CE 590CE 590

Hydrology Hydrology

Lecture # 3Lecture # 3

Paul P. MathisenWorcester Polytechnic Institute

Civil and Environmental Engineering

CE 590 HydrologyCE 590 Hydrology

Hydrologic principles

Rainfall and runoff Surface water & ground water flow Watersheds and terrestrial inputs to

surface water bodies

Examples developed from Wachusett Reservoir

Instructor: Paul Mathisen (with some assistance from others)

http://cee.wpi.edu/hydro

Web site:

Last time ...Last time ...

Brief reviewBrief review Some clarifications on definitionsSome clarifications on definitions Quantitative analysis of rainfallQuantitative analysis of rainfall Rainfall measurementRainfall measurement

Today ...Today ...

ReviewReview AbstractionsAbstractions Catchments Catchments RunoffRunoff Intro to infiltrationIntro to infiltration

Water BudgetWater Budget

T

G

R

EPI

Rainfall / runoffRainfall / runoff

rainfallrainfall

depression storage

overland flow

streamflow

AbstractionsAbstractions

Processes acting to reduce total Processes acting to reduce total ppt into effective ppt., which ppt into effective ppt., which ultimately produces runoffultimately produces runoff– InterceptionInterception– surface or depression storagesurface or depression storage– infiltration infiltration – evaporationevaporation– evapotranspirationevapotranspiration

InterceptionInterception

Abstraction by vegitation or other surface Abstraction by vegitation or other surface covercover

throughfall - part of ppt that reaches the throughfall - part of ppt that reaches the groundground

fx of storm, vegatative cover, seasonfx of storm, vegatative cover, season amountsamounts

– light storms - 25 percentlight storms - 25 percent– moderate storms - 7 to 36 % in growing seas.moderate storms - 7 to 36 % in growing seas.– heavy & longer storms - smallheavy & longer storms - small

InterceptionInterception

ComponentsComponents– Interception storage - retained by Interception storage - retained by

foliagefoliage– evaporation lossevaporation loss

L= S + K E t

Where ..L=interception loss (mm)S = interception storage depth (mm)K= evap.foliage surf/its horiz projectionE= evap. Rate (mm/hr)t= storm duration

Surface/depression Surface/depression storagestorage

Abstracted ppt is retained in puddles, Abstracted ppt is retained in puddles, ditches , and other depressions in surfaceditches , and other depressions in surface

milder the relief, greater the depression milder the relief, greater the depression storagestorage

ex - ex - – sand - 5mmsand - 5mm - pervious urban - 6.25 - pervious urban - 6.25

mmmm– loam - 3.75 mmloam - 3.75 mm - paved areas - 1.5 mm- paved areas - 1.5 mm– clay - 2.5 mmclay - 2.5 mm

Depression storageDepression storage

QuantificationQuantification– lump in with other components such as lump in with other components such as

infiltrationinfiltration– Peak flow correction factor (SCS TR55)Peak flow correction factor (SCS TR55)

– VVss = S = Sd d (1 - e(1 - e-kPe-kPe) where Vs is the equiv ) where Vs is the equiv depth of depress storage (mm), Pe is depth of depress storage (mm), Pe is precip excess, Sd is depression storage precip excess, Sd is depression storage capacity (mm) [typically 10 to 50 mm], capacity (mm) [typically 10 to 50 mm], and k is a constand k is a const

Infiltration Infiltration

R

(in)

t (hrs)

Infiltration - seepage of rainfall into the ground(contribution to groundwater)

Antecedent moistureAntecedent moisture Infiltration has an important effect on Infiltration has an important effect on

abstracted ppt. abstracted ppt. Infiltration is dependent on initial level of Infiltration is dependent on initial level of

soil moisture, or antecedent moisturesoil moisture, or antecedent moisture Antecedent ppt index (API) Antecedent ppt index (API) typical depletion ratetypical depletion rate

– IIi i = K I= K I I-1 I-1

– where Iwhere Iii is index for day, I is index for day, Ii-1i-1 is index for is index for preceding day, and K= recession factor (.85-.98)preceding day, and K= recession factor (.85-.98)

Antecedent Precipitation Antecedent Precipitation IndexIndex

High API, greater runoffHigh API, greater runoff Alternative definitionsAlternative definitions

– Antecedent moisture condition (AMC)Antecedent moisture condition (AMC)– by SCS .. I(dry), II(avg), or III(wet)by SCS .. I(dry), II(avg), or III(wet)– SSARR - soil moisture index (SMI) - SSARR - soil moisture index (SMI) -

relates runoff to SMI and ppt. relates runoff to SMI and ppt. intensityintensity

Runoff percent (R/P)*100Runoff percent (R/P)*100

Surface runoffSurface runoff

runoff depends on the antecedent runoff depends on the antecedent ppt indexppt index

water flowing on earth’s surfacewater flowing on earth’s surface overland flowoverland flow flow in rills, gullies and streamsflow in rills, gullies and streams

3 components contribute 3 components contribute to runoffto runoff

surface flowsurface flow interflowinterflow groundwater flowgroundwater flow

Surface runoff in Surface runoff in catchmentscatchments

Overland flow - sheet flow over land Overland flow - sheet flow over land surf.surf.

rill flow - small rivulets (conc of rill flow - small rivulets (conc of overland)overland)

gully flow - runoff with erosive gully flow - runoff with erosive cababilitycabability

streamflow - concentrated runoffstreamflow - concentrated runoff river flow - confluence of streamsriver flow - confluence of streams

Catchment characteristicsCatchment characteristics

areaarea SlopeSlope ShapeShape Flow lengthFlow length streams (location, density, nature)streams (location, density, nature)

Catchment areaCatchment area

Drainage areaDrainage area– leads to potential runoff volumeleads to potential runoff volume

catchment dividecatchment divide– may differ from groundwater dividemay differ from groundwater divide

Estimate: Q Estimate: Q peakpeak=Ca=Cann

A

divide

Catchment shapeCatchment shape FormForm

– KKff=A/L=A/L22 where Kf is form ratio, and L is where Kf is form ratio, and L is catchment lengthcatchment length

CompactnessCompactness– KKcc=0.282P/A=0.282P/A1/21/2 where K where Kcc is a compactness is a compactness

ratio, and P is the perimeter ratio, and P is the perimeter Catchment response - conc. & timing of runoffCatchment response - conc. & timing of runoff If Kf high, or Kc~1, then rapid runoffIf Kf high, or Kc~1, then rapid runoff Factors: relieve, veg. cover, drainage density, ..Factors: relieve, veg. cover, drainage density, ..

Flow length - Flow length - approximate equationsapproximate equations

Approximate estimateApproximate estimate– LLoo=1/(2D)=1/(2D)

– where D=drainage density since overland where D=drainage density since overland flow length is approx 1/2 of mean distance flow length is approx 1/2 of mean distance between channelsbetween channels

More precise estimateMore precise estimate– LLoo=1/[2D{1-(S=1/[2D{1-(Scc/S/Sss)})}1/21/2]]

– where Swhere Scc is the mean channel slope and S is the mean channel slope and Sss is the mean surface slopeis the mean surface slope

Linear measuresLinear measures

G

LcL

Catchment length -length Catchment length -length along principle watercoursealong principle watercourse

length to centroid (often est. length to centroid (often est. as point to 2 or more as point to 2 or more bisecting straight linesbisecting straight lines

OrderOrder– 0 = overland flow0 = overland flow– 1 = gets flow from 0 orders1 = gets flow from 0 orders– 2 = gets flow when 2 1st order 2 = gets flow when 2 1st order

streams combinestreams combine– etc.etc.

Estimating the overland Estimating the overland flow lengthflow length

collector collectorcollector

Lo

Lo Lo

Slope/catchment reliefSlope/catchment relief

Relief - an elevation differenceRelief - an elevation difference max relief = max elev diff between max relief = max elev diff between

highest & lowest pointshighest & lowest points Relief ratio=max relief/longest Relief ratio=max relief/longest

straight lgthstraight lgth

Land surface slopesLand surface slopes

Often use grid Often use grid methods to get methods to get slopes slopes

hypsometric hypsometric analysis = curve analysis = curve showning showning elevation of elevation of catchment above catchment above this elevationthis elevation

Ei-Emin

Emax-Emin

Ai/Ac

Stream channelsStream channels S1 - S1 - from max and min elev’sfrom max and min elev’s S2 - S2 - const slope that makes const slope that makes

shaded area above equal to shaded area above equal to shaded area belowshaded area below

S3 - S3 - equivalent slope - equivalent slope - – break channel into break channel into

subreaches & obtain slopesubreaches & obtain slope E

Distanceup Down

Slope 0.10 - mountains 0.000006 - some tidal rivers

S3=Li

(Li/Si 1/2)

2

Stream-types and Stream-types and baseflowbaseflow

perennial perennial – (always flowing)(always flowing)– flow maintained by “base flow” during flow maintained by “base flow” during

dry weatherdry weather ephemeralephemeral

– (only in response to ppt)(only in response to ppt) intermittentintermittent

– (only in certain times of the year)(only in certain times of the year)

HydrographsHydrographs

• Characteristics of the hydrograph

• Distribution of uniform rainfall

RunoffRunoff

Volume or flow rateVolume or flow rate varies with timevaries with time may express in flow per unit may express in flow per unit

drainage area, per unit runoff drainage area, per unit runoff depth, or per bothdepth, or per both

surface flow - direct runoffsurface flow - direct runoff also get indirect runoffalso get indirect runoff

Q(cfs)

T (hr)

Runoff coefficientsRunoff coefficients

R=k PR=k P

surfacesurface k k urban residential: singleurban residential: single 0.30.3 aptsapts 0.50.5 commerial and industrialcommerial and industrial 0.90.9 forestsforests 0.05-0.200.05-0.20 parks; farmsparks; farms 0.05-0.300.05-0.30 asphalt and pavementasphalt and pavement 0.85-1.000.85-1.00

First part of class ...First part of class ...

ReviewReview AbstractionsAbstractions Catchments Catchments RunoffRunoff

Next ...Next ...

InfiltrationInfiltration– DefinitionsDefinitions– Physical aspectsPhysical aspects– Simple modelsSimple models– Physically based modelsPhysically based models– measurementmeasurement

3 components contribute 3 components contribute to runoffto runoff

surface flowsurface flow interflowinterflow groundwater flowgroundwater flow

InfiltrationInfiltration Infiltration - process by which ppt is abstracted by seeping Infiltration - process by which ppt is abstracted by seeping

into soil below ground surfaceinto soil below ground surface define it by define it by

– an instantaneous infiltration rate (mm/hr)an instantaneous infiltration rate (mm/hr)– an average infiltration rate (mm/hr)an average infiltration rate (mm/hr)

Function of rainfall intensity, soil properties and soil type, Function of rainfall intensity, soil properties and soil type, surface conditions, vegitative cover, and water qualitysurface conditions, vegitative cover, and water quality

Physical problemPhysical problem

unsaturatedflow

saturatedflow

Close-upview onnext slide

Moisture in the Moisture in the unsaturated zoneunsaturated zone

unsaturated saturated

air water water

moisture content=Vwater/Vtot

porosityn=Vw /Vt=Vvoid/Vtot

Capillarity & capillary Capillarity & capillary fringefringe

capillary forces result in rise of fluid

rwgR

(2 cos )hc =

hc

2R

In subsurface, we get a capillary fringe

capillary fringe

Vadose/unsaturated zone

Conditions in unsaturated Conditions in unsaturated zonezone

total potential or headtotal potential or head h = z + h = z + where z is the where z is the

elevation head and elevation head and is the is the pressure head (or moisture pressure head (or moisture potential)potential)

is a function of is a function of Darcy’s law applies:Darcy’s law applies:

– q=K(q=K( dh/dz dh/dz

Controls on the Range of Controls on the Range of moisture contentmoisture content

Field capacity Field capacity – maximum amount of moisture the soil maximum amount of moisture the soil

structure can hold agains the force of structure can hold agains the force of gravitygravity

– upper level of moisture before rapid upper level of moisture before rapid drainagedrainage

Wilting pointWilting point– soil mosture at which permanent soil mosture at which permanent

wilting of plants starts to occurwilting of plants starts to occur

[NEXT TIME] [NEXT TIME] Infiltration - quantitative Infiltration - quantitative

approachesapproaches

Estimation from water balancesEstimation from water balances Horton EquationHorton Equation Philip’s EquationPhilip’s Equation IndexIndex Green-Ampt modelGreen-Ampt model MeasurementMeasurement