Introduction to Hydrology, Part 2

Notes, Handouts

Precipitation• Much of hydrology deals with precipitation

– How much?– How frequently/infrequently?– What form?– How quickly?– Seasonal variation?– Drought frequency?– How much will run off/ be infiltrated?

• Much of hydrology for hydraulics looks like:– What design flows will a certain rainfall cause for my

project?

Precipitation Cont.• All design precipitation estimates need large

amounts of data to determine quantities/ratesNotre Dame

Average Annual Rainfall (NOAA)

Design Storm• An engineering structure must be designed for some specified

loading• Tied to performance criteria

– Collapse– Life safety– Post-storm functionality with minor repairs– Continuously operational

• Design storm tied to return period of design event– Greater return period for more severe consequences– Example: Reservoir must be able to pass 100 year flood. Or Probable

Maximum Precipitation if lives would be in danger.– Example: Local stormwater sewer must have capacity for 10 year

storm– Often designated by law

• Rainfall Duration for given return period – generally depends on size of catchment

Most severe states

Design Rainfall• Design rainfall for a given return period has three

components: 1. Magnitude (Total amount in inches)2. Storm length (hours)3. Rainfall distribution within storm

• Magnitude determined from SCS or other tabulated values (NOAA Precipitation Frequency Data Server) http://hdsc.nws.noaa.gov/hdsc/pfds/index.html• Distribution in time comes from curves normalized to total rainfall amount

– Varies with location: Different places have different types of storms– May have different types of curves at same location depending on when peak rainfall occurs (first quartile of storm, second quartile, etc)

Too advanced for this class

Temporal Variation of Rainfall

Four SCS Rainfall Distribution Types Temporal Variation of Rainfall for 24 hr storm: Numerical values for these curves given in text

SCS 24 Hour Rainfall Distributions•Gives fraction of total rainfall in each ½ hour interval•Four time histories for different regions (I,IA,II,III)•Other distributions available for different storm lengths

Other Rainfall Variations

• Many more rainfall curves for advanced design– Other time periods (6h, 24h)– Quartile of storm that sees maximum intensity

(when rainfall is strongest in storm)– Huff probability level (percent exceeded in x% of

storms)– Not used much in this class, important for other

situations– In Indiana Stormwater Drainage Manual

Design Rainfall Depth and Storm Length

• Taken from Statistical analyses – SCS or other tabulated values (NOAA Precipitation

Frequency Data Server) http://hdsc.nws.noaa.gov/hdsc/pfds/index.html

– 10 year storm, 100 year storm, etc.

• Storm length determined by code or by engineering analysis (largely time of concentration)

10 year, 24 hour Rainfall (SCS)

Moreau Seminary Depth-Duration-Frequency Curves

•NOAA compilations of Return Period vs Storm Length vs Total Precipitation•Available at many locations•For selected return periods (6, 12, 24, 96 hour) NOAA also provides rainfall variation in time

Hydrographs

• Plot of discharge (stream, channel, etc.) vs time is called a hydrograph

• Hydrographs are separated into direct surface runoff and base flow (groundwater contribution to steady flow more or less)1. Straight line between start of rising limb and point

of max curvature on receding limb, OR2. Horizontal line between start of rising limb and next

intersection point, OR3. Empirical extrapolation techniques dependent on

watershed area

Hydrograph Example

Point of maximum curvature

Start of rising limb

Alternate Methods for Separating Base Flow/Runoff

Horizontal line

•Separate using horizontal line AD to next intersection point, OR

•Continue slope of downward trend to peak of discharge AB; then straight line BC to intersection point at N past peak

•N=A0.2

•N in days•A in km2

The Unit Hydrograph• Relates a unit runoff amount (over some relatively short time)

to the time history of surface runoff– i.e. Discharge history for 1 inch of runoff averaged over basin

generated by 12 hour rainfall event– Runoff will always be less than rainfall amount

• Approximate, but very important concept• Once the unit hydrograph is obtained, assume linearity in both

space and time to obtain hydrograph for any storm– Runoff from 2 inch storm = 2× Runoff from 1 inch storm– Runoff from 24 hour storm = Runoff from 2 shifted 12 hour storms– Often use these as inputs for hydraulics

• Often based on data from rain gauges/stream discharge

Making a Composite Hydrograph for Arbitrary Runoff

Synthetic Unit Hydrograph• Knowing time of concentration and watershed

parameters, can develop synthetic hydrographs

• Combine with runoff history to create discharge history

• Most important parameters are time to peak Tp, effective rainfall duration, ∆D, watershed area, and region characteristics

Time to Peak and Effective Rainfall

• For each watershed, there are characteristic times for the unit hydrograph

• Based on the time of concentration, Tc

– Tp, time to peak of unit hydrograph

– ∆D, duration of effective rainfall for that watershed

– Use ∆D =0.133 Tc

Tp=0.67Tc

Runoff increments must be produced in time units of ∆D

Synthetic Unit Hydrograph – Peak Discharge

• Given Watershed Area A, Time to Peak, Tp, empirical constant Kp (usually 484, can change)

• Peak discharge qp is

( ) /

in cfs

in square miles is time to peak (hrs)

Empirical Constant (usually 484)

p p p

p

p

p

q K A T

qATK

=

Synthetic Unit Hydrograph (Finally)

• Given Tp, qp, synthetic unit hydrographs give variation of flow q/qp, and fraction of overall runoff Qa/Q as functions of T/Tp

• This will be for a unit runoff generated over time ∆D– Will either need to change runoff so it is in intervals of ∆D or use superposition of unit hydrographs to make a longer time unit hydrograph

• This will also vary with empirical coefficient Kp, but Kp=484 is mostly used

Synthetic Unit Hydrograph for Kp=484

Thought Experiments

1. How will the time of concentration, Tc, vary if an area goes from undeveloped woods or fields to a developed subdivision?

2. How will the volume of runoff be affected?3. How will this affect peak flows?4. What are the implications for downstream

areas?

Overall Procedure for SCS Synthetic Unit Hydrographs

• For 10-year, 24 hour design storm1. Find 10-year, 24 hour rainfall amount2. Find the Storm type (I, IA, II, III), and then time

variation of rainfall during event3. Determine time variation of runoff produced4. Make SCS synthetic unit hydrograph (long)

– May need to change time interval to match rainfall intervals

5. Use unit hydrograph linearity and superposition to generate 10-year design hydrograph

6. Use hydrograph to design engineering structure