Glenn E. Moglen Department of Civil & Environmental Engineering Virginia Tech Introduction to NRCS/SCS Methods (continued) CEE 5734 – Urban Hydrology and Stormwater Management Lecture 5

For next time: Please install VTPSUHM program available at Scholar under, “Resources: Week 3” Review from Lecture #4 Basic Equations Curve Number Questions from last time? Continue NRCS Methods Time of Concentration SCS Graphical Peak Discharge Method Begin SCS Tabular Method Design Storm Construction Today’s Agenda

SCS Method – Basic Concept P IaIa F Q time S = potential storage Premise: ratio of filling of storage ( F/S ) equals ratio of outputs ( Q ) relative to inputs ( P-I a )

P [=] inches F [=] inches S [=] inches I a [=] inches Q [=] inches (note: NOT Q [=]ft 3 /s) CN [=] inches -1 SCS Method – A Note on Units

Actual retention is: Substituting into earlier equation: Re-arranging to solve for Q : SCS Method – Basic Concept

Initial abstraction is often assumed to be a fixed percentage of storage: Substituting in equation for runoff: Recent research suggests f may be as little as 0.05: SCS Method – Basic Concept

So the central quantity is “ S ” (potential storage). How do we determine “ S ”? Enter the “Curve Number” ( CN ) Value between 0 and 100 Higher CN indicates less infiltration CN varies spatially CN = f (Land Use, Soil Type, Soil Wetness) Relationship between Curve Number and Storage SCS Method – Curve Number

Table 9-5: Urban part of overall CN table

Ex: TIA=P imp =20%, R=0.5. CN p =75 – yields CN c =78 Urban Areas: Unconnected Imperviousness Example (Nomograph)

> TIA=P imp =20%, R=0.5. CN p =75 Urban Areas: Unconnected Imperviousness Example (Equation) (1-0.5R)

Time of Concentration Def: Time of concentration ( T c ): is the time for runoff to travel from the hydraulically most distant point (see Point “A” below) of the watershed to a point of interest (Point “D” below) within the watershed. SCS segments the flow into: Sheet Flow (AB) Shallow Concentrated Flow (BC) Channel Flow (CD)

Time of Concentration – Total Travel Time Time of Concentration is just the sum of all the individual segment travel times T t, sheet T t, shallow T t, channel sheet shallow channel TcTc

Time of Concentration – Sheet Flow First L (<100) feet of longest flow path T t,sheet : travel time [hrs] n : from table at right L : length(<100) [ft] P 2 : 2-year, 24-hour precip [in.] S : land slope in [ft/ft]

T t,sheet : [hrs] n : woods, some underbrush: 0.4 L : 100 feet P 2 : 2.64 inches (from Blacksburg, NOAA 14) S : 0.01 in [ft/ft] Time of Concentration – Sheet Flow - Example Solve for T t,sheet >

Time of Concentration – Shallow Concentrated Flow Velocity, v shallow [ft/s] is a function of slope and surface conditions (what do you think of these significant figures?!) k = (unpaved) k = (paved) Travel time, T t, shallow [hrs] is then just length of shallow concentrated flow path divided by velocity

Time of Concentration – Shallow Concentrated Flow - Example Unpaved surface S = 0.04 L = 1000 feet Result (from graph): v = 3.2 ft/s Solve for T t, shallow >

Time of Concentration – Channel Flow Manning’s equation is used to determine the velocity, v channel [ft/s] in the channel flow portion of the longest flow path: Travel time, T t, channel [hrs] is then just length of channel flow path divided by velocity

4 ft Time of Concentration – Channel Flow - Example Use Mannings n = S = ft/ft L channe l = 5000 ft Solve for T t, channel > 1.5 ft

Time of Concentration – Summing Travel Times T t, sheet : 0.52 hrs T t, shallow : 0.09 hrs T t, channel : 0.16 hrs Solve for T c >

Q p : peak discharge [ft 3 /s] q u : unit peak discharge [ft 3 /(s-in-mi 2 )] A : drainage area [mi 2 ] Q : runoff [in] F p : pond & swamp factor SCS Graphical Peak Discharge Method

SCS Graphical Peak Discharge Method – Storm Distributions

Unit Peak Discharge, q u TcTc ququ See Figure 4-II in TR-55

Analytical form for q u : C 0, C 1, and C 2 depend on storm distribution: See Table F-1 Unit Peak Discharge, q u

“The F p factor can be applied only for ponds or swamps that are not in the T c flow path.” Pond & Swamp Adjustment Ponds & Swamps

Given: A : 4.3 mi 2 CN : 75.1 P : 10-year, 24-hour event =4.08 in T c : 0.77 hrs (from earlier) No ponds or swamps Solve for Q p > Calculating SCS Graphical Method Peak Discharge

Non-homogeneous sub-areas (differing geology, development, curve number, etc.) Need full hydrograph, not just peak Need hydrographs at one or more internal points within a watershed. SCS Tabular Method – Why do we use it?

When NOT to use Tabular Method

Q p : peak discharge [ft 3 /s] q u : unit peak discharge [ft 3 /(s-in-mi 2 )] A : drainage area [mi 2 ] Q : runoff [in] F p : pond & swamp factor Comparison – Graphical Peak Discharge vs. Tabular Method Q t : peak discharge [ft 3 /s] at time, t q t : unit peak discharge [ft 3 /(s-in-mi 2 )] at time, t A : drainage area [mi 2 ] Q : runoff [in]

Examining a sheet of q t values Comment on: q t ordinates, hydrograph time increments, travel time increments, T c values, I a /P values, visible trends in the q t ordinates.

Rounding “Rules” (Time) Round T c and T t separately to the nearest table value and sum. Round T c down and T t up to the nearest table value and sum Round T c up and T t down to the nearest table value and sum From these three alternatives, choose the pair of rounded T c and T t values whose sum is closest to the sum of the actual T c and T t. If two rounding methods produce sums equally close to the actual sum, use the combination in which rounded T c is closest to actual T c. Valid T c Values: {0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.75, 1.0, 1.25, 1.5, 2.0} Valid T t Values: {0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.75, 1.0, 1.25, 1.5, 2.0, 2.5, 3.0} Example: T c = 0.7, T t = 1.3,

Rounding “Rules” (cont.) Comment on interpolation of T x : - Don’t do it! I a /P : “The computed I a /P value can be rounded to the nearest I a /P value in exhibits 5-I through 5-III, or the hydrograph values (csm/in) can be linearly interpolated because I a /P interpolation generally involves peaks that occur at the same time.”

Sub-dividing a Watershed Idealized System Actual System

Simple Example – Consider a Single Sub-Area CN = 75 S = 1000/(75) – 10 = 3.33 in I a = 0.2(3.33) = 0.67 in P = 3.05 in (arbitrary – for this example) Q =(3.05 – 0.67) 2 / ( – 0.67) = 1.00 in I a /P = 0.67 / 3.05 = 0.22 (use 0.3) Assume Type II storm (see comment on Type II) Use T c = 0.5 hrs. Determine at outlet of subarea, T t = 0 hrs. From Exhibit 5-II (Sheet 5 of 10) ordinates ( q t ) are: {0, 0, 0, 1, 9, 53, 157, 314, 433, 439, 379, 299, 237, 159, 118, 95, 81, 71, 65, 56, 50, 46, 42, 38, 34, 31, 30, 28, 25, 22, 19, 0} T c = 0.5 hrs

Aside on Type II storm Based on TP-40 NOAA Atlas 14 suggests new design storm distribution How to build a design storm?

Aside on Type II storm 0.1 hour timestep data provided at class website. Question: How does Type II storm compare to symmetric 24-hr storm from NOAA Atlas 14?

Aside: How to build a design storm… AEP, 100-year depths for BLACKSBURG 3 SE, VIRGINIA ( ) are shown in above table (units are inches). 5 min10 min 15 min 30 min 60 min 120 min 3 hr6 hr12 hr24 hr Example: Distribute two shortest durations around 12 hours.

Aside: How to build a design storm… Question: Do we get the same design storm at different locations? Question: Do we get the same design storm at same location for different frequencies? RP yrs 5 min 10 min 15 min 30 min 60 min 120 min 3 hr6 hr12 hr24 hr AEP, BLACKSBURG 3 SE, VIRGINIA ( ) (units are inches).