Types of River Models

Hydrologic Hydraulic Load Biological (Channel & Floodplain)

Conservation of Mass{continuity}

predicts: Water discharge rateover time

Rational methodHEC-1HEC-HMSTR-20TR-55

Conservationof MassConservationof Momentum (energy)

predicts: Depth, Velocity distributions over time

WSP HEC-2HEC-RASHEC-4SWMM

Conservationof Momentumand Massfor solvent and solutes

predicts: Conc.& transportOver time

HEC-6SWMMAGNIPSSWATHEC-RASBASINS

HSIIFIMRIVPAKS{SEM}{MLR}

Various

predicts: habitat quality or Population sizeOr composition

The

ory

base

Storm ( DRO) hydrographs

Storm ( DRO) hydrographs

Time base

Time to peak [from midpoint of precip event ]Time of rise

HEWLETT's METHOD (1967) of flow separation

Hewlett's method provides a standardized graphical approach to flow separation based upon the flowing algorithm:

A. let diff=(Q(day)-Q(day-1))B. if diff>0 then let baseflow(day)=baseflow(day-1) + KC. if diff<=0 then let baseflow(day)=baseflow(day-1)D. if baseflow(day)>Q(day) then let baseflow(day)=Q(day)

K= c * catchment area (sq miles); c=.001-.00001 Wild River, Me

Base flow separation

[ from 411 worksheet Flowsep.mcd]

Storm ( DRO) hydrographs the Rational Method

the Rational MethodQp = C I A (Mulvaney 1851, Kuichling 1889)

Qp is peak discharge at time of concentration (tc)

I is rainful intensity at chosen frequency for duration equal to tc [in/hr]

A is catchment area in acres [ <1 sq mile]

tc time of concentration: time for rainfall at most distant region of catchment

to travel to the outlet

C is the runoff coefficient ~ (Runoff volume) / (Rainfall volume)

Rainfall IDF curves:

Assumes tc=duration; what determines tc?

DRO Hydrograph

Obs. Hydrograph

Unit Hydrographs

Adjust Q togive 1 unit DROby dividing Q valuesby 1/DRO total as depth

Unit Hydrograph

DRO Hydrograph

Because of their assumed linearity...Unit hydrographs (UH) of short durationcan be used to generate longer duration UH

S-curve Method

S-curve Method

Hydrograph Convolution

UH’s can also be used to estimate DRO hydrographs from complexprecip events...

Qn = PiU n-i+1

n

i

Hydrograph Convolution

Qn = PiU n-i+1

n

i

Synthetic unit hydrographs

Empirical relationships for key parameters

Issues:sloperoutingstorage

Methods:SnyderSCSEpsey

Synthetic unit hydrographs

Empirical relationships for key parameters

Methods:SnyderSCSEpsey

Qp = Peak Q; tp = time to peak Q; Tr = rise timeD = precip duration; Tr + B = time base

tp(hrs)= Ct(L Lc )0.3

Qpeak(cfs) = 640 Cp AREA(mi2) tp

Cp= storage coeff. from .4 to .8Ct= coeff. ususally 1.8-2.2 [0.4-8.0]

Tbase(days) = 3 + tp/8

Lc=length along channel to watershed centroid

L= length of main stem to divide (ft)

Snyder’s Synthetic Unit Hydrograph method

t lag

.length ft.8 ( )abstraction 1 .7

.1900slope %.5

T riseDuration

2t lag

Q peak.LFcoef

Area

T rise

VOL.Q peak T rise

2

..Q peak 1.67T rise

2

SCS Method [ TR-20; TR-55]

Lfcoef = 484 or fitted [10- 500]

abstraction1000

curve number10

SCS_runoff#

= 30 Units

45

57

70

82

94

SCS_LANDUSE

1 (42205) Forest land

2 (1100) Pastures,

3 (56501) Cultivated

4 (6330) Urban

SCS_soilclass

1

2

3

4

5

SCS_runoff#

= 30 Units

45

57

70

82

94

Q = D V W implies all are functions of Q

Typically, at any cross section, relation modeled as a power function: V = a Qb where a and b are constant coefficients W = c Qd where c and d are constant coefficients D = e Qf where e and f are constant coefficients

Since D V W = Q

a Qb * c Qd * e Qf = a*c*e *Q b+d+f = Q

and therefore the coeffs are constrained such that,

a*c*e = 1 AND b+d+f =1

Hydraulic Geometry Relations for a cross-section {Station Geometry}

Given that the water balance implies Qmean = x AREAy

where x and y are coefficients, continuity implies: Vmean = a AREAb where a and b are constant coefficients Wmean = c AREAd where c and d are constant coefficients Dmean = e AREAf where e and f are constant coefficients

similarly..a AREAb * c AREAd * e AREAf = a*c*e *AREA b+d+f = Q

and therefore the coeffs are constrained such that,

a*c*e = x AND b+d+f =y

Hydraulic Geometry Relations between Stations {Basin Geometry}

Catchment AREA

Predictive Modeling of Flow Duration Curves

Exceedence Flows (5% --> 95%) can be estimated by multiple regression using geology, land use and other landscape factors as predictive variables.

General form of the Synthetic Flow Duration Model is

Qex = a*Catchment_Areab1 + landscape_factor1b2*landscape_factor2b3 … landscape_factorN bN-1

Landscape factor variables are derived from GIS analysis of statewide digital map covers and include: mean annual precipitation, average catchment slope, % of various landcover types, % of certain surficial geology types.

Relative fits (R2 values) for Synthetic Flow Duration Models of streamflow in Michigan’s lower peninsula

Percent Ground Water Runoff streams Exceedence R2 R2

5 0.96 0.9910 0.97 0.9825 0.97 0.9650 0.97 0.9375 0.94 0.9190 0.93 0.9195 0.92 0.90

Presettlement ca.1830 MIRIS 1978

Landcover for Michigan

N

EW

S

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AgricultureForestForested WetlandNon-Forested WetlandBarrenRangeUrbanWater

0.0

61.419.0

3.5

0.0005

13.6

0.0

2.4

MIRIS (1978)

27.3

33.4

9.9

5.0

0.03

10.0

11.72.7

Presettlement (1830)

Percentage Landcover Type

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Low Flow Yield is a measure of baseflow conditions standardized by catchment area.

Nearly 6 of 10 rivers in this study (59.8%) have lower baseflow yields now.

However, many rivers have increased baseflow yields.

Red have become lower

Blue have become higher

The Runoff Coefficient is a measure of magnitude of the difference between the high flows and the low flows The majority of catchments had increased runoff coefficients (57.6%).

Both increases and decreases were observed.

Red have become higher

Blue have become lower or not changed

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Types of River Models

Hydrologic Hydraulic Load Biological (Channel & Floodplain)

Conservation of Mass{continuity}

predicts: Water discharge rateover time

Rational methodHEC-1HEC-HMSTR-20TR-55

Conservationof MassConservationof Momentum (energy)

predicts: Depth, Velocity distributions over time

WSP HEC-2HEC-RASHEC-4SWMM

Conservationof Momentumand Massfor solvent and solutes

predicts: Conc.& transportOver time

HEC-6SWMMAGNIPSSWATHEC-RASBASINS

HSIIFIMRIVPAKS{SEM}{MLR}

Various

predicts: habitat quality or Population sizeOr composition

The

ory

base