Introduction toIntroduction toHydrologic Hydrologic Processes - Processes -

Rainfall & Streamflow - 2004Rainfall & Streamflow - 2004

Dr. Philip B. BedientDr. Philip B. BedientCivil and Environmental EngCivil and Environmental Eng

Rice UniversityRice University

• Important hydrologic characteristic

• Elongated Shape

• Concentrated Shape

• Affects Timing and Peak Flow

• Determined by geo - morphology of stream

Watershed ShapesWatershed Shapes

Watershed - Elevation ContoursWatershed - Elevation Contours

Water flows at right angles to elevation contours and from higher to lower elevations

Subareas - Subareas - divided according to divided according to topography and hydrology topography and hydrology

OutletOutlet

Sub A

Texas River BasinsTexas River Basins

Hydrologic features with several different types of flow processes

Red

Trinity

BrazosRio Grande

Colorado

San Jacinto

Precipitation

Water on Surface Overland Flow

ChannelFlow

The Hydrologic Cycle

Ground Water Ground Water Flow

Ocean

Reservoir

Sources of RainfallSources of Rainfall

• Severe Storms - Convective CellsSevere Storms - Convective Cells• Low Pressure Systems - HurricanesLow Pressure Systems - Hurricanes• Frontal Systems - Cold or WarmFrontal Systems - Cold or Warm• Dew and FogDew and Fog• Hail and Ice StormsHail and Ice Storms• CondensationCondensation

• Thunderstorm cell with lightningThunderstorm cell with lightning

• Characterized by updrafts and downdraftsCharacterized by updrafts and downdrafts

• Strong convergence and divergenceStrong convergence and divergence

1. Orographic lifting over mountain ranges

2. Convective heating at or near surface - summer

3. Frontal systems and buoyancy effects - winter

Causes of PrecipitationCauses of Precipitation

Fronts and Low PressureFronts and Low Pressure• Cold/Warm Front

• Lifting/Condensation

• High and Low P

• Rainfall Zone

• Circulation Issues

• Main weather    makers

Track of Hurricane Andrew -1992Track of Hurricane Andrew -1992

• Formed in the Atlantic

• Moved directly to Florida

• Winds in excess of 150

   mph

• $ 25B damage to Florida

• Moved over Gulf and

   strengthened and hit LA

Average Annual PrecipitationAverage Annual Precipitation

The HyetographThe Hyetograph

Graph of Rainfall Rate (in/hr) vs Time (hr) at a Graph of Rainfall Rate (in/hr) vs Time (hr) at a

single gage locationsingle gage location

Usually plotted as a bar chart of gross RFUsually plotted as a bar chart of gross RF

Net Rainfall is found by subtracting infiltrationNet Rainfall is found by subtracting infiltration

Integration of Net Rainfall over time = Integration of Net Rainfall over time =

Direct RO Vol (DRO) in inches over a WatershedDirect RO Vol (DRO) in inches over a Watershed

Mass Curves & Mass Curves & Rainfall HyetographsRainfall Hyetographs

• Alvin, Texas

• 43 inches in 24 hours

• Measured in one gage

• Associated with T.S.

Claudette in July 1979

• Texas accounts for 12

world rainfall records

Largest One Day U.S. Largest One Day U.S. Total RainfallTotal Rainfall

Tipping Bucket Rain GageTipping Bucket Rain Gage

• Recording gage

• Collector and Funnel

• Bucket and Recorder

• Accurate to .01 ft

• Telemetry- computer

• HCOEM website

9-Hour Total Rainfall - TS Allison

Intensity-Duration-FrequencyIntensity-Duration-Frequency• IDF curves

• All major cities

• Based on NWS data

• Various return   periods & durations

• Used for drainage design of pipes & roads

• Used for floodplain   designs - watersheds

Design RainfallsDesign Rainfalls

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0:30 1:00 1:30 2:00 2:30 3:00 3:30 4:00 4:30 5:00 5:30 6:00

Time

Rainfall (in)

100 Year Storm8.4 inches

10 Year Storm5.6 inches

25 Year Storm6.6 inches

5 Year Storm4.8 inches

Design Storm from Design Storm from HCFCD and NWSHCFCD and NWS

Based on Based on Statistical Analysis Statistical Analysis of Dataof Data

5, 10, 25, 50, 100 5, 10, 25, 50, 100 Year Events Year Events

Various Durations Various Durations of 6 to 24 hoursof 6 to 24 hours

Six Hour Rainfall

T.S. Allison – Radar DataT.S. Allison – Radar Data

1 a.m.

NEXRAD data is measured every 5 min over each grid cell as storm advances (4 km x 4 km cells)

The radar data can be summed over an area to provide total rainfall depths

T.S. ALLISON RADAR RAINFALL OVER BRAYS BAYOU WATERSHED12 HOUR TOTALS BY SUBAREA

T.S. Allison Storm TotalJune 8-9, 2001June 8-9, 2001

Bayous

Counties

Highways

Drainage

TMCÊÚStorm Total (in)

0.01 - 0.250.25 - 0.50.5 - 11 - 22 - 44 - 66 - 88 - 1010 - 1212 - 1414 - 1616 - 1818 - 2020 - 2222 - 25> 25

ÊÚ

.-,45

.-,10

.-,59

N

0 5 10 Miles

26.6 in

• Connect gages with lines

• Form triangles as shown

• Create perpendicular

     bisectors of the triangles

• Each polygon is formed

     by lines and WS boundary

• P = (Ai*Pi) / A

Thiessen Polygons - Avg PThiessen Polygons - Avg P

Gage Averaging Gage Averaging MethodsMethods

• Arithmetic

• Thiessen Polygon

• Isohyetal Contours

Horton’s Infiltration Capacity fHorton’s Infiltration Capacity f

Horton (1933 - 1940) studied the response of different soils to application of water at varying rates

Rate of rainfall must exceed the rate of infiltration andantecedent condition is an important parameter

Sand > Silt > Clay

Horton’s Infiltration ConceptHorton’s Infiltration Conceptf(t) = Rate of water loss into soilf(t) = Rate of water loss into soil

f = fc + (fo - fc) exp (-kt)

fc = final rate value

fo = initial rate value

K = decay rate

Can integrate to get

F(t) = Vol of infiltration

Horton’s EqnHorton’s Eqn

€

Vol = Area fdt =∫ A [ fc∫ + ( f0 − fc )e−kt ]dt

FF

STREAMFLOW STREAMFLOW Brays Bayou - Main StBrays Bayou - Main St

Typical Streamflow GageTypical Streamflow Gage

High FlowHigh Flow

Brays Bayou Flooding at Loop 610Brays Bayou Flooding at Loop 610

Main ChannelMain Channel

OverbankOverbank

Brays Bayou - T.S. Allison in June, TS TS Allison level reached 41.8 ft MSL

TMC is at 44 ft & Rice Univ is at 50 ft

€

Q =1.49

nAR2 / 3S1/ 2

Where R = A /P and S = Slope

n = Manning's roughness coeff

• Measure V (anemometer) at 0.2 and 0.8 of depth

• Average V and multiply by (width * depth)

• Sum up across stream to get total Q = (Vi Di Wi)

Stream Cross-Section for QStream Cross-Section for Q

The HydrographThe Hydrograph

Graph of discharge vs. time at a single locationGraph of discharge vs. time at a single location

Rising Limb, Crest Segment, Falling Limb,and Rising Limb, Crest Segment, Falling Limb,and

Recession Recession

Base Flow is usually subtracted to yield DROBase Flow is usually subtracted to yield DRO

Peak gives the maximum flow rate for the eventPeak gives the maximum flow rate for the event

Area under curve yields volume of runoff (inches)Area under curve yields volume of runoff (inches)

Small Basin ResponseSmall Basin Response

• Rainfall falls over the basin

• Rainfall reaches the outlet -   

  response based on travel time

• Produces a total storm response

  hydrograph as shown

• Some delay and little storage

• The above only occurs in small

  urban basins or parking lots

Ii

QQi i = CI= CIii A A

Small BasinSmall Basin

0

200

400

600

800

1000

1200

1400

1600

1800

2000

6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00

Time

Outflow (cfs)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

Rainfall (in)

Rainfall and Runoff ResponseRainfall and Runoff Response

Rainfall Measuredfrom USGS Gage 400at Harris Gully Outlet

Rainfall Measuredfrom USGS Gage 400at Harris Gully Outlet

February 12, 1997 on Harris Gully

Flow Measuredfrom USGS Gage 403Inside Harris Gully

Flow Measuredfrom USGS Gage 403Inside Harris Gully

Net Rainfall * Area = integration of direct runoff hydrographNet Rainfall * Area = integration of direct runoff hydrograph

Vol under blue bars * Area = Volume under red line (hydrograph)Vol under blue bars * Area = Volume under red line (hydrograph)

Time-Area Time-Area MethodMethod

• Watershed travel times

• Time Area Graph

• Rainfall Intensities

• Add and Lag Method

• Resulting Hydrograph

Time Area HydrographTime Area Hydrograph

• Q1 = P1 * A1

• Q2 = P2*A1 + P1*A2

• Q3 =P3*A1 + P2*A2 +

   P1*A3

• And So Forth

Peak Flow at QPeak Flow at Q33

Each area contributes according to its Each area contributes according to its time of travel and rainfall intensitytime of travel and rainfall intensity

Hydrograph - Hydrograph - Watershed Flow Watershed Flow Response to RainfallResponse to Rainfall

Peak Flow and time to peak relate to area/shape of watershed

Area under curve is the volume of DRO

Time Base is time that flow exceeds baseflow

Time to peak or Lag is measured from center of mass of rainfall pattern

Hydrograph

Volume of Runoff

DRO

Ou

tflo

w

Time

Time Base

Peak Flow

Lag or time to peak

RFRF

Unit Hydrograph (UH) MethodUnit Hydrograph (UH) Method

T

Q

• 1 Inch of net rainfall

   spread uniformly over the

   basin

• Response is unique for

   that basin and duration D

• UH - from measurements

• UH - Synthetic equations

• Still used today for most

   watershed studies in U.S.

Pi

Uj

UH for a Complex RainfallUH for a Complex Rainfall

T

Q

• Linear transform method

• Converts complex rainfall to

  streamflow at outlet

• Produces a total storm

  hydrograph from given UH

• Used in complex watersheds

• Each subarea is uniform

• Storage effects considered

Qn = Pn U1 + Pn-1 U2 + Pn-2 U3 + … +P1 Uj

Pi

Uj

Synthetic UH MethodsSynthetic UH Methods

Methods to characterize ungaged basins - 1938

Use data and relationships developed from gages

Variety of approaches but most based on tp and Qp,

Where tp = lag time (hr) and

Qp = peak flow in cfs

Snyder’s UH MethodSnyder’s UH Method

€

tp = Ct (LLc )0.3

Qp = 640Cp (A / t p )

TB = 3 to 5 times t p

Duration D = t p /5.5

Snyder’s MethodSnyder’s Method

5 to 7 points

Hydrograph Hydrograph ConvolutionConvolution

1

2

0.5

0.51 2

Add up the ordinates of all three to produce storm hydrograph

STORMHYDRO

Add and Lag Method

Hydrograph Flood Routing to Hydrograph Flood Routing to Next Downstream LocationNext Downstream Location

Recession

RisingLimb

Crest

Falling Limb

Time Base of Hydrograph

1

2

Flood wave is Flood wave is laggedlagged and and attenuatedattenuated as it moves downstream as it moves downstream

Flood Flows Cause Major Flood Flows Cause Major DamageDamage

The EndThe End