Introduction

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Introduction Flood Hydrologic Analysis

• CE154 - Hydraulic Design
• Lectures 1-2

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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

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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 Reclamations 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 PMPs 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.htmlHR
  58

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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 1Outline 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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PMP Computation Example
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PMP Computation Example

• 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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PMP Computation Example
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PMP Computation Example
Step 4 Ratios for Auburn Drainage (Table 2.1 HMR58) Ratios for Auburn Drainage (Table 2.1 HMR58) Ratios for Auburn Drainage (Table 2.1 HMR58) Ratios for Auburn Drainage (Table 2.1 HMR58) Ratios for Auburn Drainage (Table 2.1 HMR58) 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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PMP Computation Example

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

Step 5 Auburn drainage 10-mi2 PMP Auburn drainage 10-mi2 PMP Auburn drainage 10-mi2 PMP Auburn drainage 10-mi2 PMP Auburn drainage 10-mi2 PMP 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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PMP Computation Example

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

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PMP Computation Example

• Fig 2.15, HMR 58

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PMP Computation Example
Step 6 Area Reduction Factors Area Reduction Factors Area Reduction Factors Area Reduction Factors Area Reduction Factors Area Reduction Factors
Duration (hr) 1 6 12 24 48 72
Factors .64 .67 .70 .72 .77 .80
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PMP Computation Example

• Step 7Apply aerial reduction by multiplying
  PMPs from Step 5 by factors from Step 6

Step 7 Auburn Drainage average PMP Depths Auburn Drainage average PMP Depths Auburn Drainage average PMP Depths Auburn Drainage average PMP Depths Auburn Drainage average PMP Depths 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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PMP Computation Example

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

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PMP Computation Example

• Extract cumulative depths from Fig. 2.19

Step 8 6-hr Cumulative Rainfall Depths 6-hr Cumulative Rainfall Depths 6-hr Cumulative Rainfall Depths 6-hr Cumulative Rainfall Depths 6-hr Cumulative Rainfall Depths 6-hr Cumulative Rainfall Depths 6-hr Cumulative Rainfall Depths 6-hr Cumulative Rainfall Depths 6-hr Cumulative Rainfall Depths 6-hr Cumulative Rainfall Depths 6-hr Cumulative Rainfall Depths 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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PMP Computation Example

• Compute incremental depths

Step 9 6-hr Incremental Rainfall Depths 6-hr Incremental Rainfall Depths 6-hr Incremental Rainfall Depths 6-hr Incremental Rainfall Depths 6-hr Incremental Rainfall Depths 6-hr Incremental Rainfall Depths 6-hr Incremental Rainfall Depths 6-hr Incremental Rainfall Depths 6-hr Incremental Rainfall Depths 6-hr Incremental Rainfall Depths 6-hr Incremental Rainfall Depths 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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PMP Computation Example

• 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 6 hr incremental rainfall depths 6 hr incremental rainfall depths 6 hr incremental rainfall depths 6 hr incremental rainfall depths 6 hr incremental rainfall depths 6 hr incremental rainfall depths 6 hr incremental rainfall depths 6 hr incremental rainfall depths 6 hr incremental rainfall depths 6 hr incremental rainfall depths 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
  1930s, 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 (SkO), 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
Rainfall excess precipipation - loss
Lag time
Receding limb
Q
Time of concentration
Point of inflection
Rising limb
Peak Time
time
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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

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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

L
Lca
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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 Mannings
  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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Bureaus 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/en
  g-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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Clark Unit Hydrograph Method

• 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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Clark Unit Hydrograph Method

• 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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Clark Unit Hydrograph

• Step 2 Identify major watercourses

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Clark Unit Hydrograph

• 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 Mannings roughness coefficientL flow
  length in ftP2 2-yr, 24-hr rainfall in
  inchesS slope in ft/ft

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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_repo
  rts/Volume20XI20California/1973/North202420hr
  20precipitation20charts.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 Mannings 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 Tc8 hr., choose
  8 subdivisions with ?t1 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 Example
Map 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

• ApproachTime-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 SRO
• Estimate from recorded hydrographThe 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 R5.5 hours and ?t 2 hours,C 0.308

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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-1Oi
  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-n1 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
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