Financial allocation and network recovery for interdependent wastewater treatment infrastructure: development of resilience metrics

Figures & data

Figure 1. Proposed framework for WWTP’s flood resilience improvement by financial allocation and prioritized asset restoration.

Figure 2. Sub-criteria defined for quantifying WWTPs’ flood resilience (Adapted from Karamouz & Hojjat-Ansari, 2020).

Table 1. 9-level fuzzy scale for the pairwise relative importance.

Crisp scale	Linguistic scale	Triangular fuzzy scale
1	No difference	(1,1,1)
2	Intermediate	(1,2,3)
3	Moderate importance	(2,3,4)
4	Intermediate	(3,4,5)
5	Strong importance	(4,5,6)
6	Intermediate	(5,6,7)
7	Extreme importance	(6,7,8)
8	Intermediate	(7,8,9)
9	Outmost importance	(9,9,9)

Table 2. Economic sub-criteria with their corresponding marginal costs in USD. (Adapted from Karamouz & Hojjat-Ansari, 2020).

Economic sub-criteria	Unit	Marginal cost
Plants design capacity (Ra3)	MLD	$2.64 million
Generator capacity (Ra8)	1000 kW	$0. 8 million
Percent of not-at-risk equipment (Ro4)	%	$1 million for sandbagging, $1.75 million for elevating critical equipment, and $1.25 million for waterproofing the critical equipment
Number of technical staff (Rs1)	-	$0.043 million for each annual staff wage ($21 hourly wage)
Availability of dewatering facilities (Rs2)	-	$7 million
On-site storage (Rd3)	m^3	$159 million
Additional generators (Rd4)	2000 kW	$1.6 million

Figure 3. An example network before and after the failure of one of its nodes.

Figure 4. Post-disaster behavior and the system’s recovery curve. (Adapted from Bristow, 2015).

Figure 5. Classification of INM components according to their score.

Table 3. Specifications of the WWTPs in the study area (Retrieved from NYCDEP (New York City Department of Environmental Protection), 2013).

Plant’s Name	Design Capacity (MLD)	Population Served	Receiving Waterbody	Drainage Area (km^2)
Owls Head	454.25	758,007	Upper New York Bay	52.39
Coney Island	416.39	596,236	Jamaica Bay	61.05
Rockaway	170.34	90,474	Jamaica Bay	37.47

Table 4. Values of sub-criteria for WWTPs in the study area.

Sub-criteria	ID	Owl’s Head	Coney Island	Rockaway
Hurricane flood elevation	$\mathrm{R}{\mathrm{a}}_1$ (m)	2.82	3.07	3.47
level of serviceability	$\mathrm{R}{\mathrm{a}}_2$ (%)	0	100	100
Plant design capacity	$\mathrm{R}{\mathrm{a}}_3$ (MLD)	454.25	416.39	170.34
Post-stress recovery	$\mathrm{R}{\mathrm{a}}_4$ (hr)	16	112	180
Population served	$\mathrm{R}{\mathrm{a}}_5$ (#)	758	596	90
Untreated effluent discharge	$\mathrm{R}{\mathrm{a}}_6$ (MCM)	0.144	0.134	44.8
Average electricity consumption	$\mathrm{R}{\mathrm{a}}_7$ (kW hr)	2645	3639	2600
Back-up generator capacity	$\mathrm{R}{\mathrm{a}}_8$ (kW hr)	2750	6733	2000
Additional load	$\mathrm{R}{\mathrm{o}}_1$ (MLD)	454.25	416.39	170.34
Critical flood elevation	$\mathrm{R}{\mathrm{o}}_2$ (m)	4.42	4.72	4.42
Maximum inundation depth	$\mathrm{R}{\mathrm{o}}_3$ (m)	1.22	0.91	2.13
Critical assets not at risk	$\mathrm{R}{\mathrm{o}}_4$ (%)	71	73	62
DMR violations	$\mathrm{R}{\mathrm{o}}_5$ (%)	1.4	2.1	1.9
Damage from hurricane	$\mathrm{R}{\mathrm{o}}_6$ ($)	48.4	84.9	49.3
Flood elevation at unit substation	$\mathrm{R}{\mathrm{o}}_7$ (m)	0.73	1.63	1.74
Power loss period	$\mathrm{R}{\mathrm{o}}_8$ (hr)	8	28	72
Asset operators	$\mathrm{R}{\mathrm{s}}_1$ (#)	68	68	41
Availability of dewatering facilities	$\mathrm{R}{\mathrm{s}}_2$ (-)	0	0	0
Risk avoided for every dollar spent	$\mathrm{R}{\mathrm{s}}_3$ ($)	13.8	22.6	13.1
Underground tunnel system	$\mathrm{R}{\mathrm{d}}_1$ (-)	1	1	1
Availability of neighboring WWTPs	$\mathrm{R}{\mathrm{d}}_2$ (km)	7.9	9	9
On-site storage	$\mathrm{R}{\mathrm{d}}_3$ (m^3)	0.5	0	1.51
Number of back-up generators	$\mathrm{R}{\mathrm{d}}_4$ (#)	4	5	2

Figure 6. The study area with its wastewater infrastructure and its related power facilities.

Table 5. Hydrological and technical data sources used in the study.

Data	References
Rainfall hyetograph (JFK airport)	https://www.ncdc.noaa.gov/
Soil type, land use, Boundary	https://opendata.cityofnewyork.us
Dem (30 m)	https://earthexplorer.usgs.gov
Wastewater infrastructure	https://openseweratlas.tumblr.com
Power infrastructure	https://hifld-geoplatform.opendata.arcgis.com

Table 6. Sources used for determining the failure probability and recovery coefficients of different INM components.

	Failure Probability	Recovery Coefficient
WWTP	NYCDEP (New York City Department of Environmental Protection; 2013)	NYCDEP (New York City Department of Environmental Protection; 2013)
Substation	FC (Sánchez-Muñoz et al., 2020)	Depth-damage, and damage-time curves (Sánchez-Muñoz et al., 2020)
Pumping stations	FC (Yu et al., 2021)	Depth-damage functions (FEMA, 2013) Damage-time functions (FEMA, 2003)
Transmission line	Averaged FCs (Salman & Li, 2016)	~N (3.5,2.5; Ouyang & Dueñas-Osorio, 2014)

Figure 7. For a typical electrical substation: a) Fragility curve, b) water depth versus damage, and c) repair time versus damage (From Sánchez-Muñoz et al., 2020).

Table 7. Estimated fuzzy and crisp weights calculated for the sub-criteria.

Rapidity (Ra)				Robustness (Ro)				Resourcefulness (Rs)				Redundancy (Rd)
Fuzzy			Crisp	Fuzzy			Crisp	Fuzzy			Crisp	Fuzzy			Crisp
0.211	0.334	0.576	0.347	0.167	0.298	0.487	0.302	0.113	0.172	0.263	0.173	0.124	0.196	0.300	0.178
Ra1				Ro1				Rs1				Rd1
0.082	0.148	0.263	0.148	0.057	0.102	0.176	0.098	0.183	0.298	0.519	0.307	0.183	0.306	0.537	0.315
Ra2				Ro2				Rs2				Rd2
0.045	0.078	0.128	0.072	0.091	0.158	0.292	0.161	0.245	0.447	0.732	0.452	0.141	0.236	0.393	0.238
Ra3				Ro3				Rs3				Rd3
0.087	0.148	0.260	0.148	0.049	0.087	0.148	0.082	0.161	0.255	0.449	0.262	0.120	0.215	0.372	0.216
Ra4				Ro4								Rd4
0.071	0.120	0.214	0.119	0.054	0.095	0.167	0.091					0.144	0.244	0.399	0.244
Ra5				Ro5
0.083	0.136	0.223	0.133	0.099	0.177	0.310	0.178
Ra6				Ro6
0.099	0.175	0.309	0.176	0.108	0.176	0.296	0.176
Ra7				Ro7
0.057	0.099	0.163	0.094	0.057	0.101	0.177	0.098
Ra8				Ro8
0.056	0.095	0.161	0.091	0.060	0.104	0.176	0.100

Figure 8. Fuzzy and crisp resilience metrics obtained for the WWTPs in the study area.

Figure 9. Fuzzy and crisp UFs for the three WWTPs of Owls Head (a), Coney Island (b), and Rockaway (c).

Figure 10. Final financial allocations and their corresponding potential resilience improvement.

Figure 11. The simulated inundation map of the study area obtained from hydrological modeling.

Table 8. Maximum inundation depth at network nodes under simulated Sandy Superstorm.

Node	Water depth (m)	Node	Water depth (m)
S^a 1	1.32	S 11	1.74
S 2	1.05	S 12	1.1
S 3	0	P^b 1	1.48
S 4	0	P 2	0
S 5	1.2	P 3	1.05
S 6	0.2	P 4	1.92
S 7	0	P 5	1.16
S 8	1.08	WWTP 1	0.73
S 9	1.42	WWTP 2	1.63
S 10	1.22	WWTP 3	1.74

^aelectric substation, ^b pumping station

Figure 12. The INM of the study area developed in MATLAB.

Figure 13. The recovery curves and their corresponded resilience metrics obtained from the INM before and after the optimization.

Figure 14. Prioritized network components for restoration in the study area.

Table A1. Descriptions of sub-criteria.

Sub-criteria	Description
$\mathrm{R}{\mathrm{a}}_1$	Flood elevation based on North American Vertical Datum of 1988 (NAVD88)
$\mathrm{R}{\mathrm{a}}_2$	Adverse environmental impacts on the surrounding area due to treatment failure
$\mathrm{R}{\mathrm{a}}_3$	Capacity as function of the plant users
$\mathrm{R}{\mathrm{a}}_5$	Number of residents that are served by the plant
$\mathrm{R}{\mathrm{o}}_1$	The difference between WWTP capacity for the total maximum wet and dry weather flow (Maximum wet weather flow is the maximum flow received during any 24 hours. Maximum dry weather flow is the maximum daily flow during periods without rainfall.)
$\mathrm{R}{\mathrm{o}}_2$	100-year flood elevation +30 inches for expected sea-level rise by the 2050s (This is determined based on the FEMA’s 100-year flood elevation maps)
$\mathrm{R}{\mathrm{o}}_3$	Due to the flat terrain of the plant, several areas may be flooded by up to this value of water during the critical flood event
	The percentage of discharge monitoring reports that resulted in effluent violations (The Discharge Monitoring Report (DMR) violation percentages indicate how well each treatment plant can cope with daily operational stresses.)
$\mathrm{R}{\mathrm{o}}_6$	Damage cost from the most severe historical hurricane without flood protection for the plant
$\mathrm{R}{\mathrm{s}}_1$	Number of plant’s technical staff
	Availability of facilities to drain sludge to decrease 90% of its liquid volume
$\mathrm{R}{\mathrm{s}}_3$	Total risk avoided for every single dollar spent on improving operation and maintenance over 50 years
$\mathrm{R}{\mathrm{d}}_2$	Distance from the closest WWTP
$\mathrm{R}{\mathrm{d}}_3$	Volume of lakes in the WWTP’s zone

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