ce154 - lecture 1-2 hydrologic study

CE154 1Fall 2009 1

Introduction & Flood Hydrologic Analysis

CE154 - Hydraulic DesignLectures 1-2

CE154 2Fall 2009 2

Green Sheet

Course Objective - Introduce design concept and procedure for a few basic types of hydraulic structures that an engineer may encounter

Hydraulic structures:- Water supply and distribution systems including spillways, reservoirs, pipeline systems - Flood protection systems including culverts, storm drains, & natural rivers

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Green Sheet

Lecture Schedule Homework assignments Exams Grading Office hour Communication – email address, web

site Emergency evacuation route Grader selection

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Introduction

Hydraulic Design – Design of Hydraulic Structures

Elements of Design (class discussion)- design objective- design criteria - design data and assumptions- design procedure- design calculations- design drawings- design report

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Hydraulic Design example

Design a channel that can safely carry the storm runoff generated from a 1% flood from a residential development that is 20 square miles in drainage area.

Design objective: Design criteria: Design data and assumptions: Design procedure:

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Flood Hydrology

Design flood Discharge (design flow)- peak flow rate governing the design of relevant hydraulic structures

Design flood Hydrograph- time-flow history of a design flood

Sample Flood Hydrograph

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Hydrology

Rainfall – Runoff Process

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Hydrologic Parameters

Precipitation intensity & duration for design Infiltration rate (watershed soil type and

moisture condition) Watershed surface cover – overland roughness Watershed drainage network geometry Watershed slope Time of concentration

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Rainfall – Runoff Process

Gauged Watershed-flood frequency analysis to determine peak design flow rate-Gauge data to calibrate unit hydrograph and generate design flood hydrograph

Ungauged Watershed-Hydrologic Modeling (HEC-HMS or HEC-1)-Regional regression analysis-Synthetic unit hydrograph

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Flood Hydrology Studies

determine design rainfall duration and intensity- design rainfall ranges from probable maximum precipitation (PMP) on the high end to 100-year or 10-year return period rainfall event

develop design runoff hydrograph – includes peak flow rate and runoff volume to size reservoir and design spillway and other pertinent structures

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Our Topics

Determine probable maximum precipitation (PMP) -”Theoretically the greatest depth of precipitation for a given duration that is physically possible over a given storm area at a particular geographical location at a certain time of the year” (HMR55A)

Bureau of Reclamation’s S-graph & dimensionless unit hydrograph methods of developing synthetic unit hydrograph

Clark unit hydrograph method

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PMP

National Weather Service Hydrometeorological Reports (HMR)provide maximum 6, 12, 24, 48 and 72 hour PMP’s for areas of 10, 200, 1000, 5000 and 10,000 mi2.

HMR 58 – Probable Maximum Precipitation for California – Calculation Procedures, NOAA, Oct. 1998 (supersedes HMR36, Note errata for pp. 22 & 27)

http://www.weather.gov/oh/hdsc/studies/pmp.html#HR58

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Rainfall Losses

Surface retention, evaporation and storage (usually small compared to infiltration)

Infiltration- Ranges 0.05 0.5 in/hr approximately- L = Lmin + (Lo – Lmin)e-kt

L = resulting infiltration rate Lmin = minimum rate when saturated Lo = maximum or initial infiltration rate

Rainfall – losses = Rainfall Excess

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PMP Computation Example

Read pp. 43-48 of HMR 58 973 mi2 Auburn drainage above Folsom

Lake Step 1

Outline drainage boundary and overlay the 10-mi2, 24-hour PMP map from Plate 2, HMR 58

Step 2Determine to use all-season or seasonal PMP for design

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Plate 2 California – Northern General Storm PMP Index Map (in inches)

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Step 3Calculate average PMP value (for 10 mi2 and 24-hr) over drainage area = 24.6 inches (using a planimeter or griddled paper overlay)

Step 4Depth-Duration Relationship- Auburn drainage is within the Sierra region. Use Table 2.1 to obtain ratios for durations from 1 to 72 hours

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Step 4 Ratios for Auburn Drainage (Table 2.1 HMR58)

Duration (hours)

1 6 12 24 48 72

Ratios .14 .42 .65 1.00 1.56 1.76

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Multiply the average value for 10-mi2, 24-hour PMP of 24.6 inches by these ratios

Step 5 Auburn drainage 10-mi2 PMP

Duration (hr)

1 6 12 24 48 72

PMP (in) 3.4 10.3 16.0 24.6 38.4 43.3

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Step 6Determine aerial reduction factors using the Auburn drainage area of 973 mi2 & Fig. 2.15

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Fig 2.15, HMR 58

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Step 6 Area Reduction Factors

Duration (hr)

1 6 12 24 48 72

Factors .64 .67 .70 .72 .77 .80

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Step 7Apply aerial reduction by multiplying PMP’s from Step 5 by factors from Step 6

Step 7 Auburn Drainage average PMP Depths

Duration (hr)

1 6 12 24 48 72

PMP (in) 2.2 6.9 11.2 17.7 29.6 34.6

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Step 8Plot the depth-duration data on Fig. 2.19

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Extract cumulative depths from Fig. 2.19

Step 8 6-hr Cumulative Rainfall Depths

Hr. 6 12 18 24 30 36 42 48 54 60 66 72

PMP (in)

6.9 11.2 14.6 17.7 20.8 23.8 26.7 29.6 31.6 32.7 33.7 34.6

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Compute incremental depths

Step 9

6-hr Incremental Rainfall Depths

Hr. 6 12 18 24 30 36 42 48 54 60 66 72

PMP (in)

6.9 4.3 3.4 3.1 3.1 3.0 2.9 2.9 2.0 1.1 1.0 0.9

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Adjust temporal-distribution of these incremental rainfall based on historical data or by experiments. Keep the 4 highest increments in a series. A PMP isohyetal distribution may be

6 hr incremental rainfall depths

Hr 6 12 18 24 30 36 42 48 54 60 66 72

PMP1 6.9 4.3 3.4 3.1 3.1 3.0 2.9 2.9 2.0 1.1 1.0 0.9

PMP2 3.1 3.0 2.9 2.9 3.1 4.3 6.9 3.4 1.1 0.9 2.0 1.0

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PMP Computation - summary

Need Hydrometeorological Report HMR 58 for northern California

Define general storms up to 72 hours in duration and 10,000 mi2 in area and local storms up to 6 hours and 500 mi2

Start with a total PMP depth for a general area and end with intensity-time distribution of rain for a specific watershed – this is the design rainfall

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How to turn PMP (design rainfall) into PMF (design runoff)? Unit hydrograph

– a rainfall-runoff relationship characteristic of the watershed - developed in 1930’s, easy to use, less data requirements, less costly- many methods, most often seen include Soil Conservation Service (SCS) method, Snyder, Clark, and Bureau of Reclamation dimensionless unit hydrograph and S-curve methods

hydrologic modeling – used widely since PC became popular, requiring data of topo contours, surface cover, infiltration ch., etc., HEC-HMS (HEC-1)

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Unit Hydrograph Basic unit hydrograph theory

A storm of a constant intensity over a duration (e.g, 1 hour), and of uniform distribution, produces 1 inch of excess that runs off the surface. The hydrograph that is recorded at the outlet of the watershed is a 1-hr unit hydrograph

Define several parameters to characterize the watershed response: e.g., lag time or time of concentration, time-discharge relationship, channel storage attenuation – synthetic unit hydrograph

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Unit Hydrograph Assumptions

Rainfall excess and losses may be lumped as basin-average values (lumped)

Ordinates of runoff is linearly proportional to rainfall excess values (linearity)

Rainfall-runoff relationship does not change with time (time invariance)

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Hydrograph Development

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Unit Hydrograph Approaches

Conceptual models of runoff – single-linear reservoir (S=kO), Nash (multiple linear reservoirs), Clark (consider effect of basin shape on travel time)

Empirical models – Snyder, Soil Conservation Service dimensionless method

Different methods use different parameters to define the unit hydrograph

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Unit Hydrograph Parameters

Time lag – time between center of mass of rainfall and center of mass of runoff, original definition by Horner & Flynt [1934], (SCS, Snyder). Different formulae were developed based on different watershed data (e.g., SCS & BuReC)

Time of concentration - time between end of rainfall excess and inflection point of receding runoff (Clark)

Time to peak – beginning of rise to peak (SCS) Storage coefficient – R (Clark) Temporal distribution of runoff (BuReC, SCS)

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Unit Hydrograph & parameters

Q

time

Lag time

Rainfall excess = precipipation - loss

Rising limb

Receding limb

Point of inflection

Peak Time

Time of concentration

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Synthetic Unit Hydrograph

Uses Lag Time and a temporal distribution (dimensionless or S-graph) to develop the unit hydrograph

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Lag Time

Unit Hydrograph Lag Time (Tlag or Lg) per Bureau of Reclamation

Ncag

SLLL

C )( 5.0

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Lag Time

Lg = unit hydrograph lag time in hours L = length of the longest watercourse

from the point of concentration to the drainage boundary, in miles

Lca

L

Point of concentration

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Lag Time

Lca = length along the longest watercourse from the point of concentration to a point opposite the centroid of the drainage basin, in miles

S = average slope of the longest watercourse, in feet per mile

C, N = constant

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Lag Time

Based on empirical data, regardless of basin location

N = 0.33 C = 26Kn where Kn is the average

Manning’s roughness coefficient for the drainage network

Note: other methods such as Snyder and SCS define lag time slightly differently

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Lag Time

To allow estimate of lag time, the Bureau of Reclamation reconstituted 162 flood hydrographs from numerous natural basins west of Mississippi River to provide charts for lag time for 6 different regions of the US

Use Table 3-5 & Fig. 3-7 of DSD for lag time estimate for SF Bay Area

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Lag Time

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Lag Time

Example, Table 3-5 on p.42, DSD- San Francisquito Creek near Stanford University, drainage area 38.3 mi2, lag time 4.8 hours, Kn 0.110

- Matadero Creek at Palo Alto, drainage area 7.2 mi2, lag time 3.7 hours, Kn 0.119

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UH Temporal Distribution

Time vs. Discharge relationship Bureau of Reclamation uses 2 methods

to develop temporal distribution based on recorded hydrographs divided into 6 regions across the US:- dimensionless unit hydrograph method, &- S-graph technique

Tables 3-15 and 3-16 (Design of Small Dams) for the SF Bay Area

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Temporal Dist. – Table 3-16

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Temp. Dist. - S-graph Method

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S-graph method - Example

Read pp. 37-52 of Design of Small Dams drainage area = 250 mi2

lag time = 12 hours unit duration = 12/5 2 hours (SCS

recommendation) Ultimate discharge = drainage area in

mi2 times 52802/3600/12 and divided by unit duration, in this case = 80662.5 cfs

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S-graph method - example

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Bureau’s Method - summary

Estimate lag time and time-flow distribution

Based on recorded hydrographs Regionalized approach – does not

consider specific local condition Works better for larger watersheds, such

as for dam construction For smaller watersheds, or smaller design

flood events, consider another method, such as the Clark unit hydrograph method

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Clark Unit Hydrograph Method

Reading Materials:- Chapter 7 of Flood-Runoff Analysis, EM 1110-2-1417, Corps of Engineers, Aug. ’94http://www.usace.army.mil/publications/eng-manuals/em1110-2-1417/toc.htm

- if you have more time, read - Unit Hydrograph Technical Manual, National Weather Service, www.nohrsc.noaa.gov/technology/gis/uhg_manual.html

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Uses the concept of instantaneous unit hydrograph (IUH) – hydrograph resulted from 1 unit of rainfall excess occurring over the basin in zero time

Uses IUH to compute a unit hydrograph for any unit duration equal to or greater than the time interval used in computation

Uses 2 parameters and a time-area relationship to define IUH

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Need 2 parameters: time of concentration (Tc) and storage coefficient (R)

Tc = travel time from the most upstream point in the basin to the outflow location

or Tc = time from the end of rainfall to the inflection point on the recession limb

R = Q/(dQ/dt) at point of inflection – estimate from recorded flood hydrographs

Example – reconstitute a flood hydrograph for Thomas Creek at Paskenta, CA for Jan/1963

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Clark Unit Hydrograph

Step 1 – Delineate watershed boundary

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Step 2 – Identify major watercourses

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Step 3 – Estimate time of concentration by estimating overland and river travel times through the watershed. Identify watershed slopes, surface cover types and river channel geometries, and use simplified relationships to estimate travel time.

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Time of Concentration

Watershed flow characteristics:

• sheet flow – approximately 0.1 ft deep, less than 300 ft in length

• shallow concentrated flow

• channel flow

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Sheet Flow Roughness Coef. [Engman 1986]

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Sheet Flow travel time

Sheet flow travel time (Tt)Tt = travel time in hrn = Manning’s roughness coefficientL = flow length in ftP2 = 2-yr, 24-hr rainfall in inchesS = slope in ft/ft

SPT

nLt 4.05.0

2

8.0)(007.0

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Sheet Flow travel time

NOAA Atlas – precipitation distribution maps

Northern California 2-yr, 24-hour rainfall http://hydrology.nws.noaa.gov/oh/hdsc/On-line_reports/Volume%20XI%20California/1973/North%2024%20hr%20precipitation%20charts.djvu

For San Jose area, 2.2 inches

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Shallow Concentrated Flow velocities

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Time of Concentration (Step 3)

Channel flow – use Manning’s equation travel time = channel length/velocity Time of concentration = summation of

travel times from sheet flow, shallow concentrated flow and channel flow

Do this for the entire watershed separated into subareas based on slope and surface cover

Sum up the travel time through the watershed and divide into equal-travel-time subareas (isochrones)

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Clark Method (Step 3) - isochrones

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Clark UH Procedure (Step 4)

Draw isochrones to subdivide the basin into chosen number of parts, e.g., if Tc=8 hr., choose 8 subdivisions with t=1 hr.

Measure the area (ai) between each pair of isochrones and tabulate. ai = ordinate in units of area (mi2 or km2)

Plot (% of Tc) versus (cumulative area). Tabulate increments at 1 t apart

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Clark UH ExampleMap Area #

Planimeter Value

Accum. Value

Accum. Area (km2)

Travel time in %Tc

1 0.08 0.08 12 12.5

2 0.15 0.23 35 25.0

3 0.40 0.63 96 37.5

4 0.36 0.99 151 50.0

5 0.45 1.44 220 62.5

6 0.45 1.89 288 75.0

7 0.66 2.55 389 87.5

8 0.68 3.23 493 100.0

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Clark UH Procedure

Approach

Time-Cumulative Area curve Translation hydrograph Linear reservoir routing Instantaneous Unit Hydrograph Unit Hydrograph of a duration

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Clark UH Procedure

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Clark UH Procedure

Convert areas into flows (area x unit rainfall / unit time) of a translation hydrograph Ii = Kai/t

where Ii = ordinate of translation hydrograph in unit of discharge (cfs or cms) at end of period i, K = conversion factor (645 to convert in-mi2 to cfs or 0.278 to convert mm-km2 to cms) 0.278 = 1000x1000/1000/3600

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Clark UH Example

(1)

Time (hr)

(2)

Rain over ai

(mm-km2)

(3)

Inflow Ii Of translation hydrograph (cms)

(4)

IUH Oi

(cms)

(5)

2-hr UH

Qi (cms)

0 0 0

2 35 5

4 116 16

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Storage Coefficient R (Step 5)

For linear reservoir S=RO Estimate from recorded hydrograph:

The inflection point of a recession limb, by definition, is when inflow ceases, because time of concentration is from end of rainfall to the inflection point, and is when the last rain reaches the end of the watershed.dS/dt = I-O = -O continuity equationdS/dt = R dO/dt for linear reservoir R = -O/(dO/dt) at the inflection point

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Storage Coefficient R

R is used to define a dimensionless routing constant C:

C =

with R=5.5 hours and t = 2 hours,

C = 0.308

tR

t

2

2

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Clark UH Procedure (Step 6)

Route the inflows (Col. 3) to the outflow location (Col. 4)Oi = CIi + (1-C)Oi-1

Oi = outflow from the basin at the end of period iIi = inflow from each area at the end of period i

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Clark UH Example

(1)

Time (hr)

(2)

Inflow ai

(mm-km2)

(3)

Inflow Ii

(cms)

(4)

IUH Oi

(cms)

(5)

2-hr UH

Qi (cms)

0 0 0 0

2 35 5 1.55

4 116 16 5.97

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Clark UH Example

6 137 19 10.01

8 205 29 15.69

10 0 0 10.85

12 7.50

14 5.19

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Clark UH Procedure

Average the ordinates of the IUH to create the unit hydrograph (Col. 5) Qi = 0.5 (Oi + Oi-1)

The duration of the UH may be different from t (provided that it is an exact multiple of t), and the UH follows this formulaQi = 1/n (0.5Oi-n + Oi-n+1 + … + Oi-1 + 0.5Oi)

where

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Clark UH Procedure

Qi = ordinate at time i of unit hydrograph of duration D and tabulation interval t

n = D/ t D = unit hydrograph duration t = tabulation interval

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Clark UH Example

(1)

Time (hr)

(2)

Inflow ai

(mm-km2)

(3)

Inflow Ii

(cms)

(4)

IUH Oi

(cms)

(5)

2-hr UH

Qi (cms)

0 0 0 0 0

2 35 5 1.55 0.78

4 116 16 5.97 3.76

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Clark UH Example

6 137 19 10.01 7.99

8 205 29 15.69 12.85

10 0 0 10.85 13.27

12 7.50 9.17

14 5.19 6.35

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Clark UH Example

Continue the UH calculation to Hour 46 when the discharge diminishes to 0

For each 2-hour interval of the Jan/Feb 1963 storm, compute rainfall excess, multiply by the UH ordinates and lag the time of occurrence to obtain the flood hydrograph

Compare with the measured hydrograph

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The END

ce154 - lecture 1-2 hydrologic study

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