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Types of River Models
Theory base
Hydrologic
Hydraulic
(Channel & Floodplain)
Conservation
of Mass
{continuity}
predicts: Water
discharge rate
over time
Rational method
HEC-1
HEC-HMS
TR-20
TR-55
Conservation
of Mass
Conservation
of Momentum (energy)
predicts: Depth,
Velocity distributions
over time
WSP
HEC-2
HEC-RAS
HEC-4
SWMM
Load
Biological
Conservation
of Momentum
and Mass
for solvent and solutes
Various
predicts: Conc.& transport
Over time
predicts: habitat
quality or
Population size
Or composition
HEC-6
SWMM
AGNIPS
SWAT
HEC-RAS
BASINS
HSI
IFIM
RIVPAKS
{SEM}
{MLR}
Storm ( DRO) hydrographs
Storm ( DRO) hydrographs
Time of rise
Time to peak [from midpoint of precip event ]
Time base
Base flow separation
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) + K
C. 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
[ from 411 worksheet Flowsep.mcd]
Wild River, Me
the Rational Method
Storm ( DRO) hydrographs
the Rational Method
Qp = 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?
Unit Hydrographs
Obs. Hydrograph
DRO Hydrograph
DRO Hydrograph
Unit Hydrograph
Adjust Q to
give 1 unit DRO
by dividing Q values
by 1/DRO total as depth
Because of their assumed linearity...
Unit hydrographs (UH) of short duration
can 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 complex
precip events...
n
Qn = SPiU n-i+1
i
Hydrograph Convolution
n
Qn = SPiU n-i+1
i
Synthetic unit hydrographs
Issues:
slope
routing
storage
Methods:
Snyder
SCS
Epsey
Empirical relationships for key parameters
Synthetic unit hydrographs
Methods:
Snyder
SCS
Epsey
Empirical relationships for key parameters
Qp = Peak Q; tp = time to peak Q; Tr = rise time
D = precip duration; Tr + B = time base
Snyder’s Synthetic Unit Hydrograph method
Qpeak(cfs) = 640 Cp AREA(mi2)
tp
Tbase(days) = 3 + tp/8
tp(hrs)= Ct(L Lc )0.3
Cp= storage coeff. from .4 to .8
Ct= coeff. ususally 1.8-2.2 [0.4-8.0]
Lc=length along channel to watershed centroid
L= length of main stem to divide (ft)
SCS Method [ TR-20; TR-55]
Duration
T rise
2
Q peak
VOL
t lag
t lag
Area
.
LFcoef
T rise
Lfcoef = 484 or fitted [10- 500]
Q peak. T rise
.
Q peak. 1.67T
rise
2
2
.8
.7
length ft . ( abstraction 1)
.5
.
1900slope
%
abstraction
1000
10
curve number
SCS_runoff#
45
57
70
82
94
= 30 Units
SCS_soilclass
SCS_LANDUSE
1
SCS_runoff#
45
2
3
57
4
70
5
82
1
(42205)
2
(1100)
Forest land
Pastures,
3
(56501)
Cultivated
4
(6330)
Urban
94
= 30 Units
Hydraulic Geometry Relations for a cross-section {Station Geometry}
Q = D V W implies all are functions of Q
Typically, at any cross section, relation modeled as a power function:
V = a Qb
W = c Qd
D = e Qf
where a and b are constant coefficients
where c and d are constant coefficients
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 between Stations {Basin 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
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
Exceedence
5
10
25
50
75
90
95
Ground Water
R2
0.96
0.97
0.97
0.97
0.94
0.93
0.92
Runoff streams
R2
0.99
0.98
0.96
0.93
0.91
0.91
0.90
Landcover for Michigan
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Percentage Landcover Type
2.4
0.0
13.6
0.0
0.0005
3.5
19.0
61.4
Agriculture
Forest
Forested Wetland
Non-Forested Wetland
Barren
Range
Urban
Water
11.7
2.7
27.3
10.0
0.03
5.0
9.9
33.4
Presettlement (1830)
MIRIS (1978)
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Low Flow Yield is a measure
of baseflow conditions
standardized by catchment
area.
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Nearly 6 of 10 rivers in this
study (59.8%) have lower
baseflow yields now.
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However, many rivers have
increased baseflow yields.
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Red have become lower
Blue have become higher
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The Runoff Coefficient is a
measure of magnitude of the
difference between the high
flows and the low flows
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The majority of catchments had
increased runoff coefficients
(57.6%).
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Both increases and decreases
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Red have become higher
Blue have become lower or
not changed
Types of River Models
Theory base
Hydrologic
Hydraulic
(Channel & Floodplain)
Conservation
of Mass
{continuity}
predicts: Water
discharge rate
over time
Rational method
HEC-1
HEC-HMS
TR-20
TR-55
Conservation
of Mass
Conservation
of Momentum (energy)
predicts: Depth,
Velocity distributions
over time
WSP
HEC-2
HEC-RAS
HEC-4
SWMM
Load
Biological
Conservation
of Momentum
and Mass
for solvent and solutes
Various
predicts: Conc.& transport
Over time
predicts: habitat
quality or
Population size
Or composition
HEC-6
SWMM
AGNIPS
SWAT
HEC-RAS
BASINS
HSI
IFIM
RIVPAKS
{SEM}
{MLR}