Using rainfall measures to evaluate hydrologic performance of green infrastructure systems under climate change

Figures & data

Table 1. Analyses carried out in this study and associated time periods

Time period	Dates	Time step	Cities	Data source
Observed	July 2015 to July 2018	5-minute	Pittsburgh	On-site rain gauge and water depth sensors (Civil & Environmental Consultants, Inc and 3 Rivers Wet Weather 2018)
Historical	January 1983 to December 2014	1-hour	All cities in sample	National Centers for Environmental Prediction (NCEP) (NOAA, 2016)
Future	January 2020 to December 2059	1-hour	2 selected cities	4 NA-CORDEX RCM/ESM simulations (Mearns et al., 2017)

Figure 1. Overview of steps used to predict performance of the bioretention basin using annual rainfall measures

Figure 2. Flow schematic of site and model (not to scale), left, and profile view of the bio-retention layers, right. The impervious areas drain to the surface of each garden. Rain garden 1 can drain to rain garden 2 through surface runoff or under drain flow

Table 2. Selected parameters of the bioretention basin (downstream) from the SWMM model

Parameter (units)	Value	Estimation method/source
Surface berm height (in)	3	As-built drawings (CH2MHILL, and Viridian Landscape Studio, 2011)
Surface slope (%)	0.01	As-built drawings (CH2MHILL, and Viridian Landscape Studio, 2011)
Soil thickness (in)	24	As-built drawings (CH2MHILL, and Viridian Landscape Studio, 2011)
Soil porosity (volume fraction)	0.36	Soil sampling (A&L Great Lakes Laboratories, Inc, 2015); Adjustment to reflect observed performance
Soil conductivity (in/hr)	2.0	SWMM Reference Manual range (Rossman & Huber, 2016); Adjustment to reflect observed performance
Storage layer thickness (in)	12	As-built drawings (CH2MHILL, and Viridian Landscape Studio, 2011)
Storage layer seepage rate (in/hr)	2.5	As-built drawings (CH2MHILL, and Viridian Landscape Studio, 2011); Adjustment to reflect observed performance

Table 3. Rainfall indices evaluated in this study. The ‘set’ column represents the different variations of each index that were tested

Index	Set	Description	Implication	Indicator
total	n/a	Total annual precipitation (mm)	Wet or dry year	Central tendency
nintd	nε (µ, q50)	Mean or median daily intensity of rain days (mm)	Intensity of rain days
ninthr	nε(µ, q50)	Mean or median hourlyintensity of rain hours (mm)	Intensity of rain hours
maxnd	nε (1,2,3) days	Greatest n-day totalprecipitation (mm)	Measure of extremeswith duration less thanor equal to drainagerequirement	Extreme magnitude
qpd	pε (90,95,99) quantile	pth percentile of rain dayamounts (mm/day)	Intermediate to raredaily extremes
qph	pε (90,95,99) quantile	pth percentile of rain houramounts (mm/hr)	Intermediate to rarehourly extremes
totqp	pε (90,95,99) quantile	Total rain from daily qthpercentile or greater (mm)	Total from intermediateto rare extremes	Extreme total
propqp	pε (90,95,99) quantile	Proportion of total annualrainfall above qth percentile (%)	Measure of extremescompared to total received	Extreme proportion
excdn	nε (10,25,50) mm	Number of rain days withprecipitation ≥ n mm (days)	Intermediate to raredaily extreme events	Extreme frequency
raind	n/a	Number of rain days whereprecipitation > 0.1 mm (days)	Daily precipitationoccurrence	Frequencywet & dry
ncwd	nε (µ, max)	Mean or max number ofconsecutive wet days whereprecipitation > 0.1 mm (days)	Measure of average tolong-duration storms
ncwh	nε (µ, max)	Mean or max number ofconsecutive wet hours whereprecipitation > 0.01 mm (hours)	Measure of average tolong-duration storms
ncdd	nε (µ, max)	Mean or max number ofconsecutive dry days whereprecipitation < 0.1 mm (days)	Measure of risk ofdryness and antecedentsoil conditions

Figure 3. Annual rain garden performance over historical period [1983–2014] for 17 cities, including: (a) percent of runoff captured annually, (b) the volume of discharge to the sewer, (c) the frequency of these discharges, and (d) the maximum number of hours to drain the surface. The marker represents the median value across all years, the size of the marker represents the average total annual rainfall in that city, and the color of the marker represents an average annual rainfall index (listed in color bar legend). The cities are ranked based on their average total annual rainfall, from lowest to highest across the x-axis

Figure 4. Number of cities (out of 17) where a strong correlation exists between rainfall indices (rows) and rain garden performance metrics (columns) in the historical period [1983–2014]. The rainfall indices that have the highest number of strong correlations for each performance metric are outlined in blue

Figure 5. Correlations between rainfall indices and all performance metrics in Pittsburgh (left) and Memphis (right) for historical period [1983–2014]. Grey colors represent positive correlations, while reds represent negative correlations

Figure 6. Rainfall indices most indicative of performance for historical period [1983-2014]. The colors for each performance metric correspond to the rainfall indices presented in Figure 7

Figure 7. Percent change in rainfall indices for two climate model simulations, drier future (orange) and wetter future (purple) in Pittsburgh (top) and Memphis (bottom). The box and whisker plots represent the range of the percent change for each year and each climate model for the future period [2020–2059], with respect to the historical period [1983–2014]. The middle line of the box plot represents the median over the 40-year future period; the box outline shows the 25th and 75th quantiles, and the whiskers show the 5th and 95th quantiles. Outliers are shown as orange dots (for the drier future) and purple stars (wetter future). The grey shading represents the historical range (in terms of percent change from the median). The black dashed line at zero represents no future change. The indices highlighted with color are those that were selected as most indicative of each performance metric, including capture efficiency (blue), volume discharged (yellow), frequency of discharge (green), and maximum drainage time (pink)

Figure 8. Predicted and simulated changes in performance metrics in the future [2020–2059] for both cities (Pittsburgh and Memphis) and both climate model scenarios (drier and wetter future) with respect to the historical period [1983–2014]. Predicted changes are based on projected changes in rainfall indices most indicative of each performance metric and simulated changes are calculated from the SWMM model simulations using climate projections. For all performance metrics except percent capture, the direction of change is equal to the direction predicted by the rainfall index. However, percent capture is inversely correlated with the associated rainfall indices, thus an increase in the associate rainfall index leads to a predicted decrease in the percent capture

Figure 9. CDFs of four performance metrics (as rows), (a) percent of runoff captured, (b) volume of discharge, (c) frequency of discharge, and (d) maximum hours to drain the surface for all simulations, historical [1983–2014] (black), drier future [2020–2059] (orange), and wetter future [2020–2059] (purple), for Pittsburgh (left) and Memphis (right). The dotted lines cross the x-axis at the median value. The grey shading shows the historical range

Table A1. Characteristics of cities used in this study

City	State	Bukovsky climate region	Elevation (m)	Latitude	Longitude
Amarillo	TX	C. Plains	1100	35.2	−101.7
Boise	ID	Great Basin	815	43.6	−116.2
Boston	MA	North Atlantic	4	42.4	−71.0
Boulder	CO	S. Rockies	1654	40.0	−105.3
Charlotte	NC	Mid Atlantic	234	35.2	−80.9
Chicago	IL	Great Lakes	187	41.8	−87.8
El Paso	TX	Mezquital	1201	31.8	−106.4
Fargo	ND	N. Plains	273	46.9	−96.8
Memphis	TN	Deep South	79	35.1	−90.0
Minneapolis	MN	Prairie	254	44.9	−93.2
Missoula	MT	N. Rockies	972	46.9	−114.1
New Orleans	LA	Southeast	6	29.9	−90.1
Phoenix	AZ	Southwest	337	33.4	−112.0
Pittsburgh	PA	Appalachia	367	40.4	−80.0
Portland	OR	Pacific NW	6	45.6	−122.6
St. Louis	MO	Prairie	176	38.8	−90.4
San Antonio	TX	S. Plains	230	29.5	−98.3
San Jose	CA	Pacific SW	29	37.3	−121.9

Table A2. Regional climate model simulations from NA-CORDEX used in this study

RCM/ESM Combination	Regional Climate Model (RCM)	Earth System Model (ESM)	Abbreviation
RegCM4/MPI-ESM-LR	RegCM4 RCM	‘Max Planck Institute Earth System Model at base resolution’ (MPI-ESM-LR)	MPIREG
WRF/MPI-ESM-LR	WRF RCM	MPI-ESM-LR	MPIWRF
WRF/GFDL-ESM2M	WRF RCM	Geophysical Fluid Dynamics Laboratory Earth System Model, Modular Ocean Version” (GFDL-ESM2M)	GFDWRF
CanRCM4/CanESM2	CanRCM4 RCM	Second generation Canadian Earth System Model (CanESM2)	CANCAN

Table A3. Drainage area characteristics of SWMM model

Drainage Area	Sq. Ft	Sq. Meters	Slope	% Impervious	% Zero-Impervious	Drains to
Roof 1	1440	134	2%	100	100	Upstream RG
Roof 2	1360	126	2%	100	100	Upstream RG
Pavement 1	1500	139	2%	100	25	Upstream RG
Roof 3	700	65	2%	100	100	Downstream RG
Roof 4	2500	232	2%	100	100	Downstream RG
Pavement 2	860	80	2%	100	25	Downstream RG
Upstream RG	1262	117	0.1%	0	25	Downstream RG
Downstream RG	907	84	0.1%	0	25	Outfall

Figure A1. View of rain garden site at East Liberty Presbyterian Church in Pittsburgh, PA. The tipping bucket rain gauge is placed behind the sign, and the CTD sensor is below ground, near the brown grate. Image source: John K. Buck, Civil & Environmental Consultants, Inc

Figure A2. Summary of data from on-site sensors for precipitation (blue lines on top of figure) and volume discharged (red lines on bottom), which was calculated if water level surpassed the discharge pipe invert elevation

Table A4. Annual percent capture during the 4 years in the observed period calculated from observed data from on-site sensors (left column) and calculated from SWMM model simulation (right column) over the period July 2015 to July 2018

Year	Observed on-site	Simulated (observed period)
2015	100%	99%
2016	98%	86%
2017	100%	97%
2018	99%	89%

Table A5. SWMM model parameters. Parameters marked with an asterisk were adjusted to align simulated results with observed performance

Parameters (units)	Upstream RG	Downstream RG	Data Source
Subcatchments  N-Imperv/N-Perv  DStore-Imperv/Perv (in)  Percent Routed  Suction head (in)  Conductivity (in/h)  Initial soil moisture deficit   (fraction)	0.01/0.1 0/0.05 100 2 1 0	0.01/0.1 0/0.05 100 2 1 0	SWMM default SWMM default Site configuration Green Ampt SWMM default SWMM default
Bio-retention cell – surface  Berm height (in)  Vegetation volume (fraction)  Roughness (Manning’s n)  Slope (%)	3 0.8 0.65 0.01	3 0.8 0.65 0.01	As-built drawings As-built drawings/Google Earth (McCuen, 2005; Mustaffa, Ahmad, & Razi, 2016) As-built drawings
Bio-retention cell – soil  Thickness (in)  Porosity (volume fraction)*  Field capacity (volume fraction)  Wilting point (volume fraction)*  Conductivity (in/hr)*  Conductivity slope  Suction head (in)*	24 0.38 0.15 0.09 2.1 8 1.9	24 0.36 0.15 0.09 2 8 1.8	As-built drawings SWMM Reference Manual (Rossman & Huber, 2016) SWMM Reference Manual (Rossman & Huber, 2016) SWMM Reference Manual (Rossman & Huber, 2016) Rawls, Brakensiek, and Miller (1983); SWMM Reference Manual (Rossman & Huber, 2016) SWMM User Manual Rawls, Brakensiek, and Miller (1983); SWMM Reference Manual (Rossman & Huber, 2016)
Bio-retention cell – storage  Thickness (in)  Void ratio (voids/solids)*  Seepage rate (in/hr)*  Clogging factor	12 0.3 2.5 0	12 0.3 2.5 0	As-built drawings SWMM Reference Manual (Rossman & Huber, 2016) SWMM Reference Manual (Rossman & Huber, 2016) Default
Bio-retention cell – underdrain  Drain coefficient (in/hr)  Drain exponent  Drain offset height (in)	0.5 0.5 2	0.5 0.5 2	SWMM User Manual Default As-built drawings
Conduits  Roughness (Manning’s n)  Invert elevation (ft)  Pipe diameter (in)  Orifice diameter (in)  Top of weir elevation (ft)	0.012 904.25 6 2 905.75	0.009 902.25 8 2 903.75	HDPE, PVC (Bishop and Jeppson 1978) As-built drawings As-built drawings As-built drawings As-built drawings

Figure A3. Heat map of correlations among rainfall indices for Pittsburgh. Darker colors represent a stronger correlation between rainfall indices

Table A6. Median rainfall indices for each climate model simulation in Pittsburgh for the future period (2020-2059)

Rainfall index	CANCAN	GFDWRF	MPIREG	MPIWRF
Total annual rainfall (mm)	1067.5	1153.4	1056.8	1098.7
Maximum 1-day rainfall (mm)	98.3	108.5	105.9	105.5
Maximum 5-day rainfall (mm)	128.7	136.8	133.5	142.5
90th quantile of daily rainfall (mm)	16.4	21.8	19.0	19.1
Proportion of total from 90th quantile or above (%)	53.1	49.5	49.7	49.1
Number of rain days (days)	155.2	129.7	137.8	137.7
Maximum duration of consecutive dry days (days)	15.9	21.0	19.0	18.5
Average duration of consecutive dry days (days)	1.5	1.8	1.7	1.8
Number of days with rainfall > 25 mm (days)	9.6	11.3	9.5	9.9
Number of days with rainfall > 50 mm (days)	2.8	3.3	2.7	2.6

Table A7. Median rainfall indices for each climate model simulation in Memphis for the future period (2020-2059)

Rainfall index	CANCAN	GFDWRF	MPIREG	MPIWRF
Total annual rainfall (mm)	1216	1539	1384	1505
Maximum 1-day rainfall (mm)	88	65	90	71
Maximum 5-day rainfall (mm)	118	102	132	111
90th quantile of daily rainfall (mm)	12	19	21	19
Proportion of total from 90th quantile or above (%)	54	42	45	42
Number of rain days (days)	224	216	179	210
Maximum duration of consecutive dry days (days)	14	13	17	14
Average duration of consecutive dry days (days)	1.3	1.1	1.3	1.1
Number of days with rainfall > 25 mm (days)	10	12	13	13
Number of days with rainfall > 50 mm (days)	3	1	3	1

Figure A4. Future range of selected rainfall indices in Pittsburgh (left) and Memphis (right) for the future period (2020 – 2059) for the four RCMs (first four boxes; 40 values each) and all values combined into a single uncertainty range (last box; 120 values)

Figure A5. Correlation of selected rainfall indices to performancemetrics for the historical and future period (wetter and drier future). The top subplot (a) shows values for Pittsburgh and the bottom (b) shows values for Memphis. Grey colors represent positive correlations (from 0 to 1), while reds represent negative correlations (from 0 to —1). Labels on the left show the category of the rainfall index

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