Assessing Reliability, Resilience and Vulnerability of Water Supply from SuDS

Abstract

In recent decades, the impacts of urbanization on the hydrological cycle have led to an increase in the frequency and magnitude of urban flooding events, and this is also amplified by the effects of climate change. Sustainable Drainage Systems (SuDS) provide a revolutionary change in this field, improving the sustainability and resilience of cities. This research explores the integration of different SuDS with the aim of significantly reducing both the flow volume and celerity of floods in a residual urban catchment area of the metropolitan city of Querétaro (Mèxico), where extreme rainfall frequently occurs. This catchment is a representative suburb of urban pressure and environmental degradation problems. Currently, managing storm water under climate uncertainty through a multi-disciplinary approach is a major concern in this urban area. A 1D–2D coupling model of shallow water equations, the finite volume method, an unstructured meshing method, and a hybrid parallel computing application defined the optimal configuration of SuDS at catchment scale to reduce the flood vulnerability in Querétaro. Specifically, in this paper, we explore the management issues of the proposed SuDS configuration that acts as a water resource system with multiple purposes. A generic simulation model called MODSIM was applied to simulate the designed urban drainage system under a balanced IPCC future climate scenario in terms of reliability, resilience and vulnerability against water scarcity. The proposed hierarchical Reliability–Resilience–Vulnerability approach appears to be effective in evaluating the system performance, showing that the complete satisfaction of non-essential water uses in Querétaro can be assured at a 65% rate of reliability for a large range of reservoir storage conditions.

1. Introduction

Urban flooding is a growing concern influenced by factors such as climate extremes, urban growth, land-use changes and poor land-use planning [1,2]. The negative impacts of flood events include loss of life, economic damage and environmental degradation. The problem becomes even more relevant in fast-growing cities due to their changing dynamics and increasing social vulnerability [3]. The processes of urbanization, with unlimited demand from the social system and limited supply from the environmental system, generate—more likely in a neoliberal context [4] with high productive and economic growth—socio-natural risks [5], particularly in the space of urban–rural transition: the urban periphery [6]. These spaces are occupied by people who are poor, who do not plan ahead and are unaware of their susceptibility to hazard impacts [7,8,9].

Urban Drainage Systems (UDS) are an integral part of the urban infrastructure that can significantly enhance its resilience against urban floods [10]. UDS are not able to cope up with extreme uncertain events [11] that would require unsustainable engineered solutions in terms of enormous financial and environmental costs. An option to enhance the resilience against extreme events and urbanization pressure could be nature-based solutions, i.e., Sustainable Drainage Systems (SuDS) [12,13]. SuDS can realize an integrated network of engineered vegetated areas and open spaces that complements centralized conventional UDS. Rain gardens, green roofs and porous pavements are examples of SuDS that can be used to protect the natural ecosystem and to offer a wide variety of benefits to people and wildlife [14]. The state-of-the-art methods in SuDS development and their practical application have focused on technical aspects such as selection, location, size optimization [15], and performance assessment, i.e., reduction in runoff volumes and flow peaks [16] and cost–benefit analysis [17]. Particularly in arid and semi-arid regions, some SuDS (e.g., rooftop rainwater harvesting—RWH—systems) can be used to provide an additional source of water [18] and the interconnection of SuDS can constitute a water resource system (WRS), simple or complex, to minimize the pressure on water resources. These systems store stormwater runoff from rooftops and other impervious surfaces to supply different types of demands (e.g., households, irrigation, industries), possibly after temporary storage and treatment [19].

This literature clearly shows that most SuDS have not achieved widespread implementation worldwide due to the gaps in knowledge regarding designing, implementing, and maintaining SuDS or quantifying the benefits and co-benefits of their ecosystem services [20,21]. SuDS planning, design, and management is a high-level complexity problem that requires a modeling exercise to predict the behavior of SuDS configurations (type, design, and location) and predict their impact on the existing urban system. This modeling exercise, in the form of simulation, optimization or other tools like multi-criteria approaches, can be developed in a Decision Support Systems (DSS) framework. While scientific and technical literature is available on the DSS development and application of SuDS under extreme conditions in temperate regions (e.g., to minimize surface water runoff and flood risks in urban areas) [22,23], the management of SuDS as WRSs with the additional objective to increase the performance in supplying different uses in urban areas is largely ignored.

There are a variety of criteria one can use to judge and compare performances of WRS management alternatives [24]. In a pioneering paper, Hashimoto et al. [25] presented the reliability–resilience–vulnerability (RRV) analysis that has defined the standard approach in the evaluation and selection of alternative design and operating policies for a wide variety of water resource projects. Some system performance objectives may be in conflict, and in such cases, DSS can help identify the efficient tradeoffs among these conflicting measures of system performance. These tradeoffs indicate what combinations of performance measure values can be obtained from various system design and operating policy variable values. These indicators are typically quantified across large sets of possible future climate scenarios (e.g., thousands of scenarios), generated either through the downscaling of global climate model projections or through statistical hydrological models [26]. Sulis and Sechi [27] presented an extended state-of-the-art review on simulation and optimization modeling approaches in reservoir system operation problems. Specifically, Sulis and Sechi illustrated the application performances of five generic models for simulating multi-reservoir and multi-use water resource systems: AQUATOOL-SimWin (Valencia Polytechnic University) [28], MODSIM (Colorado State University) [29], RIBASIM (DELTARES) [30], WARGI-SIM (University of Cagliari) [31], and WEAP (Stockholm Environmental Institute) [32]. In this paper, MODSIM has been selected as the most promising for a preliminary analysis of alternative plans and policies on the water resources system, as an aggregation of different SuDS. MODSIM uses a minimum-cost network-flow optimization algorithm to allocate run-of-the-river flows and stored volumes among a specified set of demands, according to the institutional framework governing the distribution of water [33].

In this perspective, this paper explores a novel comprehensive approach to assess the RRV performances of a SuDS working as a WRS to supply multiple competing water uses in a peri-urban space of the metropolitan city of Querétaro (Santiago de Querétaro). The city of Querétaro, capital of the State of Querétaro (Mexico), exemplifies the problem of the unequal impacts of urban flooding that peri-urban spaces are experiencing worldwide. With the onset of metropolization and the uncontrolled expansion of the last fifty years, Querétaro has experienced an urban growth of about 10 times its 1970 size, occupying fertile and arable land, stream and lakes, and groundwater recharge areas. This accelerated growth has caused the segregation of low-income populations in spaces unsuitable for housing on the outskirts of the city [34,35] and areas with human overcrowding, a decrease in occupancy density, and the degradation of ecosystems.

Adapting to a changing climate presents an opportunity to rethink the urban development in this peri-urban space. By keeping a holistic view of the situation, the incorporation of various SuDS elements can contribute to greener and more pleasant urban spaces for the residents, even during the frequent and intense droughts.

2. RRV Methodology

The use of RRV indices for classifying and evaluating WRS performance was first suggested by Hashimoto et al. [25]. Vulnerability thresholds define the acceptable limit of each performance measure based on the planning objectives or stakeholder preferences, e.g., a water reliability target of 95%. Specifying vulnerability thresholds may be challenging when there is no empirical data about critical tipping points (such as a minimum discharge requirement for protecting downstream ecology) or when there is a lack of consensus among the experts. In such cases, analysts can define vulnerability thresholds based on the spread of historical or model-simulated performance, for example, based on the outcome at the 90th or 95th percentile value of an output variable [36,37].

Several combinations of estimators of RRV have been proposed and some of these studies discuss which are the most appropriate [24]. RRV combination criteria have been applied to existing water resources systems [38,39,40,41], in some cases under extreme events [42]. On the other hand, RRV combinations have examined the impacts of climate change [43] and variability [44] and imposed demands [45]. More recently, the ASCE Task Committee on Sustainability Criteria has recommended that these indicators are combined into an aggregated indicator of sustainability, but this gives little indication of the relative system performance for each indicator.

Rather than developing an aggregate indicator as a product of RRV, this paper presents a comprehensive approach that evaluates the single indicator in a hierarchical order. Firstly, a criterion, C, is defined for each water supply source, where an unsatisfactory value is one where the source is unable to provide a prespecified yield. The time series of simulated monthly values of either river flows or reservoir levels, X_t, are then evaluated to some future time horizon, T. Failure is defined as the inability of the system to meet the imposed demands. Each water supply source will have its own range of satisfactory, S, and unsatisfactory, U, values defined using the criterion, C [25]. The C value, which is the states of S and T, can be fixed as defined using the traditional probabilistic RRV method or can be defined in a fuzzy approach. The periods of unsatisfactory X_t are then defined as J₁, J₂,…, J_N. In this study, the focus is on water supply systems, and, therefore, the S state occurs when water supply is able to meet water demand and, hence, the U state is when supply cannot meet demand. Moving from time step t to t + 1, the system can either remain in the same state or migrate to the other state and W_t indicates a transition from an unsatisfactory to a satisfactory state.

$$X_t=\left\{X_1,X_2,...,X_T\right\}$$

(1)

$$\begin{array}{c}if X_t\ge C then X_t\in S and Z_t=1\\ \mathrm{e}\mathrm{l}\mathrm{s}\mathrm{e} X_t\in U \mathrm{a}\mathrm{n}\mathrm{d} Z_t=0\end{array}$$

(2)

$$W_t=\left\{\begin{array}{c}1\begin{array}{cccc},& if& X_t\in U& \begin{array}{cc}and& X_{t+1}\in S\end{array}\end{array}\\ 0\begin{array}{cc},& otherwise\end{array} \end{array}\right.$$

(3)

The oldest and most widely used performance criterion for water resources systems is reliability, C_R, that measures the probability of failures. C_R was defined by Hashimoto et al. [25] as the following:

$$C_R=P\left\{X_t\in S\right\}$$

(4)

This paper applies the definition C_R as occurrence reliability, which can be estimated as the following:

$$C_R=\frac{\sum _{t=1}^T{Z}_t}{T}$$

(5)

Resilience, C_RS, gives an indication of the how quickly systems return to a satisfactory state once the system has entered an unsatisfactory state. Hashimoto et al. [25] define resilience as a conditional probability:

$$C_{RS}=P\left\{X_{t+1}\in S|X_t\in U\right\}$$

(6)

and is estimated as the inverse of the mean value of the time the system spends in an unsatisfactory state, i.e.:

$$C_{RS}=\frac{\sum _{t=1}^T{W}_t}{T-\sum _{t=1}^T{Z}_t}$$

(7)

Vulnerability, C_V, is a measure of how significant the likely consequences of failure may be. C_V is defined by Hashimoto et al. [25] as a measure of the likely damage of a failure event:

$$C_V=\sum _{j\in U}P\left(j\right)H(j)$$

(8)

where H(j) is the most severe outcome of the jth sojourn in unsatisfactory state and P(j) is the probability of H(j) being the most severe outcome of a sojourn into the unsatisfactory state.

It is important to note that these criteria, as defined in the literature, may not be applicable as is to all practical cases and may need to be modified on case-by-case basis. Sulis and Sechi [27] argued that the maximum event as proposed by Moy et al. [46] might be a better estimator than the event-based mean value of Hashimoto et al. [25], i.e.,

$$C_V=max\left\{{max\left(C-X_t\right)}_{t\in J_i},i=1,\dots ,N\right\}$$

(9)

The basic assumption of the proposed model is that an RRV model can be seen as the connecting element between the real WRS and the expected demand supplies [47]. Given the total storage level in all system reservoirs (S) in the present month t, the supply D for a use j in a water system can be linked through a mathematical function f to the required levels of a performance index (Ind = {C_R, C_RS, C_V}) over a time horizon T:

$$f\left(D,T,t,{Ind}_j,S\right)=0$$

(10)

The structural assumption of the model is that the function f can be made explicit (F = f ⁽⁻¹⁾) and the D is defined as the univocal function F of a required level L of C_R. Specifically, given S in the system at t, D to j is calculated to guarantee a required level L of C_R over T:

$$D=F\left(j,T,C_R\left(L\right),S,t\right)$$

(11)

Considering the calculated D, the C_RS and C_V values of j are defined as function G and B over a time horizon Δ:

$$C_{RS}=G\left(D,∆,j\right)$$

(12)

$$C_V=B\left(D,∆,j\right)$$

(13)

3. The Menchaca Basin

Located in the eastern suburban area of the metropolitan city of Queretaro, in the Rancho Menchaca catchment area, this sub-basin is part of a topographic depression filled by sediments formed by the normal displacement of regional faults since the Miocene [48].

Groundwater has been strongly withdrawn over the last three decades in the study area, with a decline of the piezometric level exceeding 100 m and, consequently, land subsidence [49]. The climate has classified this basin as a semi-arid region; however, in higher elevations (up to 2300), the climate shifts to semi-wet cold or wet-cold class. The rainy season is from May to October with annual values between 500 mm and 600 mm. Concerning rainfall intensity and frequency, data published by the Municipal Planning Institute of the Municipality of Querètaro (2015) were used, calculated from data from the Querètaro Observatorio station, which covers a particular area of influence for the Rancho Menchaca catchment area. It is observed that in one hour the probability of rainfall reaching 22.5 mm is high, as it occurs with a return time of 2 years. This rainfall intensity can be classified as heavy rain according to official rainfall intensity classifications such as that of the National Institute of Meteorology of Spain, according to which it is considered heavy when the accumulation of rain in one hour is between 15.1 and 30 mm (Table 1). The methodological approach is based on the awareness that the knowledge of the actual climate context and its temporal pattern is actually extremely important for designing SuDS role in the future management of urban stormwater. In particular, the depth-duration-frequency (“ddf”) curves represent the climate input typically used in hydrological modeling analysis [50].

The flood risk map was identified through the perimeter of areas subject to hydraulic hazards overlapped by the value of potential damages given by the product of vulnerability and exposed elements, to obtain the areas at highest risk (Figure 1).

While its characteristics, therefore, give it a non-urban vocation, the sub-basin experienced an intensive and rapid urbanization process leading to land-use and land-cover change which inevitably affected the hydraulic properties of surface runoff (peak discharge, volume and frequency). The inhabitants, deprived of secure land ownership, are excluded from urban development plans and do not benefit from infrastructure to deal with the problem, while their daily activities, physical integrity and heritage continue to be at high risk. Its environmental characteristics, combined with the socio-economic disadvantages of the inhabitants, frequently expose the population and their properties to the damage and losses that stormwater runoff, especially in the peak rainy season, can cause. Usually, flood events are accompanied by the occupation of flood-prone sites by socially vulnerable groups that have significant disadvantages (economic, political, cultural and social) to deal with the damage, thus decreasing their capacity to respond, adapt, persist and be resilient [51,52,53].

Year after year, the inhabitants of the Menchaca Basin settlements have to face the increasing impacts of flood and solid debris from anthropogenic and natural activities, while traditional hard-engineered systems have amplified the processes of socio-economic segregation in Mexican cities in general [6] and in the city of Querétaro in particular [34].

Table 1. Rainfall intensity—duration—frequency data in the sub-basin. UoM: intensity in mm, duration in hours, frequency as return period in years.

Tr (Years)	10 min	30 min	60 min	120 min	240 min
2	21.69	22.01	22.50	23.48	25.43
5	29.54	29.98	30.65	31.98	34.65
10	34.75	35.27	36.05	37.62	40.75
25	41.35	41.97	42.90	44.77	48.50
50	46.22	46.91	47.95	50.03	54.20
100	51.04	51.80	52.95	55.25	59.86
500	55.98	56.81	58.08	60.60	65.65
1000	60.00	60.90	62.25	64.96	70.37

Source: Instituto Municipal de Planeaciòn [54].

Table 1. Rainfall intensity—duration—frequency data in the sub-basin. UoM: intensity in mm, duration in hours, frequency as return period in years.

Tr (Years)	10 min	30 min	60 min	120 min	240 min
2	21.69	22.01	22.50	23.48	25.43
5	29.54	29.98	30.65	31.98	34.65
10	34.75	35.27	36.05	37.62	40.75
25	41.35	41.97	42.90	44.77	48.50
50	46.22	46.91	47.95	50.03	54.20
100	51.04	51.80	52.95	55.25	59.86
500	55.98	56.81	58.08	60.60	65.65
1000	60.00	60.90	62.25	64.96	70.37

Source: Instituto Municipal de Planeaciòn [54].

Figure 1. This map shows the areas most at risk of flooding in Querètaro and the Menchaca micro-basin. Source: Altana’s elaboration based on ONU-Habitat maps [55].

Figure 1. This map shows the areas most at risk of flooding in Querètaro and the Menchaca micro-basin. Source: Altana’s elaboration based on ONU-Habitat maps [55].

4. Water System of Suds

In the past, urban drainage management has only been approached from a hydraulic point of view, with the aim of draining and collecting rainwater from sealed surfaces and conveying it away from urbanized areas as quickly as possible. The scientific community has, however, pointed out that urban drainage management of this type entails a series of problems, especially in light of the effects of climate change with an increase in the frequency and intensity of extreme rainfall. The traditional method of hydraulic management is therefore proving to no longer be able to respond to the current needs of hydraulic protection of the territory.

To reduce the urban flood vulnerability in Menchaca, a SuDS was designed that involved three interventions based on different hydraulic phenomena: infiltration through green roofs (1), lamination through an urban lamination park (2) and interception through a vegetated channel (3), the latter transferring water to the existing downstream reservoir. This multiple system was selected in the decision process toward the regeneration of a public space in the proximity of the river that includes hydraulic, architectural and social measures for a better quality of life (Figure 2).

The most upstream measure in the basin is the green roof (1), the main objective of which is to promote infiltration and delay the entry of water into the disposal system. A critical aspect in designing the green roof was the selection of the proper type of vegetation since we are in a semi-dry climate. The recommended plants to be placed on the roofs were those with a high resistance to direct sunlight and those that naturally store water in their tissues, such as succulents. It was also preferable to select Mexican species, without altering the vegetation by invading native ecosystems. The vegetation proposed in the project consists of plants that can withstand long periods of drought, sun, and frost, with low substrate depth and a low required maintenance in general. These belong to the botanical families of Agavaceae, Cactaceae and Crassulaceae (succulent group). Among the types of green roofs proposed in the literature, an extensive type of roof, with a minor sub-layer, was chosen, which is suitable for re-roofing in existing buildings.

The most downstream measure was the vegetated channel (3) with the main objective of runoff reduction. The slope of the road was modified to concentrate the water flux into the central vegetated lane, with a subterranean drainage system that transfers water to the existing downstream reservoir. Impermeable materials were replaced with permeable ones (Figure 3).

In the central basin area, an urban micro-lamination park (2), as an aggregation of three dams, creates temporary water detention basins and intercepts sediment before it enters the urban area.

Therefore, the opportunity was taken to identify this corridor, which is still partly natural and partly completely compromised by buildings, and to try, where possible, to free it of the superfluous constructions that insist on it in order to restore spatial continuity.

Beyond this role of engineering intervention aimed at reducing the urban flood vulnerability, the architectural project identifies this valley as an element of regeneration and social redemption. New living spaces for recreational activities and public relations are then realized in structures originally designed for a purely engineering mono-function. In addition, the dams themselves become an opportunity to create a connection from one side of the valley to the other, and the artificial hillsides can contribute to reduce the water celerity, assuming the dams can be overflooded.

5. Operation and Performance of the System

The aggregation of SUDS can be seen as a water system of reservoirs and demands. The masterplan in Querètaro shows five reservoirs supplying four demands (Figure 4). Reservoir 1 is the largest operating reservoir in the system with a 36,500 cubic meters gross storage capacity.

Practical real-time operations for multiple purposes require the specification of reservoir operating rules to determine the amount of water to release and storage for each reservoir at each time step. The presumption [56] of these rules is that a system of reservoirs can be operated to produce greater benefits than operating the individual reservoirs independently.

The masterplan in Querètaro shows five reservoirs in a series for multiple purposes (Figure 5):

• Reservoir 1: water supply for non-essential secondary residential demand (irrigation of public and private green, road cleaning);
• Reservoir 2: emergency water resource (tankers, users not served via the water mains, livestock watering);
• Reservoirs 3 and 4: flood control;
• Reservoir 5: recreation and flood control.

Conceptual rules for reservoirs in a series in

Table 2. Seasonal operating rules in the system reservoirs.

	Season/Period
Purpose	Refill	Drawdown
Water supply	Fill upper reservoirs (Reservoir 1) first	Empty lower reservoirs (Reservoir 2) first
Flood control	Fill upper reservoirs (Reservoir 3 and Reservoir 4) first	Empty lower reservoirs (Reservoir 5) first
Recreation		Equalize marginal recreation improvement of additional storage among reservoirs

are adapted from Lund and Guzman. An operation for multiple purposes can be derived through combining these rules. For Reservoir 1 and Reservoir 2 providing the water supply, a reasonable objective is to maximize the amount of water available. The resulting rule for single-purpose water supply reservoirs in a series would simply be to fill the Reservoir 1 first and the Reservoir 2 last. For Reservoir 3 and Reservoir 4 with intermediate inflows and storage serving solely for flood control downstream, it is optimal to regulate floods by filling the Reservoir 3 first and emptying the Reservoir 4 first.

An operation for multiple purposes can be derived by combining these rules. Fortunately, many of the operating rules presented here for Querètaro show compatibility between different reservoir purposes, such as flood control and water supply for refill periods on reservoirs in series.

In MODSIM, the water system was represented as a network of nodes and links, illustrated schematically in Figure 5. The nodes are representative of reservoirs and demands. The links are connections between the nodes and are representative of river reaches or canal/pipeline conveyors. Singular consumptive demands were aggregated for typology in two classes:

• Non-essential water uses in residential compounds (three nodes);
• Secondary water uses (one node).

Water consumption in a community is characterized by several types of demand, including domestic, public, commercial, and industrial uses. Here, non-essential demand is defined as the sum of domestic and public demand percentages for uses in the residential compounds, as the irrigation of public and private green, aesthetic uses (such as fountains and ponds), road cleaning and motor vehicle washing. It is assumed that supplies for non-essential uses can be reduced by the application of hedging rules in the reservoirs without significant comfort losses in the population. Specifically, the irrigation of public and private garden (as green roof) in the j-compound is assessed using the following:

$$T_j=\sum _{i=1}^{12}\left[{\left(\frac{D}{N}\right)}_i{S}_{1,j}{U}_{1,j}+{\left(\frac{D}{N}\right)}_i{S}_{2,j}{U}_{2,j}\right]$$

(14)

where symbols are presented in

Table 3. Average monthly rainy days in Querètaro city.

	January	February	March	April	May	June	July	August	September	October	November	December
Di	2	1	3	7	10	16	20	19	17	9	4	3
Ni	31	28	31	30	31	30	31	31	30	31	30	31

.

Table 4. Compound (compound are numbered from north to south) total annual demands.

Compound	Private Area (S1) [m2]	Unitary Monthly Demand (U1) [m3/m2]	Public Area (S2) [m2]	Unitary Monthly Demand (U2) [m3/m2]	Total Annual (T) [m3]
1	30,000	0.1	10,000	0.15	8000
2	22,000		7000		6000
3	28,000		8000		7000

shows the total annual demands in the three compounds.

Other non-essential uses (namely aesthetic uses, road cleaning and motor vehicle washing) in the residential compounds were assessed based on the estimation of 4000 inhabitants and 3800 m of internal road length.

Secondary water uses are aggregated in a single node and referred to as consumptive (water for wild animals in that area—e.g., dogs, cats, horses—and the irrigation of two main athletic fields) and non-consumptive (a water-based fire protection system and water tanks for residential uses during water scarcity) uses.

The current operating rules of the system prioritize water allocation to secondary demands. Recreation requirements have been considered as a restriction and are captured using the operating rules of the reservoirs.

Table 5. Main structure parameters of the existing reservoirs.

Reservoir	Surface Area [m2]	Max Total Volume [m3]
Reservoir 1	18,200	36,500
Reservoir 2	8500	17,000

shows the main parameters of the existing reservoirs. The main goal for reservoir flood control is to minimize the damage due to peak outflow from Reservoir 3, 4 and 5 at critical downstream locations in the urbanized area of Quéretaro. According to the critical-designed section of the downstream open channel, the maximum flow rate is assumed as 80 m³/s (

Table 6. Main structure parameters of the designed reservoirs.

Reservoir	Crest Length [m]	Height [m]	Max Total Volume [m3]
Reservoir 3	60	5	2100
Reservoir 4	65	6	3500
Reservoir 5	80	9	18,500

). The goal of MODSIM is to minimize the number of maximum total outflow discharge from Reservoir 5 exceeding 80 m³/s. The desired monthly pool volume is defined in a trial-and-error simulation approach. The rule curves at each reservoir are developed using MODSIM, where releases are a function of current water surface elevation and inflow rate.

The region’s annual average precipitation is expected to diminish in a range of 10–20%, while its temperature is projected to rise from 1.5 °C to 2.5 °C in the next 50 years [57]. The climate change scenarios were obtained from Global Circulation Models (GCMs) under the six IPCC emission scenarios, and a hydrological model was applied to determine monthly surface runoff under future climate conditions (year 2050) [58]. Here, we focus on the evaluation of SuDS performances over a 500-year monthly runoff timeseries based on an A1B IPCC scenario. A1B is the “balanced scenario” of the A1 family, characterizing alternative developments of energy technologies. A1B gives runoff behaviors with high temporal variability with frequent droughts, alternating with months of substantially high runoff.

6. Results and Discussion of RRV Analysis

MODSIM simulates the expected performance of the SuDS in Quéretaro at different total storage levels (expressed as percentage total capacity) in the five reservoirs (Figure 5). Using Equation (5), supplies that can be assured to a demand at an assigned level of reliability is calculated. For 10% wide ranges of the total storage level,

Table 7. Supply to secondary water uses at 95% of reliability.

Storage Volume	50–60%	60–70%	70–80%	80–90%	90–100%
Supply	100%	100%	100%	100%	100%

shows the supplies to the secondary water uses with a 5% probability of failure. As 5% is the accepted probability of failure in supplying secondary demands, those demands are considered completely satisfied and the vulnerability is equal to zero at 95% of supply reliability. Resilience, as the inverse of the mean value of the time the system spends in an unsatisfactory state, is not calculated (

Table 8. Resiliencies and vulnerabilities to secondary water uses at 95% of reliability.

Storage Volume	50–60%	60–70%	70–80%	80–90%	90–100%
1-Year Resilience	-	-	-	-	-
2-Year Resilience	-	-	-	-	-
1-Year Vulnerability	0%	0%	0%	0%	0%
2-Year Vulnerability	0%	0%	0%	0%	0%

). Supplies to non-essential water uses in residential compounds at a 95% rate of reliability show significant reduction for low storage levels. Specifically, if a low (5%) probability of supply failure is required, the system can assure a low (44%) mean supply to non-essential uses in the case of a total storage level between 50% and 60% of the total storage capacity (

Table 9. Supply to non-essential water uses in residential compounds at 95% of reliability.

Storage Volume	50–60%	60–70%	70–80%	80–90%	90–100%
Supply	44%	93%	95%	96%	98%

).

Table 10. Resiliencies and vulnerabilities to non-essential water uses in residential compounds at 95% of reliability.

Storage Volume	50–60%	60–70%	70–80%	80–90%	90–100%
1-Year Resilience	18%	25%	35%	44%	43%
2-Year Resilience	20%	24%	33%	46%	41%
1-Year Vulnerability	62%	25%	10%	5%	1%
2-Year Vulnerability	70%	44%	22%	14%	6%

shows the high sensitivity of supplies to storage levels, significantly increasing from 44% to 93% for an increased storage level of 10%. For storage levels higher than 60%, the system can assure high supply (higher than 93%) with a high reliability (95%). The only use of an indicator (i.e., supply reliability) could describe a largely acceptable performance of the system. To evaluate the average resilience and vulnerability, two time windows were selected (1 and 2 years) coherently with the storage behavior, over which the average values were calculated. As expected, the 1-year resilience was significantly low (18% of conditional probability) in the case of a total storage level between 50% and 60% of the total storage capacity. In terms of the average time over 1 year, the result highlights that the system spends almost 5 months in an unsatisfactory state. The conditional probability remains significantly low, even for high total storage level. For a reservoir close to the maximum filling condition (90–100%), the unsatisfactory average time over 1 year is close to 2 months. This last result makes clear that the non-resilience of the system failing to supply to non-essential water uses are prolonged events. Resilience does not appear to be sensitive to the time window, at least for the considered length, where 2-year resilience is within the interval ±2% compared to 1-year resilience. These transition probabilities are independent of the length. This behavior can be reasonably justified by considering that failure structures are identical at each year.

Vulnerability as a maximum event over the selected time windows (1 and 2 years) shows the expected behavior. Vulnerability significantly decreases with an increase in total storage level and slightly increases with a wider time window. In the case of a total storage level between 50% and 60% of the total storage capacity, non-essential uses are under high-stress conditions, with a maximum supply reduction of 62%; the latter increases up to 70% over 2 years. Coherently, with an increase in available stored water and without any hedging rule, the vulnerability plunges to 1% and 6%, respectively, over 1 and 2 years. Even in the case of a total storage level between 70% and 80% of the total storage capacity, the maximum supply reduction is largely acceptable (10% over 1 year) for non-essential uses.

MODSIM iteratively simulated the Quéretaro SuDS to find the reliability of the complete satisfaction of the non-essential uses level. The results show that a supply to non-essential water uses of 100% for total storage levels higher than 50% can be assured at 65% of reliability (

Table 11. Supply to non-essential water uses in residential compounds at 70% of reliability.

Storage Volume	50–60%	60–70%	70–80%	80–90%	90–100%
Supply	98%	100%	100%	100%	100%

). At that level, the non-essential water uses are not vulnerable to the water scarcity condition and resilience is not defined.

These results are only partially in concordance with Hashimoto et al. [25] where resiliency shows the same trend as reliability and the vulnerability trend is different from that obtained with the other risk-related performance criteria. This paper shows that when required, supply reliability is high (e.g., 95%), the resilience is significantly low, while the vulnerability is high, particularly for intermediate cumulative storage volumes. However, this confirms that an unavoidable tradeoff between vulnerability and reliability may exist for various project and no-project alternatives. The proposed approach uses a hierarchical two-step methodology to assess vulnerability and resilience at a requested level of supply reliability. This approach can overcome some limitations of the traditional RRV methodology and properly describe the undesirable events that compromise the efficiency of the SuDS in Querètaro.

7. Conclusions

Year after year, the inhabitants of these suburban settlements have to deal with the problems caused by floods and debris that abound in the streets, making it complicated and sometimes impossible to pass, and the phenomenon is accentuated by social vulnerability that limits opportunities for mitigation and response.

The need to remedy this problem is seized as an opportunity to intervene in this urban context, that today claims a new look. Among the existing Sustainable Urban Drainage Systems (SuDS), the most appropriate ones have been studied and chosen according to the objectives they promote and have been customized for the needs of this case, which is a completely different context from those where SuDS are usually applied: the proposed solution through the designed SuDS will increase the resilience of the Menchaca area to hydraulic risk, and bring interesting benefits in terms of ecosystem services such as climate regulation, hydrological regulation, and cultural values. Under ordinary rain conditions, these SuDS can be seen as an aggregation of elements forming a WRS. The multiple purposes of the WRS are modeled and its performance is evaluated in the proposed RRV analysis. This paper highlights that these criteria, as defined in the literature, may not be applicable as is to all practical cases and may need to be modified on case-by-case basis.