table was exported into an Excel file using the Conversion Tools-Excel-TabletoExcel from the ArcToolBox (

Table 1. Data about NBSWT, impermeable draining area and street dimensions, and drained water volume into the systems.

	Built-Up Area (m2)	Water Volume Subcatchment (m3)	Street Length (m)	NBSWT Area (m2)	NBSWT Width (m)
NBSWT1	2178	52.27	50	75	1.5
NBSWT2	676	16.22	24	24	1
NBSWT3	6692	160.61	80	200	2.5
NBSWT4	3679	88.29	42	105	2.5
NBSWT5	6759	162.22	100	250	2.5
NBSWT6	13,529	324.69	250	500	2
NBSWT7	5292	127.01	250	250	1
NBSWT8	11,607	278.57	195	390	2
NBSWT9	7723	185.35	190	285	1.5
NBSWT10	5714	137.14	75	187.5	2.5
NBSWT11	6527	156.65	105	210	2
NBSWT12	2748	65.95	70	140	2
NBSWT13	5468	131.23	115	230	2
NBSWT14	6753	162.07	130	260	2
NBSWT15	5597	134.33	100	200	2

).

Minimum rainfall depth to be treated by NBSWT was fixed as 30 mm, according to the performed studies in humid tropical areas [21]. Specifically, the current systems implemented in St. Louis (United States) are focused on sediment control with a minor flooding mitigation function. The depth has been adjusted to small rain gardens such as those constructed in temperate regions of the United States, which tend not to exceed 1 or 1.14 inches, equivalent to around 25 to 30 mm [22]. Furthermore, according to Burszta-Adamiak et al. [23], NBSWT must be designed on the rule of a maximum depth of 30 mm not to compromise the ponding time (lower than 48 h), to reduce the risk of having detained water for longer periods causing exposure to mosquito disease transmission. Runoff water volume retained by the system was calculated as the product of total impervious draining area and the aforementioned value. Design adjustments were made to enlarge bioretention basins, adapting NBSWT areas to meet available street layout space ensuring minimum pedestrian pathway requirements. Final design was established considering effective retention of, at least, 50% of the mentioned minimum rainfall depth, in the limited available street area for their implementation.

2.3. Inputs and Outputs Assessed

In order to implement the shadow prices methodology to obtain the environmental benefit of sediment retention, some variables have been quantified: (i) the total sediment load and the retained water volume, and (ii) the construction, operation, and maintenance costs for the NBSWT proposed. In this context, pollutants have been found to be closely related to the finest fractions of suspended particles in runoff, based on the assumption that total suspended solids (TSS) or sediment mass washed off by rainstorm events could be used as indicators in pollutant wash-off studies for urban areas [24,25]. Sediment load retained by each NBSWT was calculated using the built-up function of Sartor and Boyd [24], which is commonly adopted in several urban drainage models, such as SWMM, and derived from an analysis of accumulation of pollutants in built-up areas in the United States in the 1970s. This equation considers the initial loading and the accumulated loading, performs hydrological modelling and then quantifies the total water volume to be retained for the targeted removal efficiency. The aforementioned equation presents the accumulation of sediment as a finite process, with increasing accumulation to a certain value of equilibrium:

$$B=a\left(1-e^{-bt}\right)$$

(1)

where B = built-up mass, g/m², a = maximum accumulation, g/m², b = accumulation rate, dimensionless, t = antecedent dry period, days.

Built-up sediment load values by square meter were estimated using the previous expression. This estimation was carried out by introducing values of maximum accumulation, subcatchment sediment accumulation rate, and the elapsed time since the last rainstorm or street washout, based on available local studies performed in this field [24,26].

Table 2. Estimation of sediment load retained by the proposed NBSWT.

	Water Quality Volume (m3)	Sediment NBSWT (kg)	Built-Up Mass (B) (g/m2)	Accumulation (b)	Max Accumulation (a) (g/m2)	Dry Days (t) (Days)
NBSWT1	18.75	12.2	6.998	0.015	27	20
NBSWT2	6	3.8	6.998	0.015	27	20
NBSWT3	50	37.5	6.998	0.015	27	20
NBSWT4	26.3	20.6	6.998	0.015	27	20
NBSWT5	62.5	37.8	6.998	0.015	27	20
NBSWT6	125	75.7	6.998	0.015	27	20
NBSWT7	62.5	29.6	6.998	0.015	27	20
NBSWT8	97.5	64.9	6.998	0.015	27	20
NBSWT9	71.3	43.2	6.998	0.015	27	20
NBSWT10	46.9	31.9	6.998	0.015	27	20
NBSWT11	52.5	36.5	6.998	0.015	27	20
NBSWT12	35	15.4	6.998	0.015	27	20
NBSWT13	57.5	30.6	6.998	0.015	27	20
NBSWT14	65	37.8	6.998	0.015	27	20
NBSWT15	50	31.3	6.998	0.015	27	20

shows the results of sediment mass retained by each NBSWT considering the aforementioned equation and the draining built-up total surface to each system. Furthermore, Table 2 shows the results of Water Quality Volume (m³), which was established according to 90% sediment reduction and the ability of the system to retain the first-flush volume, as simulated using the EPA-XPSWMM software. The initial accumulated loads in the post-developed site of the study area at the beginning of the rainstorm and end of the rainstorm were calculated. The NBSWT basins were sized to retain the water quality volume. Thus, each NBSWT had a storage capacity large enough to control 90% of the total initial sediment load accumulated overland before the rainfall events.

If the NBSWT are periodically maintained (e.g., by periodic removal of accumulated sediment to prevent system clogging), NBSWT can provide the most effective sediment retention volume in isolated events with no remaining sediment load from a previous rainfall. This is because, among other variables such as land use typology, initial sediment load accumulated depends upon the elapsed time after the last rainfall event. In this study, those rainfall events occurred after more than 7 days without precipitation have been considered as isolated events. If isolated events are treated, the volume of sediment washed off from impervious surfaces will therefore be higher than in frequent medium-to-intense rainfall periods. Thus, a prediction of NBSWT performance in dry weather conditions was used to estimate outputs. Gauged data of rainfall depth distribution over the year were used to set an estimated number of 6 rainfall events in a regular dry weather period, annually. This information has been obtained from IRRIGART, a foundation in charge of the Piracicaba, Capivari, and Jundiaí basins. Sapucaí-Mirim, which is the locality of the study area, is part of this larger watershed [27]. Considering this information, the final outputs are shown in

Table 3. Results of the estimation of outputs 1 and 2.

	Water Quality Volume (m3)		Sediment NBSWT (kg)
	1 Rainstorm	6 Rainstorms	1 Rainstorm	6 Rainstorms
NBSWT1	18.8	112.5	12.2	73.2
NBSWT2	6	36	3.8	22.7
NBSWT3	50	300	37.5	224.8
NBSWT4	26.3	157.5	20.6	123.6
NBSWT5	62.5	375	37.8	227
NBSWT6	125	750	75.7	454.4
NBSWT7	62.5	375	29.6	177.8
NBSWT8	97.5	585	64.9	389.9
NBSWT9	71.3	427.5	43.2	259.4
NBSWT10	46.9	281.3	31.9	191.9
NBSWT11	52.5	315	36.5	219.2
NBSWT12	35	210	15.4	92.3
NBSWT13	57.5	345	30.6	183.7
NBSWT14	65	390	37.8	226.8
NBSWT15	50	300	31.3	188
		Output 1		Output 2

.

Total cost for construction, maintenance, and operation was then estimated considering a fixed average value, based on previous monitoring and the published literature, as shown in

Table 4. Costs of construction, operation, and maintenance obtained for the proposed NBSWT.

	Construction Costs (USD)	Operation and Maintenance Costs (USD/year)
NBSWT1	28,200	2775
NBSWT2	9024	888
NBSWT3	75,200	7400
NBSWT4	39,480	3885
NBSWT5	94,000	9250
NBSWT6	188,000	18,500
NBSWT7	94,000	9250
NBSWT8	146,640	14,430
NBSWT9	107,160	10,545
NBSWT10	70,500	6938
NBSWT11	78,960	7770
NBSWT12	52,640	5180
NBSWT13	86,480	8510
NBSWT14	97,760	9620
NBSWT15	75,200	7400
		Input 1

. The construction costs related to NBSWT consider the soil infiltration media, excavation costs, and underground storm drain implementation, and actual construction costs were used to establish construction cost per water quality volume, based on literature reviewed [28]. Specifically, this study has estimated the total costs of NBSWT as USD 4,233,969, considering a useful life of 25 years.

2.4. Shadow Prices Methodology

The estimation of the shadow prices of runoff sediment was based on the methodological approach proposed by Färe et al. [29]. This approach assumes that the production of desirable output (water without runoff sediment) involves the accumulation of runoff sediment in NBSWT (undesirable outputs), which must be removed to guarantee both the efficiency and the suitable performance of NBSWT. The estimation of the shadow prices is based on the directional-distance function, which is a generalization of Shephard’s distance function. The advantage of using the directional-distance function is that it allows the simultaneous expansion of desirable output and reduction of undesirable outputs [30].

The inputs $x=\left(x_1,\dots ,x_{\mathrm{N}}\right)\in {\mathfrak{R}}_{+}^{\mathrm{N}}$ are used for production of desirable outputs $y=\left(y_1,\dots ,y_{\mathrm{M}}\right)\in {\mathfrak{R}}_{+}^{\mathrm{M}}$ and the undesirable outputs produced $b=\left(b_1,\dots ,b_{\mathrm{J}}\right)\in {\mathfrak{R}}_{+}^{\mathrm{J}}$ are related and defined by the technology of the production process, where:

$$P\left(x\right)=\{\left(y,b\right):x \mathrm{c}\mathrm{a}\mathrm{n} \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{e}\left(y,b\right)\in {\mathfrak{R}}_{+}^{\mathrm{M}} x {\mathfrak{R}}_{+}^{\mathrm{J}}\}$$

(2)

The output set–$P\left(x\right)$–satisfies both the usual convex and compact assumptions and inputs free disposability, which means that:

$$\mathrm{I}\mathrm{f} x^{\prime }\ge x {\mathfrak{R}}_{+}^{\mathrm{N}}\Rightarrow P(x)\subseteq P\left(x^{\prime }\right)$$

(3)

By using a greater or equal amount of inputs, the output set will also be greater or equal. Taking into account that the production of desirable outputs is linked to the production of non-desirable outputs, it is assumed that the output set accomplishes other additional assumptions, such as the weak disposability for desirable and non-desirable outputs:

$$\mathrm{I}\mathrm{f}\left(y,b\right)\in P\left(x\right) \wedge 0\le \theta \le 1\Rightarrow (\theta y,\theta b)\in P\left(x\right)$$

(4)

This assumption implies the proportional joint reduction of both the desirable and non-desirable outputs. Hence, any reduction of non-desirable outputs will be associated with the reduction of desirable outputs. The free disposability of desirable outputs is also assumed:

$$\left(y,b\right)\in P\left(x\right)\wedge y^{\prime }\le y\Rightarrow \left(y^{\prime },b\right)\in P\left(x\right)$$

(5)

Finally, both desirable and non-desirable outputs accomplish the null-jointness condition. This means that desirable outputs cannot be produced without the generation of non-desirable outputs. Hence, there is a joint production of both types of outputs:

$$\mathrm{I}\mathrm{f}\left(y,b\right) \in P\left(x\right)\wedge b=0\Rightarrow y=0$$

(6)

The previous assumptions provide the framework that contextualizes the production technology. On the basis of the above, the directional-distance function used is defined by [31]:

$${\overrightarrow{\mathrm{D}}}_0(x,y,b;g_y, g_b)=\max \{\beta :\left(y+\beta g_y,b-\beta g_b\right)\in P\left(x\right)\}$$

(7)

where $g =$ ($g_y, -g_b)>0$ is the directional vector that specifies the direction of both desirable and non-desirable outputs, and ${\beta }^{\ast }={\overrightarrow{\mathrm{D}}}_0(x,y,b;g_y, g_b)\ge 0$ is the distance between a decision-making unit (DMU) and its frontier projection of $P\left(x\right)$, a measure of its efficiency. Hence, the directional-distance function increases desirable outputs and reduces non-desirable outputs of a DMU in the $g$ direction with the aim of $P\left(x\right)$ hitting the frontier at $(y+{\beta }^{\ast }{g}_y,b-{\beta }^{\ast }{g}_b)$.

The directional-distance function, defined in Equation (6), includes the following properties [32]:

$$(\mathrm{a}) {\overrightarrow{\mathrm{D}}}_0\left(x,y,b;g_y, g_b\right)\ge 0,\forall (y,b) \in P\left(x\right)$$

$$(b) {\overrightarrow{\mathrm{D}}}_0\left(x,y^{\prime }, b;g_y, g_b\right)\ge {\overrightarrow{\mathrm{D}}}_0\left(x,y, b;g_y, g_b\right), \forall (y^{\prime },b) \le (y,b)\in P\left(x\right)$$

$$(\mathrm{c}) {\overrightarrow{\mathrm{D}}}_0\left(x,y, b^{\prime };g_y, g_b\right)\le {\overrightarrow{\mathrm{D}}}_0\left(x,y, b;g_y, g_b\right), \forall (y,b^{\prime })\le (y,b)\in P\left(x\right)$$

$$(\mathrm{d}) {\overrightarrow{\mathrm{D}}}_0\left(x,\theta y, \theta b;g_y, g_b\right)\ge 0, \forall (y,b)\in P\left(x\right) \wedge 0\le \theta \le 1$$

$$(\mathrm{e}) {\overrightarrow{\mathrm{D}}}_0\left(x,y, b;g_y, g_b\right) \mathrm{i}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{a}\mathrm{v}\mathrm{e} \forall (y,b)\in P\left(x\right)$$

$$(\mathrm{f}){\overrightarrow{\mathrm{D}}}_0\left(x,y+{\alpha g}_y,b-{\alpha g}_b;g_y, g_b\right)={\overrightarrow{\mathrm{D}}}_0\left(x,y,b;g_y, g_b\right)-\alpha , \alpha \in {\mathfrak{R}}_{+}$$

(8)

Property (a) implies that the directional distance function is non-negative for outputs of $P\left(x\right)$. Property (b) is a monotonicity property related to the strong disposability of desirable outputs. When less or equal production of desirable outputs occurs, the inefficiency of the DMU analysed will increase. Property (c) is a monotonicity property corresponding to non-desirable outputs. This property means that inefficiency does not decrease while inputs and desirable outputs remain constant. Property (d) represents the weak disposability of desirable and non-desirable outputs. Property (e) allows us to determine the sign of the elasticity of the output’s substitution. Finally, property (f) refers to the translation, which means that if a non-desirable output is contracted by ${\alpha g}_b$ and desirable output is expanded by ${\alpha g}_y$, the value of the directional distance function will be more efficient by the amount of $\alpha$, where $\alpha$ is a positive scalar [33]. To obtain the shadow prices for non-desirable outputs, the relationship between the output-oriented distance function and the revenue function has been used [29,34]. If both vectors are given as $p=\left(p_1,\dots ,p_{\mathrm{M}}\right)\in {\mathfrak{R}}_{+}^{\mathrm{M}}$, which represents the price of desirable outputs, and $q=\left(q_1,\dots ,q_{\mathrm{J}}\right)\in {\mathfrak{R}}_{+}^{\mathrm{J}}$, which represents the price of non-desirable outputs, the revenue function is defined as:

$$\mathrm{R}(x,p,q)={max}_{y,b}\{py-qb:{\overrightarrow{\mathrm{D}}}_0\left(x,y,b;g_y, g_b\right)\ge 0\}$$

(9)

The revenue function determines the largest feasible revenue obtained, when the DMU is faced with desirable and non-desirable output prices ($p$ and $q$) [33]; the revenue is the difference between desirable and non-desirable output values. Taking into account the duality of the relationship between distance and revenue functions, the directional-distance function (in terms of maximal revenue function) can be written as:

$${\overrightarrow{\mathrm{D}}}_0\left(x,y,b;g_y, g_b\right)\le {\displaystyle \frac{\mathrm{R}\left(x,p,q\right)-\left(py-qb\right)}{p{·g}_y+q·g_b}}={min}_{p,q}\left\{{\displaystyle \frac{\mathrm{R}\left(x,p,q\right)-\left(py-qb\right)}{p{·g}_y+q·g_b}}\right\}$$

(10)

If the directional-distance function (Equation (6)) and revenue function (Equation (7)) are differentiable, the first-order conditions related to desirable and non-desirable outputs are:

$${\nabla }_y {\overrightarrow{\mathrm{D}}}_0\left(x,y,b;g\right)={\displaystyle \frac{-p}{p{·g}_y-q·g_b}}$$

(11)

$${\nabla }_b {\overrightarrow{\mathrm{D}}}_0\left(x,y,b;g\right)={\displaystyle \frac{q}{p{·g}_y-q·g_b}}$$

(12)

Hence, assuming that the market price of desirable output $m$-th equals its shadow price $p_m$, the shadow price of the non-desirable output $j$-th is derived as follows:

$$q_j= -p_m\left({\displaystyle \frac{\partial {\overrightarrow{\mathrm{D}}}_0\left(x,y,b;g\right)}{\partial b_j}}/{\displaystyle \frac{\partial {\overrightarrow{\mathrm{D}}}_0\left(x,y,b;g\right)}{\partial y_m}}\right)$$

(13)

where the input and output values need to be standardized by their average. This implies that it is necessary to increase the result of the derivative’s ratio (Equation (11)) through multiplication of the ratio of the mean value of $y$ to the mean value of $b$ [34].

The directional-distance function can be determined by either parametric or non-parametric methods. This study is focused on the shadow prices of non-desirable outputs, which involves obtaining the ratio of Equation (11); hence, the parametric method is required. Specifically, the quadratic function has been used to set the parameters for the directional-distance function because it satisfies the translation property and is twice differentiable [32,33,34,35]. Since it was of interest to achieve the simultaneous expansion of desirable outputs and the reduction of non-desirable outputs, the directional vector chosen was $g=(1, -1)$. Assuming $k=1,\dots ,K$ (wastewater treatment plants in our case study), the quadratic directional-distance function for the $k$-th units is:

$$\begin{array}{cc}\hfill {\overrightarrow{\mathrm{D}}}_0\left(x_k,y_{k,}{b}_k;1, -1\right)& \\ \hfill =& \alpha +{\displaystyle \sum _{n=1}^{\mathrm{N}}}{\alpha }_n{x}_{nk}+ {\displaystyle \sum _{m=1}^{\mathrm{M}}}{\beta }_m{y}_{mk}+{\displaystyle \sum _{j=1}^{\mathrm{J}}}{\gamma }_j{b}_{jk}+{\displaystyle \frac{1}{2}} {\displaystyle \sum _{n=1}^{\mathrm{N}}}{\displaystyle \sum _{n^{\prime }=1}^{\mathrm{N}}}{\alpha }_{n{n}^{\prime }}{x}_{nk}{x}_{n^{\prime }k}\hfill \\ \hfill +& {\displaystyle \frac{1}{2}} {\displaystyle \sum _{m=1}^{\mathrm{M}}}{\displaystyle \sum _{m^{\prime }=1}^{\mathrm{M}}}{\beta }_{m{m}^{\prime }}{y}_{mk}{y}_{m^{\prime }k}+{\displaystyle \frac{1}{2}} {\displaystyle \sum _{j=1}^{\mathrm{J}}}{\displaystyle \sum _{j^{\prime }=1}^{\mathrm{J}}}{\gamma }_{j{j}^{\prime }}{b}_{jk}{b}_{j^{\prime }k}+{\displaystyle \sum _{n=1}^{\mathrm{N}}}{\displaystyle \sum _{m=1}^{\mathrm{M}}}{\delta }_{nm}{x}_{nk}{y}_{mk}+{\displaystyle \sum _{n=1}^{\mathrm{N}}}{\displaystyle \sum _{j=1}^{\mathrm{J}}}{\eta }_{nj}{x}_{nk}{b}_{jk}\hfill \\ \hfill +& {\displaystyle \sum _{m=1}^{\mathrm{M}}}{\displaystyle \sum _{j=1}^{\mathrm{J}}}{\mu }_{mj}{y}_{mk}{b}_{jk}\hfill \end{array}$$

(14)

Following the work of Aigner and Chu [36], the unknown parameters of Equation (12) have been estimated through linear programming. These parameters have been chosen to minimise the sum of the distance between the frontier technology and each DMU analysed [33]. Specifically:

$$Min \sum _{k=1}^K [{\overrightarrow{\mathrm{D}}}_0\left(x_k,y_{k,}{b}_k;1, -1\right)-0]$$

s.t.

$$(1) {\overrightarrow{\mathrm{D}}}_0\left(x_k,y_{k,}{b}_k;1,-1\right)\ge 0, \forall \mathrm{k}=1,\dots ,\mathrm{K}$$

$$(2) (\partial {\overrightarrow{\mathrm{D}}}_0\left(x_k,y_{k,}{b}_k;1,-1\right)/\partial b_j)\ge 0, \forall \mathrm{k}=1,\dots ,\mathrm{K}\wedge \mathrm{j}=1,\dots ,\mathrm{J}$$

$$(3) (\partial {\overrightarrow{\mathrm{D}}}_0\left(x_k,y_{k,}{b}_k;1,-1\right)/\partial y_m)\le 0, \forall \mathrm{k}=1,\dots ,\mathrm{K}\wedge m=1,\dots ,\mathrm{M}$$

$$(4) (\partial {\overrightarrow{\mathrm{D}}}_0\left(\overline{x},y_{k,}{b}_k;1,-1\right)/\partial x_n)\ge 0, \forall \mathrm{k}=1,\dots ,\mathrm{K}\wedge n=1,\dots ,\mathrm{N}$$

$$\begin{array}{ll}(5)& \sum _{m=1}^{\mathrm{M}}{\beta }_m-\sum _{j=1}^{\mathrm{J}}{\gamma }_j=-1; \sum _{m^{\prime }=1}^{\mathrm{M}}{\beta }_{m{m}^{\prime }}-\sum _{j=1}^{\mathrm{J}}{\mu }_{mj}=0, \forall m=1,\dots ,\mathrm{M}\\ & \sum _{j^{\prime }=1}^{\mathrm{J}}{\gamma }_{j{j}^{\prime }}-\sum _{m=1}^{\mathrm{M}}{\mu }_{mj}=0, \forall \mathrm{j}=1,\dots ,\mathrm{J}\\ & \sum _{m=1}^{\mathrm{M}}{\delta }_{nm}-\sum _{j=1}^{\mathrm{J}}{\eta }_{nj}=0, \forall n=1,\dots ,\mathrm{N}\end{array}$$

$$(6) {\alpha }_{n{n}^{\prime }}={\alpha }_{n^{\prime }n} , \forall n\ne n^{\prime };{\beta }_{m{m}^{\prime }}={\beta }_{m^{\prime }m, }\forall m\ne m^{\prime }; {\gamma }_{j{j}^{\prime }}={\gamma }_{j^{\prime }j, }\forall \mathrm{j}\ne {\mathrm{j}}^{\prime }$$

(15)

Restriction (1) ensures that both vectors (inputs and outputs) are feasible for each DMU; this means that the distance to the frontier will be null (just above the frontier) or positive (under the frontier). Restrictions (2) and (3) impose the monotonicity conditions. Hence, the inefficiency will increase as the production of non-desirable outputs will also increase—which causes the reduction in the desirable output production. Restriction (4) involves the positive monotonicity of the inputs for the mean level of input usage. Finally, restrictions (5) and (6) are related to the translation property and symmetry conditions, respectively.

3. Results and Discussion

Information obtained has been presented in two sections. As part of the sizing and design approach, Section 3.1 presents the results of the NBSWT minimum volume for runoff sediment removal targets, and Section 3.2 includes the results of monetary valuation of the environmental benefit from sediment retention and treatment using the shadow prices methodology.

3.1. Results of the NBSWT Volume and Sizing Design

Studies conducted in the field demonstrated that higher rates of sediment accumulation over the street surface occur during the first days without rain after a given rainfall event. Further, highest concentrations of sediment in runoff are associated with first millilitres of runoff and tend to decrease as runoff travels over the catchment of a built-up area [24,26,37,38]. According to this, management of runoff pollution by the implementation of NBSWT as a decentralised system, has been proven to be an effective approach to diffuse contamination loads control in impaired watersheds. Therefore, several actions demonstrated the benefits from NBSWT in urban areas to perform as a decentralised strategy for urban stormwater runoff control, mitigating water quality impacts to the receiving water bodies [39]. In the case study, NBSWT, designed to retain the first millimetres of runoff, were localised in the street available space downstream of each catchment.

The NBSWT were projected as off-line systems for first-flush control in the streets of the selected urban area. NBSWT were adapted to street dimensions, with variable width between 1 and 2.50 m, and a fixed depth of 0.25 m. The results from ArcMap geospatial processing are displayed in Figure 2. These results are based on geospatial processed data and satellite images on Google Earth Pro that are shown in the sequence.

3.2. Environmental Benefit of Sediment Retention by the Proposed NBSWT

Considering the environmental benefit of reducing stormwater runoff sediment loads by using NBSWT is a key aspect to support local decision-making, providing policy-makers evidence of the economic value of these natural technologies. The inclusion of these kinds of studies in the planning processes will support the mainstreaming of effective local actions that can help to mitigate the environmental challenges related to the presence of large quantity of fine sediment in aquatic systems, which has been proven to be a main cause of ecosystem degradation [6]. Aquatic systems have a specific quantity of sediment that can be tolerated without jeopardising the ecosystem balance. However, runoff sediment increases the fine solids that arrive at the aquatic system, and they cannot be naturally managed, causing imbalance in ecosystem dynamics. NBSWT imply exploiting the potential of natural water cleaning processes to effectively mitigate the effects of build-up on water quality.

These systems retain runoff sediment based on abiotic (hydraulics and geomorphology) and biotic (biofilm, macrophytes, and riparian vegetation) properties of aquatic ecosystems. Abiotic properties are focused on reducing the speed of the water stream with the aim of forcing the particles to be deposited and accumulate in the NBSWT, whereas biotic properties are based on the relationship between organisms and the environment (e.g., natural biofilms of NBSWT enhance sediment deposition due to the increase of particle cohesion; plant species help to reduce water speed). The different treatment mechanisms provided by these natural technologies help to manage runoff sediment. Therefore, NBSWT are suitable to be integrated in watersheds where the increase of built-up areas, deforestation, and the introduction of new sources of pollution by human activities have modified the ecosystem dynamics [40].

Once NBSWT are sized and designed, the monetary quantification of the environmental benefits is needed to assess the feasibility of the system as a strategy to reduce runoff sediment in the study area. For this, the shadow prices methodology has been used to obtain the environmental benefits since it allows the consideration of objective data from sediment retention and the characteristics of the study area. Results obtained show that the shadow price of retained sediment in the proposed NBSWT is 530 USD/kg. Considering this information, the environmental benefits of the NBSWT located in the study area are shown in

Table 5. Environmental benefit obtained for the proposed NBSWT for the study (expressed in USD/year).

	Environmental Benefit (USD/Year)
NBSWT1	38,774
NBSWT2	12,034
NBSWT3	119,135
NBSWT4	65,496
NBSWT5	120,328
NBSWT6	240,852
NBSWT7	94,211
NBSWT8	206,635
NBSWT9	137,490
NBSWT10	101,724
NBSWT11	116,198
NBSWT12	48,921
NBSWT13	97,345
NBSWT14	120,221
NBSWT15	99,641.5
TOTAL	1,619,010.2

. These results can be compared with previous shadow prices studies focused on the different pollutants identified in wastewater treatment plants [41]. The total amount of environmental benefits generated for ecosystems is USD 1,619,010/year. Hence, using shadow prices allows the environmental benefit to be obtained in monetary units to demonstrate the importance of retaining sediment in this area since it provides mineral water resources that drain to the largest water reservoir of the state of São Paulo, the Cantareira system. Considering again a useful life of 25 years for the NBSWT, total environmental benefits are estimated as USD 40,475,255.

The NBSWT are capable of retaining the runoff sediment loads, decreasing first-flush contaminant concentrations, and mitigating peak flow volumes downstream [42,43,44]. The work of Yang et al. [45] demonstrated the effectiveness of natural technologies to retain organic matter and debris in medium-to-intense storm events in Melbourne through implementing bioretention basins. Additionally, Robotham et al. [46] quantified the sediment loads retained by NBSWT from a 3.4 km² area in 83 T. For the case of the NBSWT designed in the proposed case study, it is estimated that around 3 T/m³ of water runoff from an approximately 3300 m² area in isolated storms occurred between May and September. This result demonstrates the effectiveness of NBSWT to retain sediment loads in small contribution catchments and is in line with the abovementioned studies’ results. At the same time, the monetary valuation of the environmental benefit demonstrates that the incorporation of NBSWT is an optimal mechanism to manage urban and rural stormwater runoff, especially during isolated storm events in dry seasons. The results highlight the importance of assessing the socio-environmental benefit that natural technologies for water treatment such as bioretention basins can bring towards urban resilience and ecological protection for this region, which can be extrapolated to other similar urbanised areas in humid tropical and subtropical biomes.

The implementation, management, and operational aspects of NBSWT are different from those required for conventional hydraulic infrastructure, such as piping systems, storm tanks, and other traditional drainage systems. NBSWT lifespan and efficiency over time depend upon maintenance and operational works that guarantee their correct performance (periodic removal of debris, inspections, and vegetation, etc.). In addition, monitoring of the system and operational inspections are also necessary to decrease the risks of potential damage of the system in the long term, even though these are not as frequent and costly as in conventional drainage infrastructure. The total cost of the 15 proposed NBSWT has been calculated as USD 4,233,969 for the total useful life of 25 years (Section 2.3). It is important to compare this value with the environmental benefits assessed by the shadow prices methodology. In this case, the total environmental benefits generated by the 15 NBSWT for 25 years are USD 40,475,255, which is almost ten times higher than the required costs. These results reinforce the adequacy of installing NBSWT in the study area to retain sediment and increase the water and ecosystem quality. Furthermore, the lower costs of constructing and managing the NBSWT are in line with the conclusions from Le Coent et al. [47], which demonstrates the adequacy (in terms of costs) of NBSWT versus conventional drainage systems. Therefore, benefits resulting from NBSWT are quantified as higher than those related to their construction and implementation and serve as a basis to corroborate the cost–benefit assessment results provided by the literature [15]. As a result, this verifies the socio-economic advantages from including the proposed NBSWT and environmental assessment approach in applying funding strategies by decision-makers and public institutions.

As part of the NBSWT direct benefits, the authors highlight the environmental benefit from retaining sediment loads as presented by applying the shadow prices methodology, which is higher than the quantified construction and operation cost. Secondly, as part of retaining sediment, benefits from retaining nitrogen and phosphorus in runoff are also contemplated. Literature demonstrates NBSWT effectiveness to retain and remove both contaminants in runoff [48,49,50,51,52]. Nitrogen and phosphorus retention reduce the eutrophication impacts derived from their presence in excessive amounts in aquatic ecosystems [53]. With regard to the phosphorus, the work from Robotham et al. [46] quantifies a reduction between 5% and 10% of its concentration in water retained through NBSWT. On the other hand, La Notte et al. [54] quantifies the monetary value of nitrogen in bio-retention systems as USD 2167/km. These values show the good performance of NBSWT to retain sediment from runoff and its suitability for delivering additional environmental value associated with the removal of nitrogen and phosphorus loads.

Currently, NBS have been used to reduce the impact of sediment on river basins. The work of Tal-maon et al. [55] analyses the optimum location of nature-based solutions in interurban areas. The authors highlight the importance of identifying the suitable location for nature-based solutions to achieve the maximum benefits of sediment retention for society and biodiversity. Specifically, these authors present a methodology to easily place the nature-based solutions focused on the infiltration rates as a hydrological proxy of nature-based solutions’ effects. According to Koutsovili et al. [56], including all stakeholders and citizens in the development of measures to control floods and sediment by nature-based solutions is an essential part of NBSWT design. The authors use interviews and workshops to identify the information level of residents, considering that they are aware of the consequences of floods, since they have been affected for years. Results show that participants call for public interventions based on the environmental dynamics to reduce the impact of floods (water level and sediments). This study proves that the participation of all stakeholders is necessary to help the decision-makers to understand the territory with the aim of applying the best solution according to local and environmental needs.

Considering the results and the information presented here, this study serves as a basis to corroborate that the use of NBSWT to retain sediment in stormwater runoff is an optimal solution from an environmental point of view due to their effectiveness [57]. Furthermore, the NBSWT can be adapted to geomorphological and irregular street layouts with lower environmental impact and technification needs. The design adaptability of these decentralised networks allows for both a more flexible spatial planning approach and easier integration into the watershed restoration planning. From a socio-environmental point of view, the reduction and control of runoff water volumes help to decrease the costs associated with the implementation of flooding mitigation control infrastructures and their subsequent maintenance works, which is a more economic and strategic way to approach flooding risk issues in low-income neighbourhoods. The monetary valuation of the environmental benefits from the use of NBSWT is fundamental in feasibility studies. Specifically, the advantage of using shadow prices is to provide evidence of the importance of integrating NBSWT in areas with runoff problems. As a result of the inclusion of the environmental benefits, translated into monetary value, NBSWT can be mainstreamed as a sustainable management solution for territorial planning policies and as a key strategy for climate change adaptation [58,59]. Moreover, it demonstrates the importance of the aggregated value in the territorial socio-economic contexts, improving health care and economic conditions, as other literature studies prove [60,61,62,63,64].

Results obtained are in line with Sustainable Development Goals, specifically with the Goal 15: Sustainably manage forests, combat desertification, halt and reverse land degradation, and halt biodiversity loss. Runoff significantly reduces soil coverage, affecting biodiversity, the water cycle, and climate. Considering the aims of the Goal 15, designing and implementing actions, such as NBSWT, are fundamental to guarantee the safety and the continuity of the ecosystems. Considering the importance of the proposed NBSWT on the water cycle, the influence on Goal 6: Clean water and sanitation is significant. Runoff is provoked by rainfall episodes and the soil dragged away by rain arrives at rivers, increasing water turbidity and eutrophication risk. Hence, being capable of retaining sediment by the NBSWT proposed positively affects both the soil balance and the water cycle. It is important to highlight that, although the study area proposed in this study is small, the importance of retaining sediment with NBSWT is comparatively great. Under a climate change situation, small actions around the world can bring positive developments in conservation and sustainability of the ecosystems. This evidence needs to be considered by decision-makers to promote NBSWT in mountain areas by public investments and with the participation of all the relevant stakeholders.

The use of the shadow prices methodology to obtain a monetary value of the environmental benefit demonstrates the usefulness of NBSWT to manage water flows and the impacts of human settlements and activities. This novel approach allows the monitoring of the degree of improvement achieved by the proposed NBSWT, since it depends directly on the amount of sediment that is retained. Likewise, the shadow price obtained reflects the socioeconomic importance of runoff management in impaired humid subtropical forests by providing a monetary value that can be included in economic feasibility assessments. The NBSWT are easily adaptable to the territory to preserve water ecosystems highlighting both the interrelationship between water ecosystems and society and the importance of including the environmental externalities in decision-making processes. This is an initial study that aims to quantify the environmental benefit of retaining runoff sediment. As an initial approach, the authors have not considered the indirect benefits of removing sediment, such as the improvement of river water quality (more biodiversity and better physical conditions for plant growth) or the detailed assessment of sediment typology to be used as fertiliser or construction material; these are the main limitations of this study. On the other hand, changes in soil and forest management measures could be assessed to reduce sediment load, helping the performance of NBSWT to stop the first-flush water volume. These issues have been considered for future research. Considering the results obtained in this study and the need to demonstrate the viability of NBSWT in the study area, the authors are considering future research lines focused on the economic quantification of the social impact of sediment retention by using other innovative methodologies.

4. Conclusions

Nature-based solutions are based on the natural dynamics of water ecosystems to manage different types of situations (water pollution, drainage systems, runoff retention, among others). In the case of this study, NBSWT planning and sizing are proposed to retain the runoff sediment in the Mantiqueira Mountain Range area, an Atlantic Rainforest at a high altitude in Southeast Brazil. The main purpose of NBSWT is alleviating downstream degradation caused by sediment accumulation. As a result, different economic, social, and environmental benefits have been obtained, which can be used to support the implementation of NBSWT in the affected areas. The use of NBSWT generates various economic, social, and environmental benefits that must be considered in the decision-making process to highlight the feasibility of nature-based solutions in rural areas by using monetary valuation methodologies, such as the shadow prices used in this study.

Results obtained for the NBSWT design show the adaptive capacity that these nature-based solutions have according to the territory and its climatic particularities. On the other hand, the use of shadow prices methodology has allowed for the finding that the total environmental benefit of retaining runoff sediment in the proposed NBSWT is estimated as USD 40,475,255. This value demonstrates that the retention of runoff sediment generates a direct environmental benefit related to the ecosystem improvement of the river system located downstream, preserving its environmental and social importance. The use of the shadow prices methodology as a tool for environmental benefit assessment demonstrates the usefulness of nature-based solutions to manage water flows and the impacts of human settlements and activities. Specifically, the environmental benefit obtained is an essential part of feasibility assessments, since decision-makers can identify the potentialities of NBSWT for their territory. Furthermore, obtaining an environmental benefit in monetary terms allows both the internalization of runoff externalities and the social awareness of land and vegetation cover conservation in mountain areas. This novel approach highlights the impact of runoff in impaired humid subtropical forests and the need to implement solutions adapted to specific territories to preserve water ecosystems and improve the adaptation to climate change.