CURVE NUMBERS & RUNOFF COEFFICIENTSPRACTICAL DESIGN FOR LIVING ROOF APPLICATIONS

Elizabeth Fassman-Beck, Ph.D., Stevens Institute of TechnologyDonald Carpenter, Ph.D., Lawrence Technological Univ.Bill Hunt, Ph.D., North Carolina State Univ.Rob Berghage Ph.D., Penn State Univ.Tim Kurtz, City of PortlandVirginia Stovin, Ph.D., Univ. of SheffieldBridget Wadzuk, Ph.D., Villanova Univ.

Hamilton Bldg, Portland

Oct. 2015; VUSP Stormwater Symposium

Planning & Permitting Challenges• Prescriptive hydrologic calculations for

urban drainage. • Most common in USA(?):

• Runoff Coefficients (Cv) • TR-55 a.k.a Curve Number (CN) method

(NRCS 1986)

• Assign Cv or CN based on assumed similarity to a natural surface• Auckland (New Zealand): CN=61 (pre-2013)• Michigan: CN=65

Brownstown, MI

• Performance monitoring data• “Long”-term studies ~50-80% retention• Event-based performance 40-90%

Portland Bldg

Objectives • Compile data for “best” estimate of living roof CN and Cv

• Organize results according to Kӧppen-Geiger climate zones

• Recommend with caution as an interim measure to allow/ enable regulatory/permitting process

• Co-authors are not advocating use of CN or Cvin general

21 Living Roofs in 16 Cities

Auckland, NZ

Portland

Sheffield, UK

MichiganChicagoToronto

North Carolina

NYCPA

• Substrate depths range 50-150 mm (2-6”); most 100 mm (4”), 1 pre-fab tray

• Roof slopes (pitch) range from “flat” to 8%; most ~2%• Size range 3-6968 m2 (~33-79,000 ft2)

Genoa, Italy

Methods: Runoff Coefficients• Paired rainfall (P) and observed runoff (Qobs) from

21 living roofs• Volumetric runoff coefficient for each storm

• Linear regression for paired P: Cv using DataFit 9.1.32• Model selection criteria:

1) predicted Cv must increase or remain constant for 0 < P < 100 mm

2) predicted Cv < 1 for 0 < P < 100 mm3) R2 > 0.40

𝐶𝐶𝑣𝑣 =RunoffRainfall

=𝑄𝑄𝑜𝑜𝑜𝑜𝑜𝑜𝑃𝑃

Qobs, P as depths (mm)

Runoff Coefficients Villanova 𝐶𝐶𝑣𝑣 = 1.14𝑒𝑒 �−30.85𝑃𝑃

State College 𝐶𝐶𝑣𝑣 = 0.95𝑒𝑒 �−25.85𝑃𝑃

Pittsburgh 𝐶𝐶𝑣𝑣 = 0.92𝑒𝑒 ⁄−7.99𝑃𝑃

Fassman-Beck et al. (in press) Jrnl. of Hydrologic Eng.

Methods: CN• Paired rainfall (P) and runoff (Q) from

21 living roofs• Omit winter data (Dec.-Feb)• Trial and error to determine the CN from

storm event data• Method of least squares:

𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑒𝑒 𝐹𝐹 = � 𝑄𝑄𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 − 𝑄𝑄𝑜𝑜𝑜𝑜𝑜𝑜 2

𝑄𝑄𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 =𝑃𝑃 − 𝐼𝐼𝑎𝑎 2

𝑃𝑃 − 𝐼𝐼𝑎𝑎 + 𝑆𝑆

𝑆𝑆 =1000𝐶𝐶𝐶𝐶

− 10 × 25.4

𝐼𝐼𝑎𝑎 = 0.2𝑆𝑆

(Hawkins et al. 2009)

Ia = initial abstraction (mm)S = max. potential storage (mm)

Qobs = observed (field) measured runoff depth for a given P (mm)

Limitations• CNs should be derived from

“large” storms defined as• Pmin>25.4 mm (1”)• Pmin/S>0.46 (Hawkins et al. 1985) severely reduced data sets (to unusable levels)

• “…Low rainfalls (for which there are many storms) -by definition-define high CNs” (ASCE 2009, p.47)• Pmin>2 mm (0.08”)

• n > 15 storms per site, but better if n > 30 University of Sheffield, UK, 1 m2

Chicago Walmart ~7000 m2

“Best Fit” CNs• 0.67 < r2 <0.96• Significant data scatter for low rainfall

Fassman-Beck et al. (in press) Jrnl. of Hydrologic Eng.

CN by climate zone

CfaCN=92(n=3)

Cfb CN=89(n=9)

CsbCN=80(n=2)

Dfa CN=91(n=5)

Overall average CN=89n=21 living roofs

1475 individual storm eventsDfb CN=88(n=4)

Dfb/Cfa CN=96(n=1)

Seems high?

Southfield, MI

Average across all sites with n>15 and “large” storms CN=84Average across all sites CN=89

Impervious area CN=98

Investigate empirical performance data…

(inches)

North Carolina Living Roof Retention

0.08- 0.2

0.2- 0.4

0.4- 0.6

0.6- 0.8

0.8- 1.0

1.0- 1.2

1.2- 1.6

1.6- 2.0

2.0- 2.4

> 2.4 A

Goldsboro

Raleigh1400 ft2, 7%, 4 in

Kinston290 ft2, 3%, 4 in

753 ft2, 0%, ~3 in

Q = 0.0046P2 + 0.3603P + 0.0242R² = 0.8135

0

20

40

60

80

100

120

140

160

180

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Runo

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Precipitation (P) (mm)

Threshold for runoff generation

UoA Faculty of Engineering217m2, 50-70mm (2336 ft2, 2-3”)

Tamaki “mini-roofs” Each 4m2,100&150mm (43ft2,4&6”)

Waitakere Civic Centre 171m2, ~100mm (1841 ft2, ~4”)

NYCCarson et al. (2013) Environmental Research Letters

AucklandFassman-Beck et al. (2013) Jrnl. of Hydrology

Threshold rainfall for runoff generation• NRCS (1986)

• For runoff to occur, precip. must exceed “initial abstraction” (P>Ia)• Initial abstraction is 20% of total potential storage (Ia = 0.2S)• Total potential storage is a function of the CN (S = f[CN])All CNs in TR-55 depend on this assumption

Best fit CN NRCS Ia Site Empirical Evidence for Qobs>2-3 mm

Min 75 16.9 mm Portland Bldg P> 21 mmAverage 89 6.3 mm all Chicago, NYC, NC, &

Portland: P> 21 mm

Auckland & MI: P> 11 mmMax 96 2.1 mm Brownstown (MI);

Sheffield, UKBrownstown P> 11 mm; Sheffield P> 6 mm

Impervious surface

98 1.0 mm NRCS (1986) P> 2 mm (my own observation)

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2012 Journal of Environmental Engineering 138(8):841-851

Substrate Depth(DLR)

Moisture Contentplant available water, PAW = moisture content between field capacity (-10kPa) and stress point (-1500kPa)

= max. stored water (+) per event (Sw)

0 < Sw < ~20-30 mm (~1”)

Recommended Step Function• For P < Sw

CN<1 ; Runoff volume = 0Sw = DLR x PAW ; 0 < Sw < 20 to 30 mm

Where • P = design storm depth (mm)• Sw = max. stored water in the substrate (mm) per unit area of living

roof• Dlr = finished substrate depth (mm)• PAW = plant available water (fraction)

• For P> ~30 mm or P > Sw,• climate-specific CN=79-90 ???• leniency is advocated by all co-authors, suggested CN<84

Future work• More (very) long-term data sets …

of which there are fewcurrently working on Seattle

STRONGLY recommended….• Use results with caution!

• TR-55 is not intended to recreate historic rainfalls• Some evidence of measurement scale effect (small plots or pilot scale

sites have higher CN)• Substantial variability of results

• Quantify role of plants (more variable than role of substrate) & other functional layers

• More sophisticated techniques accounting for physical processes, ET, and variable flow conditions

• Regulatory shift away from TR-55 or Rational formula and event-based design

Seattle Zoomazium

THANK YOUEFASSMAN@STEVENS.EDU