GEOS 4430/5310 Lecture Notes: Streamflowand Hydrographs

Dr. T. Brikowski

Fall 2013

0file:streamflow.tex,v (1.30), printed September 17, 20131

Rainfall/Runoff Relationships

Depending on the nature of precipitation, soil type, moisturehistory, etc., an ever-varying portion of the precipitation becomesrunoff, moving via overland flow into stream channels

I these stormflow events are typically recorded as hydrographsof discharge, or stream height (stage) vs. time

I A hydrograph (Fig. 1) is a plot of discharge vs. time at anypoint of interest in a watershed, usually its outlet.Hydrographs are the ultimate measure of a watershed’sresponse to precipitation events

I for any storm, the initial precipitation does not contributedirectly to flow at the outlet, instead it is stored or absorbed.This is termed the initial abstraction (Fig. 2), precipitationthat falls before the storm hydrograph begins.

I direct runoff is that portion of the precipitation that movesdirectly into the channel, appearing in the hydrograph

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Rainfall/Runoff Relationships (cont.)

I losses represent storage of precipitation upstream from theoutlet after the storm hydrograph begins. Often lumped withabstraction.

I excess precipitation runs off, and forms the storm hydrograph

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Typical Storm Hydrograph

Figure 1: Typical stream hydrograph. This example from USGS streamgauging station 08058900, East Fork Trinity River at McKinney.

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Idealized Rainfall-Runoff

Figure 2: Conceptual model of rainfall-runoff relationships. AfterMcCuen (1998).

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Actual Rainfall-Runoff, DFW

0

5

10

15

20

25

30

09/17 09/24 10/01 10/08 10/15 10/22

0

0.2

0.4

0.6

0.8

1

Hou

rly D

isch

arge

(cf

s)

Hou

rly P

reci

pita

tion

(in)

Date (in 2011)

Elm Fk Trinity at McKinney (USGS Gauge 8058900)

DischargeHourly Precipitation (in)

Figure 3: Rainfall-runoff at East Fork Trinity River nr McKinney,Sept-Oct. 2011. Note similar runoff despite much heavier rainfall inmid-Sept.

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Hydrologic Budget

I Idealized model: Hortonian Overland FlowI when precipitation exceeds infiltration capacity of soil,

Hortonian overland flow resultsI infiltration rate declines ∼exponentially as soil saturatesI Horton model (1940) assumes uniform infiltration capacity for

watershed

I Overland Flow (OF) actually unimportant in most watersheds(studies performed in 1960’s)

I often only 10% of a watershed regularly supplies OF during astorm event

I in those areas, often only 10-30% of precip. becomes OFI vegetation also absorbs much precip.I well-vegetated watersheds in humid climate rarely show OFI arid zones (sparse vegetation) during high-intensity rainfall will

show Hortonian OF

I Best model: variable source area (Fig. 4) (e.g. p. 271,Dunne and Leopold, 1978)

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Hydrologic Budget (cont.)

I depending on slope, soil thickness and “convergence” of runoff(amount of throughflow), some areas of the watershed yieldrunoff before others. Source areas vary during a single stormas well (contributing area vs. hydrograph image)

I interflow (subsurface stormflow) is prime contributor tostreamflow

I OF is important near streams, where slopes become saturatedby interflow

I return flow (emergence of interflow) also important nearstreams

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Variable Source Area for Runoff

Figure 4: Cartoon of runoff processes, showing that interflow source areavaries with time, contradicting the Hortononian model view. See alsoCornell VarSource Lab.

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Baseflow Characteristics

I storm hydrograph has two contributions (Fig. 5) and Fetter(Fig. 2.14, 2001)

I “Fast” response: overland flow, interflow, etc. direct runoffI Baseflow: discharge of groundwater flow to stream

I hydrograph separation helps distinguish these components

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Parts of A Storm Hydrograph

Figure 5: Storm and baseflow contribution to storm hydrograph. AfterFetter (Fig. 2.15, 2001). Note: the relation D = A0.2 is generally onlyvalid for Hortonian OF.

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Estimating Baseflow

I discharge not associated with the storm (i.e. fromgroundwater) is termed baseflow (bottom frame, Fig. 2).

I hydrograph or baseflow separation is performed to determinethe portion of the hydrograph attributable to baseflow

I Methods (Fig. 6):I Constant-discharge method:

I assume baseflow constant regardless of stream height(discharge)

I project from minimum value immediately prior to beginning ofstorm hydrograph.

I Constant-slope:I connect inflection point on receeding limb of storm

hydrograph to beginning of storm hydrographI Assumes flow from aquifers began prior to start of current

storm, arbitrarily sets it to inflection pointI for large watersheds set inflection point at at D = A0.2, where

D is number of days after hydrograph peak, A (mi2) iswatershed area

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Estimating Baseflow (cont.)

I Concave (most realistic):I assume baseflow decreases while streamflow increases (i.e. to

peak of storm hydrograph)I project hydrograph trend from minimum discharge value

immediately prior to beginning of storm hydrograph to directlybeneath hydrograph peak

I connect that point to inflection point on receeding limb ofstorm hydrograph

I Master depletion curve methodI use when the most accurate model of hydrograph recessions is

neededI combine data from several recessions to make general

recession model (Fig. 7)I from this an equation of the form qt = qoe

−Kt can be derived,which gives discharge qt at any time t after discharge qo ismeasured (Eqn. 2.4, Fetter, 2001)

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Techniques for Baseflow Separation

Figure 6: Baseflow separation techniques. After McCuen (1998).

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Master Depletion Curve Method

Figure 7: Master depletion curve method, where individual recessioncurves are plotted in order of decreasing minimum discharge to obtain anaverage slope for the linear “tail” of each curve. See McCuen (2004, p.488-501).

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Seasonal Recession Method

A common hydrogeologic approach is to use seasonal recessions(Meyboom method).

I Often applied by hydrogeologists in undeveloped watersheds

I after direct runoff ceases, stream hydrograph declinesexponentially

I this is baseflow, distinguishable by long period of steadystreamflow decline (see Figs. 2.21, Fetter, 2001))

I water table falls as baseflow drains aquifer, decreasingcross-sectional area of flow, causing reduced baseflow

I fit the recession with exponential curve Q = Qoe−at , where Qo

is flow at the start of recession, a is the recession constant forwatershed (a fit parameter), t is the time since recession began

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Indirect Methods

Chemical hydrographs (Fig. 8) are sometimes used

I use some environmental tracer (Cl−, 18O , 2H-D)

I generally show much higher baseflow than other methods

I careful isotopic analysis (e.g. Gregory, SMU, White RockCreek) shows very small baseflow component during storms

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Chemical Hydrograph

Figure 8: Chemical hydrograph, after Freeze and Cherry (Fig. 6.20,1979).

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Automated Baseflow Separation

I automated separation is desirable in some cases, e.g. forclimate change or long-term drawdown effects on streamflow

I the USBR has produced a Fortran program to do this: BFI

I see UT project notes for usage description

I the baseflow index is the ratio of baseflow to total flow (oftengiven as percent), and changes in this can be important

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Streamflow Estimation/Measurement

Streamflow is a combination of baseflow and runoff. These varyalong the stream.

I a gaining stream receives baseflow from aquifer, a losingstream contributes water to the aquifer (Fig. 9)

I bank storage is temporary loss of water from the stream intoits banks (Fig. 2.17, Fetter, 2001)

I streamflow is measured using stream gaugingI given gauging results a rating curve can be generated, relating

stage to dischargeI thereafter monitoring water level is sufficient to give discharge.

USGS online streamflow data is generated this way

I streamflow can be estimated using the rational equation orManning Equation

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Gaining/Losing Stream

Figure 9: Gaining and losing streams, after Fetter (Fig. 2.16, 2001).

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Bank Storage

Figure 10: Bank storage, after Freeze and Cherry (Fig. 6.22, 1979)

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Streamflow Estimation

I want to determine discharge Q, where Q = V · AI need to obtain an average velocity, since velocity not uniform

vertically or horizontally (Fig. 11)I use standard velocity profiling techniques (measure at regular

horizontal and vertical intervals)I or use Manning’s Eqn. (velocity in an open channel)

Vavg =1.49R

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√S

n

where R is ratio of cross-sectional area to wetted perimeter ofchannel, S is slope of water surface, n is the channel roughnesscoefficient

I see also Surface Water Modeling notes

I the USGS publishes a pictoral guide to help in selecting n. Anonline version is available at USGS Verified RoughnessCharacteristics website

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Stream Velocity Distribution

Figure 11: Variation of stream velocity with depth, (after Fig. 3.16,Sanders, 1998).

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Rational Equation

I rational equation: after a sufficient time, runoff will equalrainfall*basin area, reduced to account for infiltration

I equation form:

Q(

L3

T

)︸ ︷︷ ︸

max runoff

= C︸︷︷︸runoff coefficient

· I(

LT

)︸ ︷︷ ︸Rainfall Intensity

· A(L2)︸ ︷︷ ︸

Drainage Area

I be sure t > tc , time for water to flow across entire basin

I use rational equation only for small watersheds

I see also Surface Water Modeling notes

I heterogeneous areas can be divided into homogeneous zones,and the results added together to get final result (e.g.Maidment classnotes)

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Weir Basics

I Wiers are fixed-geometry structures that are used to measuredischarge, usually in relatively low-flow settings.

I four important variations: rectangular (spillway), V-notch,Parshall flume, and circular orifice wiers

I Parshall flume is in widespread use, since only one headmeasurement is needed (see flume in use). No longerrecommended since long-throated flumes give more accurateresults.

I see also Applied Surface Water Modelling notes

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Orifice Wier

Figure 12: Circular orifice wier. Discharge is calculated from the orificediameter and pressure behind the orifice as measured by a manometer.After U. Florida extention webpage.

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Wier Equations

I Discharge can be estimated using tabulated values for thewier equations (e.g. USBR Water Measurement Manual) forthe appropriate wier type. In the following discharge Q gal

min , Cis wier coefficient, H is height of water above wier discharge.

I turbulence and surface tension effects can be important (e.g.contraction of V-notch wier flow p. 19)

I these are incorporated empirically in the wier coefficient

I orifice: Q = 8.02CA√H

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References

Dunne, T., Leopold, L.B.: Water in Environmental Planning. W. H.Freeman, New York (1978)

Fetter, C.W.: Applied Hydrogeology. Prentice Hall, Upper Saddle River,NJ, 4th edn. (2001), http://vig.prenhall.com/catalog/academic/product/0,1144,0130882399,00.html

Freeze, R.A., Cherry, J.A.: Groundwater. Prentice-Hall, Englewood Cliffs,NJ (1979)

McCuen, R.H.: Hydrologic Analysis and Design. Prentice Hall, UpperSaddle River, New Jersey, 07458, 2nd edn. (1998),http://www.prenhall.com

McCuen, R.H.: Hydrologic Analysis and Design. Prentice Hall, UpperSaddle River, New Jersey, 07458, 3rd edn. (2004),http://www.prenhall.com

Sanders, L.L.: A Manual of Field Hydrogeology. Prentice Hall, UpperSaddle River, NJ (1998)

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