Summary number of cells / total cells CASE STUDY 6 Summary...
1
The following methodology was applied to 1) Artificial depressions and flat areas are removed from the DEM using PEM4PIT model with automatic parameter estimation (Grimaldi et al., 2007; Nardi et al., in press; Santini et al., in review); flow directions and contributing areas are characterized using the D8- LTD method (Orlandini et al., 2003) with dampening factor = 1; stream network is extracted using the automated drop analysis combined with the curvature based method (Tarboton et al., 1991; Tarboton and Ames, 2001). Slope is extracted according to maximum downhill criterion. 2) Determination of the Width Function is based on the estimation of hydrologic distances measured along the D8-LTD based steepest slope path for the river network and using the D- method (Tarboton, 1997; Bogaart & Troch, 2006) for the hillslopes. 3) Determination of basin Lag Time from observed data (Bocchiola et al., 2003): Lag time is assumed as the time difference between the net hydrograph and the net rainfall centroids (Chow et al., 1988); net hydrograph was obtained with the fixed base method while net rainfall was obtained with the SCS-CN method using a Curve Number that leads to the equivalency between net rainfall volume and direct runoff volume (USDA, 1986; Chow et al., 1988). 4) Rescaling of WFs are determined weighting the WF with the corresponding flow velocities in the following cases: a) - velocity that varies cell by cell: implementation of Maidment et al. formula (Maidment et al., 1996); V mean was iteratively incremented until the WF-rescaled mean (WFIUH centroid) was equal to previously determined basin Lag Time (Chow et al., 1988); a maximum and minimum limit of respectively 0.01 m/s and 3 m/s is set in order to avoid unrealistic estimation of flow velocities. b) - constant flow velocity for channels (2 m/s) and hillslopes (0.05 m/s) c) - constant flow velocity for channels (1 m/s) and hillslopes (0.05 m/s). d) - constant flow velocity for channels (2 m/s) and hillslopes (0.02 m/s). e) - constant flow velocity for channels (1 m/s) and hillslopes (0.02 m/s). Channel and hillslope velocities of b), c), d), e) were selected according to Botter & Rinaldo (2003). 5) Rainfall-runoff modelling using the WFIUH approach using the rescaled WF in the five approaches of a) to e) and the net rainfall. 6) Comparison results of 5) with actual net hydrographs. 1. Tuscia University, Viterbo, Italy, GEMINI Dep. ([email protected] ; [email protected] ; [email protected]) 2. H2CU, Honors Center of Italian Universities, Sapienza University of Rome , Rome, Italy 3. Tuscia University, Viterbo, Italy, DiSAFRi. ([email protected]) 4. Politecnico di Milano, Dep. of Hydraulics, Roadways, Environmental, and Surveying Engineering. ([email protected]) 1,2 1 3 4 1,2 AGU, Fall Conference 2008 Session H77 GIS Terrain Analysis for Hydrologic Applications Honors Center of Italian Universities www.h2cu.it/ The issue of the a priori estimation of runoff velocities, solved by automatically calibrating the spatially distributed flow velocity field to reproduce the estimated lag time information, provided new insights for the implementation of the WFIUH scheme for the hydrologic prediction in ungauged river basins. Results show a good agreement of simulated against observed hydrographs with particular regard to the shape, the peak and the timing (duration and time to peak) of the hydrologic response. 1) Bocchiola D., De Michele C., Pecora S., Rosso R. (2003), On the response time of Italian watersheds, L'ACQUA, 1, 45-55, In Italian with abstract in English. 2) Bogaart P. W., Troch P. A. (2006), Curvature distribution within hillslopes and catchments and its effect on the hydrological response, Hydrology and Earth System Sciences (10) 6, 925-936. 3) Botter G., and Rinaldo A. (2003), Scale effect on geomorphologic and kinematic dispersion, Water Resour. Res., 39, No 10, 1286, doi: 10.1029/2003WR002154. 4) Chow, V.T., Maidment D.R., Mays L.W. (1988), Applied Hydrology, McGraw-Hill International Editions. 5) Grimaldi S., Nardi F., Di Benedetto F., Istanbulluoglu E., Bras R.L. (2006) A physically-based method for removing pits in digital elevation models. Advances in Water Resources, 30(10) October 2007: 2151-2158 6) Orlandini S., Moretti G., Franchini M., Aldigheri B. and Testa B. (2003), Path-based methods for the determination of non-dispersive drainage directions in grid-based digital elevation models, Water Resources Research 39(6), 1144, DOI: 10.1029/2002WR001639. 7) Maidment D.R., Olivera F., Calver A., Eatherall A., Fraczek W. (1996), Unit Hydrograph derived from a spatially distributed velocity field, Hydrological Processes, Vol 10, 831-844. 8) Nardi F., Grimaldi S., Santini M., Petroselli, Ubertini L. (in press), Hydrogeomorphic properties of simulated drainage patterns using DEMs: the flat area issue, in press on Hydrological Sciences Journal, 2008. 9) Petroselli A., Santini M., Nardi F., Grimaldi S., Vivoni E. (2007), Investigating the spatial variability of hillslope flow velocities, AGU Fall Meeting 2007. 10) Santini M., Grimaldi S., Nardi F., Petroselli A., Rulli M.C. (in review), Pre-Processing algorithms and landslide modelling on remotely sensed DEMs, Geomorphology, in review. 11) Tarboton, D. G., R. L. Bras, and I. Rodriguez-Iturbe (1991), On the extraction of channel networks from digital elevation data, Hydrol. Processes, 5(1), 81- 100. 12) Tarboton D.G. (1997), A new method for the determination of flow directions and upslope areas in grid digital elevation models, Water Resour. Res., 33, 309- 319. 13) Tarboton D.G., and Ames D.P. (2001), Advances in the mapping of flow networks from digital elevation data, in World Water and Environmental Resources Congress, Orlando, Florida, May 20-24, ASCE. 14) USDA-SCS (1986), Urban hydrology for small watersheds. Technical release 55. Washington, DC. The Width Function (WF), the frequency of channel links/contributing area at the same hydrologic distance (i.e. the distance measured along the downhill flow path) to the outlet, is an important hydrogeomorphic property of river basins. The rescaled WF, obtained by weighting the flow distances with the corresponding flow velocity, provides the residency time distribution that is commonly used for representing the geomorphic IUH namely the WF Instantaneous Unit Hydrograph (distribution IUH) or WFIUH for the prediction of the hydrologic response in ungauged basins. The determination of the flow velocities is usually performed lumping the complex dynamics of the heterogenous hydrologic processes of river basins into two main categories: the channelized flow of river channels and the diffusive divergent flow of hillslopes. Nevertheless, the understanding, measuring and preliminary estimation of these variables represents an issue within the WFIUH framework. This work aims to investigate the possibility of implementing the fully spatial distribution of flow velocities throughout the basin, estimated as a function of local terrain properties (e.g. slope, land use etc) and constraining the flow velocity sample to represent the lag time of river basins. Aim is to investigate the impact of considering the heterogeneous properties of hillslope runoff dynamics on the hydrologic response represented with the WFIUH approach with particular regard to the time of concentration, time to peak, total duration, peak discharge and volume distribution (Petroselli et al., 2007). Hydrograph observations are compared to simulation results when using i) constant flow velocities for channel and hillslopes; ii) a spatially variable velocity field calibrated using the lag time information. GEMINI Department - Water Engineering Section DiSAFRi (Dept. of Forest Environment and Resources) Elevations and Blue Line v = cell velocity A = upstream drainage area S = cell steepest slope b, c = coefficients = 0.5 [S b A c ] = watershed average value of slope-area term V mean = average value of the velocity in all cells in the watershed ] [ c b c b mean A A S V v ⋅ ⋅ ⋅ = S Summary Elevations and Blue Line Summary Basin Ayasse - Dora Baltea Outlet Champorcher Code B25 Cellsize (m) 20 Precision integer Area (Km 2 ) 42 PEM4PIT Parameters (β, D, θ ) 0.01, 188, 0.5 Observed Lag Time (hours) 3.60 Summary WF max WF peak time WF centroid Max Discharge Max Discharge (hours) (hours) (hours) (m 3 /s) Observed Case 'a': (m 3 /s) Maidment et al. Formula: Vmean: 0.09 m/s 11.92 2.58 3.60 48.75 42.84 Case 'b': channel velocity: 2 m/s, hillslope velocity: 0.05 m/s 9.25 1.66 2.50 54.08 Case 'c': channel velocity: 1 m/s, hillslope velocity: 0.05 m/s 10.50 3.16 3.58 49.86 Case 'd': channel velocity: 2 m/s, hillslope velocity: 0.02 m/s 21.33 1.75 4.92 36.07 Case 'e': channel velocity: 1 m/s, hillslope velocity: 0.02 m/s 22.50 3.75 5.83 34.85 0 0.1 0.2 0.3 0 10 20 30 Time (hours) number of cells / total cells Rescaled WF - case 'a' Rescaled WF - case 'b' Rescaled WF - case 'c' Rescaled WF - case 'd' Rescaled WF - case 'e' Width Function (smoothing window: 1 hour) Summary Summary WF max WF peak time WF centroid Max Discharge Max Discharge (hours) (hours) (hours) (m 3 /s) Observed Case 'a': (m 3 /s) Maidment et al. Formula: Vmean: 0.19 m/s 7.08 3.58 2.81 327.52 360.61 Case 'b': channel velocity: 2 m/s, hillslope velocity: 0.05 m/s 14.33 3.75 4.92 298.63 Case 'c': channel velocity: 1 m/s, hillslope velocity: 0.05 m/s 17.83 7.00 7.17 290.19 Case 'd': channel velocity: 2 m/s, hillslope velocity: 0.02 m/s 31.33 3.75 9.08 256.35 Case 'e': channel velocity: 1 m/s, hillslope velocity: 0.02 m/s 34.00 7.00 11.25 251.42 Basin Mastallone Outlet Ponte Folle Code B15 Cellsize (m) 20 Precision integer Area (Km 2 ) 149 PEM4PIT Parameters (β, D, θ ) 0.01, 160, 0.5 Observed Lag Time (hours) 2.81 CASE STUDY 1 0 0.1 0.2 0.3 0.4 0 10 20 30 40 Time (hours) number of cells / total cells Rescaled WF - case 'a' Rescaled WF - case 'b' Rescaled WF - case 'c' Rescaled WF - case 'd' Rescaled WF - case 'e' Width Function (smoothing window: 1 hour) Basin Lys Outlet Gressoney St. Jean Code B33 Cellsize (m) 20 Precision integer Area (Km 2 ) 92 PEM4PIT Parameters (β, D, θ ) 0.01, 176, 0.5 Observed Lag Time (hours) 3.96 WF max WF peak time WF centroid Max Discharge Max Discharge (hours) (hours) (hours) (m 3 /s) Observed Case 'a': (m 3 /s) Maidment et al. Formula: Vmean: 0.11 m/s 14.16 3.33 3.96 36.14 37.01 Case 'b': channel velocity: 2 m/s, hillslope velocity: 0.05 m/s 17.58 2.66 3.75 35.72 Case 'c': channel velocity: 1 m/s, hillslope velocity: 0.05 m/s 19.91 4.50 5.08 35.17 Case 'd': channel velocity: 2 m/s, hillslope velocity: 0.02 m/s 40.58 4.00 7.16 31.29 Case 'e': channel velocity: 1 m/s, hillslope velocity: 0.02 m/s 42.83 6.75 8.58 30.59 0 0.1 0.2 0.3 0 10 20 30 40 50 Time (hours) number of cells / total cells Rescaled WF - case 'a' Rescaled WF - case 'b' Rescaled WF - case 'c' Rescaled WF - case 'd' Rescaled WF - case 'e' Width Function (smoothing window: 1 hour) Basin Isorno Outlet Pontetto Code A03 Cellsize (m) 20 Precision integer Area (Km 2 ) 71 PEM4PIT Parameters (β, D, θ ) 0.01, 165, 0.5 Observed Lag Time (hours) 3.3 Elevations and Blue Line 0 0.05 0.1 0.15 0 10 20 30 40 Time (hours) number of cells / total cells Rescaled WF - case 'a' Rescaled WF - case 'b' Rescaled WF - case 'c' Rescaled WF - case 'd' Rescaled WF - case 'e' Width Function (smoothing window: 0.5 hour) WF max WF peak time WF centroid Max Discharge Max Discharge (hours) (hours) (hours) (m 3 /s) Observed Case 'a': (m 3 /s) Maidment et al. Formula: Vmean: 0.14 m/s 8.33 3.58 3.30 150.80 149.29 Case 'b': channel velocity: 2 m/s, hillslope velocity: 0.05 m/s 13.25 3.00 3.83 142.64 Case 'c': channel velocity: 1 m/s, hillslope velocity: 0.05 m/s 14.75 5.50 5.75 138.12 Case 'd': channel velocity: 2 m/s, hillslope velocity: 0.02 m/s 31.00 3.67 7.00 117.24 Case 'e': channel velocity: 1 m/s, hillslope velocity: 0.02 m/s 32.41 6.42 8.75 116.01 Elevations and Blue Line Basin Bisenzio Outlet Gamberame Code A04 Cellsize (m) 20 Precision integer Area (Km 2 ) 150 PEM4PIT Parameters (β, D, θ ) 0.01, 186, 0.5 Observed Lag Time (hours) 7.08 WF max WF peak time WF centroid Max Discharge Max Discharge (hours) (hours) (hours) (m 3 /s) Observed Case 'a': (m 3 /s) Maidment et al. Formula: Vmean: 0.07 m/s 15.83 6.83 7.08 83.92 61.66 Case 'b': channel velocity: 2 m/s, hillslope velocity: 0.05 m/s 11.91 3.91 4.25 89.16 Case 'c': channel velocity: 1 m/s, hillslope velocity: 0.05 m/s 15.33 7.58 7.00 83.39 Case 'd': channel velocity: 2 m/s, hillslope velocity: 0.02 m/s 24.66 3.91 6.50 69.89 Case 'e': channel velocity: 1 m/s, hillslope velocity: 0.02 m/s 28.08 7.83 9.16 64.11 0 0.1 0.2 0 10 20 30 Time (hours) number of cells / total cells Rescaled WF - case 'a' Rescaled WF - case 'b' Rescaled WF - case 'c' Rescaled WF - case 'd' Rescaled WF - case 'e' Width Function (smoothing window: 1 hour) Elevations and Blue Line Basin Chisone Outlet Soucheres Code A06 Cellsize (m) 20 Precision integer Area (Km 2 ) 86 PEM4PIT Parameters (β, D, θ ) 0.01, 182, 0.5 Observed Lag Time (hours) 3.12 Summary WF max WF peak time WF centroid Max Discharge Max Discharge (hours) (hours) (hours) (m 3 /s) Observed Case 'a': (m 3 /s) Maidment et al. Formula: Vmean: 0.15 m/s 7.16 2.66 3.12 71.39 63.44 Case 'b': channel velocity: 2 m/s, hillslope velocity: 0.05 m/s 15.33 2.66 4.58 48.23 Case 'c': channel velocity: 1 m/s, hillslope velocity: 0.05 m/s 16.16 4.66 5.75 45.46 Case 'd': channel velocity: 2 m/s, hillslope velocity: 0.02 m/s 37.00 4.50 9.50 35.02 Case 'e': channel velocity: 1 m/s, hillslope velocity: 0.02 m/s 37.91 5.75 10.66 34.39 0 0.05 0.1 0 10 20 30 40 Time (hours) number of cells / total cells Rescaled WF - case 'a' Rescaled WF - case 'b' Rescaled WF - case 'c' Rescaled WF - case 'd' Rescaled WF - case 'e' Width Function (smoothing window: 0.25 hour) Elevations and Blue Line 0 50 100 150 200 0 40 80 120 Time (hours) Discharge (m 3 /s) 0 10 20 30 Rainfall (mm) Actual Net Discharge Net Discharge case 'a' Net Discharge case 'b' Net Discharge case 'c' Net Discharge case 'd' Net Discharge case 'e' Net Ranfall Hydrographs comparison (time interval: 0.5 hour) 0 40 80 120 0 40 80 120 Time (hours) Discharge (m 3 /s) 0 10 20 Rainfall (mm) Actual Net Discharge Net Discharge case 'a' Net Discharge case 'b' Net Discharge case 'c' Net Discharge case 'd' Net Discharge case 'e' Net Rainfall Hydrographs comparison (time interval: 1 hour) 0 20 40 60 70 90 110 130 Time (hours) Discharge (m 3 /s) 0 20 40 60 Rainfall (mm) Actual Net Discharge Net Discharge case 'a' Net Discharge case 'b' Net Discharge case 'c' Net Discharge case 'd' Net Discharge case 'e' Net Rainfall Hydrographs comparison (time interval: 1 hour) 0 10 20 30 40 70 90 110 130 150 Time (hours) Discharge (m 3 /s) 0 5 10 15 20 Rainfall (mm) Actual Net Discharge Net Discharge case 'a' Net Discharge case 'b' Net Discharge case 'c' Net Discharge case 'd' Net Discharge case 'e' Net Rainfall Hydrographs comparison (time interval 1 hour) 0 20 40 60 80 50 100 150 200 Time (hours) Discharge (m 3 /s) 0 5 10 15 20 Rainfall (mm) Actual Net Discharge Net Discharge case 'a' Net Discharge case 'b' Net Discharge case 'c' Net Discharge case 'd' Net Discharge case 'e' Net Rainfall Hydrographs comparison (time interval: 0.25 hour) Dep. of Hydraulics, Roadways, Environmental, and Surveying Engineering 0 100 200 300 400 500 0 50 100 150 Time (hours) Discharge (m 3 /s) 0 20 40 60 Rainfall (mm) Actual Net Discharge Net Discharge case 'a' Net Discharge case 'b' Net Discharge case 'c' Net Discharge case 'd' Net Discharge case 'e' Net Rainfall Hydrographs comparison (time interval: 1 hour) Flow velocity with Maidment et al. (1996) formula Flow velocity with Maidment et al. (1996) formula CASE STUDY 4 CASE STUDY 5 CASE STUDY 2 CASE STUDY 3 CASE STUDY 6 Flow velocity with Maidment et al. (1996) formula Flow velocity with Maidment et al. (1996) formula Flow velocity with Maidment et al. (1996) formula Flow velocity with Maidment et al. (1996) formula
Transcript of Summary number of cells / total cells CASE STUDY 6 Summary...
The
follo
win
g m
etho
dolo
gy w
as a
pplie
d to
1)
Art
ifici
al d
epre
ssio
ns a
nd f
lat
area
s ar
e re
mov
ed f
rom
the
DEM
usi
ng P
EM4P
IT m
odel
with
aut
omat
ic p
aram
eter
est
imat
ion
(Gri
mal
di e
t al.,
200
7; N
ardi
et a
l., in
pre
ss; S
antin
i et a
l., in
revi
ew);
flow
dir
ectio
ns a
nd c
ontr
ibut
ing
area
s ar
e ch
arac
teri
zed
usin
g th
e D
8-LT
D m
etho
d (O
rlan
dini
et a
l., 2
003)
with
dam
peni
ng fa
ctor
= 1
; str
eam
net
wor
k is
ext
ract
ed u
sing
the
auto
mat
ed d
rop
anal
ysis
com
bine
d w
ith th
e cu
rvat
ure
base
d m
etho
d (T
arbo
ton
et a
l., 1
991;
Tar
boto
n an
d A
mes
, 200
1). S
lope
is e
xtra
cted
acc
ordi
ng to
max
imum
dow
nhill
cr
iteri
on.
2) D
eter
min
atio
n of
the
Wid
th F
unct
ion
is b
ased
on
the
estim
atio
n of
hyd
rolo
gic
dist
ance
s m
easu
red
alon
g th
e D
8-LT
D b
ased
ste
epes
t sl
ope
path
for t
he ri
ver n
etw
ork
and
usin
g th
e D
- m
etho
d (T
arbo
ton,
199
7; B
ogaa
rt &
Tro
ch, 2
006)
for t
he h
illsl
opes
.3)
Det
erm
inat
ion
of b
asin
Lag
Tim
e fr
om o
bser
ved
data
(Boc
chio
la e
t al.,
200
3): L
ag ti
me
is a
ssum
ed a
s th
e tim
e di
ffere
nce
betw
een
the
net
hydr
ogra
ph a
nd t
he n
et r
ainf
all c
entr
oids
(C
how
et
al.,
1988
); ne
t hy
drog
raph
was
obt
aine
d w
ith t
he f
ixed
bas
e m
etho
d w
hile
net
ra
infa
ll w
as o
btai
ned
with
the
SC
S-C
N m
etho
d us
ing
a C
urve
Num
ber
that
lead
s to
the
equ
ival
ency
bet
wee
n ne
t ra
infa
ll vo
lum
e an
d di
rect
runo
ff vo
lum
e (U
SDA
, 198
6; C
how
et a
l., 1
988)
.4)
Res
calin
g of
WFs
are
det
erm
ined
wei
ghtin
g th
e W
F w
ith th
e co
rres
pond
ing
flow
vel
ociti
es in
the
follo
win
g ca
ses:
a) -
velo
city
that
var
ies c
ell b
y ce
ll: im
plem
enta
tion
of M
aidm
ent e
t al.
form
ula
(Mai
dmen
t et a
l., 1
996)
; Vm
ean w
as it
erat
ivel
y in
crem
ente
d un
til th
e W
F-re
scal
ed m
ean
(WFI
UH
cen
troi
d) w
as e
qual
to p
revi
ousl
y de
term
ined
bas
in L
ag T
ime
(Cho
w e
t al.,
19
88);
a m
axim
um a
nd m
inim
um li
mit
of re
spec
tivel
y 0.
01 m
/s a
nd 3
m/s
is s
et in
ord
er to
avo
id u
nrea
listic
est
imat
ion
of fl
ow
velo
citie
s.b)
-co
nsta
nt fl
ow v
eloc
ity fo
r cha
nnel
s (2
m/s
) and
hill
slop
es (0
.05
m/s
)c)
-co
nsta
nt fl
ow v
eloc
ity fo
r cha
nnel
s (1
m/s
) and
hill
slop
es (0
.05
m/s
).d)
-co
nsta
nt fl
ow v
eloc
ity fo
r cha
nnel
s (2
m/s
) and
hill
slop
es (0
.02
m/s
).e)
-co
nsta
nt fl
ow v
eloc
ity fo
r cha
nnel
s (1
m/s
) and
hill
slop
es (0
.02
m/s
).C
hann
el a
nd h
illsl
ope
velo
citie
s of
b),
c), d
), e)
wer
e se
lect
ed a
ccor
ding
to B
otte
r & R
inal
do (2
003)
.5)
Rai
nfal
l-run
off m
odel
ling
usin
g th
e W
FIU
H a
ppro
ach
usin
g th
e re
scal
ed W
F in
the
five
appr
oach
es o
f a) t
o e)
and
the
net r
ainf
all.
6) C
ompa
riso
n re
sults
of 5
) with
act
ual n
et h
ydro
grap
hs.
1. T
usci
a U
nive
rsity
, Vite
rbo,
Ital
y, G
EMIN
I Dep
. (fe
rnan
do.n
ardi
@un
itus.
it ; p
etro
@un
itus.
it ; s
alva
tore
.gri
mal
di@
unitu
s.it)
2. H
2CU
, Hon
ors
Cen
ter o
f Ita
lian
Uni
vers
ities
, Sap
ienz
a U
nive
rsity
of R
ome
, Rom
e, It
aly
3. T
usci
a U
nive
rsity
, Vite
rbo,
Ital
y, D
iSA
FRi.
(m
onia
.san
tini@
unitu
s.it)
4. P
olite
cnic
o di
Mila
no, D
ep. o
f Hyd
raul
ics,
Roa
dway
s, E
nvir
onm
enta
l, an
d Su
rvey
ing
Engi
neer
ing.
(dan
iele
.boc
chio
la@
polim
i.it)
1,2
13
41,
2
AG
U, F
all C
onfe
renc
e 20
08
Sess
ion
H77
G
IS T
erra
in A
naly
sis
for
Hyd
rolo
gic
App
licat
ions
H
onor
s C
ente
r of I
talia
n U
nive
rsiti
esw
ww
.h2c
u.it/
The
issu
e of
the
a p
riori
estim
atio
n of
run
off
velo
citie
s, s
olve
d by
aut
omat
ical
ly
calib
ratin
g th
e sp
atia
lly d
istr
ibut
ed fl
ow v
eloc
ity fi
eld
to r
epro
duce
the
estim
ated
lag
time
info
rmat
ion,
pro
vide
d ne
w
insi
ghts
for t
he im
plem
enta
tion
of th
e W
FIU
H s
chem
e fo
r the
hyd
rolo
gic
pred
ictio
n in
ung
auge
d ri
ver b
asin
s.
Resu
lts s
how
a g
ood
agre
emen
t of s
imul
ated
aga
inst
obs
erve
d hy
drog
raph
s w
ith p
artic
ular
reg
ard
to th
e sh
ape,
the
peak
and
the
timin
g (d
urat
ion
and
time
to p
eak)
of t
he h
ydro
logi
c re
spon
se.
1) B
occh
iola
D.,
De
Mic
hele
C.,
Peco
ra S
., Ro
sso
R. (2
003)
, On
the
resp
onse
tim
e of
Ital
ian
wat
ersh
eds,
L'A
CQ
UA
, 1, 4
5-55
, In
Italia
n w
ith a
bstr
act i
n En
glis
h.2)
Bog
aart
P. W
., Tr
och
P. A
. (20
06),
Cur
vatu
re d
istr
ibut
ion
with
in h
illsl
opes
and
cat
chm
ents
and
its
effe
ct o
n th
e hy
drol
ogic
al re
spon
se, H
ydro
logy
and
Ear
th S
yste
m S
cien
ces
(10)
6, 9
25-9
36.
3) B
otte
r G.,
and
Rina
ldo
A. (
2003
), Sc
ale
effe
ct o
n ge
omor
phol
ogic
and
kin
emat
ic d
ispe
rsio
n, W
ater
Res
our.
Res.
, 39,
No
10, 1
286,
doi
: 10.
1029
/200
3WR0
0215
4.4)
Cho
w, V
.T.,
Mai
dmen
t D.R
., M
ays
L.W
. (19
88),
App
lied
Hyd
rolo
gy, M
cGra
w-H
ill In
tern
atio
nal E
ditio
ns.
5) G
rim
aldi
S.,
Nar
di F
., D
i Ben
edet
to F
., Is
tanb
ullu
oglu
E.,
Bras
R.L
. (20
06) A
phy
sica
lly-b
ased
met
hod
for r
emov
ing
pits
in d
igita
l ele
vatio
n m
odel
s. A
dvan
ces
in W
ater
Res
ourc
es, 3
0(10
) Oct
ober
200
7: 2
151-
2158
6) O
rlan
dini
S.,
Mor
etti
G.,
Fran
chin
i M.,
Ald
ighe
ri B
. and
Tes
ta B
. (20
03),
Path
-bas
ed m
etho
ds fo
r the
det
erm
inat
ion
of n
on-d
ispe
rsiv
e dr
aina
ge d
irec
tions
in g
rid-
base
d di
gita
l ele
vatio
n m
odel
s, W
ater
Res
ourc
es R
esea
rch
39(6
), 11
44, D
OI:
10.1
029/
2002
WR0
0163
9.7)
Mai
dmen
t D.R
., O
liver
a F.
, Cal
ver A
., Ea
ther
all A
., Fr
acze
k W
. (19
96),
Uni
t Hyd
rogr
aph
deri
ved
from
a sp
atia
lly d
istr
ibut
ed v
eloc
ity fi
eld,
Hyd
rolo
gica
l Pro
cess
es, V
ol 1
0, 8
31-8
44.
8) N
ardi
F.,
Gri
mal
di S
., Sa
ntin
i M.,
Petr
osel
li, U
bert
ini L
. (in
pre
ss),
Hyd
roge
omor
phic
pro
pert
ies
of s
imul
ated
dra
inag
e pa
ttern
s us
ing
DEM
s: th
e fla
t are
a is
sue,
in p
ress
on
Hyd
rolo
gica
l Sci
ence
s Jo
urna
l, 20
08.
9) P
etro
selli
A.,
Sant
ini M
., N
ardi
F.,
Gri
mal
di S
., V
ivon
i E. (
2007
), In
vest
igat
ing
the
spat
ial v
aria
bilit
y of
hill
slop
e flo
w v
eloc
ities
, AG
U F
all M
eetin
g 20
07.
10) S
antin
i M.,
Gri
mal
di S
., N
ardi
F.,
Petr
osel
li A
., Ru
lli M
.C. (
in re
view
), Pr
e-Pr
oces
sing
alg
orith
ms
and
land
slid
e m
odel
ling
on re
mot
ely
sens
ed D
EMs,
Geo
mor
phol
ogy,
in re
view
.11
) Tar
boto
n, D
. G.,
R. L
. Bra
s, a
nd I.
Rod
rigu
ez-It
urbe
(199
1), O
n th
e ex
trac
tion
of c
hann
el n
etw
orks
from
dig
ital e
leva
tion
data
, Hyd
rol.
Proc
esse
s, 5
(1),
81-1
00.
12) T
arbo
ton
D.G
. (19
97),
A n
ew m
etho
d fo
r the
det
erm
inat
ion
of fl
ow d
irec
tions
and
ups
lope
are
as in
gri
d di
gita
l ele
vatio
n m
odel
s, W
ater
Res
our.
Res.
, 33,
309
-319
.13
) Tar
boto
n D
.G.,
and
Am
es D
.P. (
2001
), A
dvan
ces
in th
e m
appi
ng o
f flo
w n
etw
orks
from
dig
ital e
leva
tion
data
, in
Wor
ld W
ater
and
Env
iron
men
tal R
esou
rces
Con
gres
s, O
rlan
do, F
lori
da, M
ay 2
0-24
, ASC
E.14
) USD
A-S
CS
(198
6), U
rban
hyd
rolo
gy fo
r sm
all w
ater
shed
s. T
echn
ical
rele
ase
55. W
ashi
ngto
n, D
C.
The
Wid
th F
unct
ion
(WF)
, the
freq
uenc
y of
cha
nnel
link
s/co
ntri
butin
g ar
ea a
t the
sam
e hy
drol
ogic
dis
tanc
e (i.
e. t
he d
ista
nce
mea
sure
d al
ong
the
dow
nhill
flo
w p
ath)
to
the
outle
t, is
an
impo
rtan
t hy
drog
eom
orph
ic
prop
erty
of
rive
r ba
sins
. The
res
cale
d W
F, o
btai
ned
by w
eigh
ting
the
flow
dis
tanc
es w
ith t
he c
orre
spon
ding
flo
w v
eloc
ity, p
rovi
des
the
resi
denc
y tim
e di
stri
butio
n th
at is
com
mon
ly u
sed
for
repr
esen
ting
the
geom
orph
ic
IUH
nam
ely
the
WF
Inst
anta
neou
s U
nit
Hyd
rogr
aph
(dis
trib
utio
n IU
H)
or W
FIU
H f
or t
he p
redi
ctio
n of
the
hy
drol
ogic
resp
onse
in u
ngau
ged
basi
ns.
The
dete
rmin
atio
n of
the
flo
w v
eloc
ities
is
usua
lly p
erfo
rmed
lum
ping
the
com
plex
dyn
amic
s of
the
he
tero
geno
us h
ydro
logi
c pr
oces
ses
of r
iver
bas
ins
into
tw
o m
ain
cate
gori
es:
the
chan
neliz
ed f
low
of
rive
r ch
anne
ls a
nd t
he d
iffus
ive
dive
rgen
t flo
w o
f hi
llslo
pes.
Nev
erth
eles
s, t
he u
nder
stan
ding
, m
easu
ring
and
pr
elim
inar
y es
timat
ion
of th
ese
vari
able
s re
pres
ents
an
issu
e w
ithin
the
WFI
UH
fram
ewor
k.
This
wor
k ai
ms
to in
vest
igat
e th
e po
ssib
ility
of i
mpl
emen
ting
the
fully
spa
tial d
istr
ibut
ion
of fl
ow v
eloc
ities
th
roug
hout
the
bas
in,
estim
ated
as
a fu
nctio
n of
loc
al t
erra
in p
rope
rtie
s (e
.g.
slop
e, l
and
use
etc)
and
co
nstr
aini
ng th
e flo
w v
eloc
ity s
ampl
e to
repr
esen
t the
lag
time
of ri
ver b
asin
s.
Aim
is to
inve
stig
ate
the
impa
ct o
f con
side
ring
the
hete
roge
neou
s pr
oper
ties
of h
illsl
ope
runo
ff dy
nam
ics
on t
he h
ydro
logi
c re
spon
se r
epre
sent
ed w
ith t
he W
FIU
H a
ppro
ach
with
par
ticul
ar r
egar
d to
the
tim
e of
co
ncen
trat
ion,
tim
e to
pea
k, to
tal d
urat
ion,
pea
k di
scha
rge
and
volu
me
dist
ribu
tion
(Pet
rose
lli e
t al.,
200
7).
Hyd
rogr
aph
obse
rvat
ions
are
com
pare
d to
sim
ulat
ion
resu
lts w
hen
usin
g i)
cons
tant
flo
w v
eloc
ities
for
ch
anne
l and
hill
slop
es; i
i) a
spat
ially
var
iabl
e ve
loci
ty fi
eld
calib
rate
d us
ing
the
lag
time
info
rmat
ion.
GEM
INI D
epar
tmen
t -W
ater
Eng
inee
ring
Sec
tion
DiS
AFR
i (D
ept.
of F
ores
t Env
iron
men
t and
Res
ourc
es)
Elev
atio
ns a
nd B
lue
Line
v =
cell
velo
city
A =
ups
trea
m d
rain
age
area
S =
cell
stee
pest
slo
pe
b, c
= c
oeffi
cien
ts =
0.5
[Sb A
c ] =
wat
ersh
ed a
vera
ge v
alue
of s
lope
-are
a te
rmV
mea
n =
aver
age
valu
e of
the
velo
city
in a
ll ce
lls in
the
wat
ersh
ed
][
cb
cb
mea
n
AA
SV
v⋅
⋅⋅
=S
Sum
mar
y
Elev
atio
ns a
nd B
lue
Line
Sum
mar
y
Basi
nA
yass
e - D
ora
Balte
aO
utle
tC
ham
porc
her
Cod
eB2
5C
ells
ize
(m)
20Pr
ecis
ion
inte
ger
Are
a (K
m2 )
42PE
M4P
IT P
aram
eter
s (β,
D, θ
)0.
01, 1
88, 0
.5O
bser
ved
Lag
Tim
e (h
ours
)3.
60
Sum
mar
yW
F m
axW
F pe
ak ti
me
WF
cent
roid
Max
Dis
char
geM
ax D
isch
arge
(hou
rs)
(hou
rs)
(hou
rs)
(m3 /s
)O
bser
ved
Cas
e 'a
':(m
3 /s)
Mai
dmen
t et a
l. Fo
rmul
a: V
mea
n: 0
.09
m/s
11.9
22.
583.
6048
.75
42.8
4C
ase
'b':
chan
nel v
eloc
ity: 2
m/s
, hill
slop
e ve
loci
ty: 0
.05
m/s
9.25
1.66
2.50
54.0
8C
ase
'c':
chan
nel v
eloc
ity: 1
m/s
, hill
slop
e ve
loci
ty: 0
.05
m/s
10.5
03.
163.
5849
.86
Cas
e 'd
':ch
anne
l vel
ocity
: 2 m
/s, h
illsl
ope
velo
city
: 0.0
2 m
/s21
.33
1.75
4.92
36.0
7C
ase
'e':
chan
nel v
eloc
ity: 1
m/s
, hill
slop
e ve
loci
ty: 0
.02
m/s
22.5
03.
755.
8334
.85
0
0.1
0.2
0.3
010
2030
Tim
e (h
ours
)
number of cells / total cells
Res
cale
d W
F - c
ase
'a'
Res
cale
d W
F - c
ase
'b'
Res
cale
d W
F - c
ase
'c'R
esca
led
WF
- cas
e 'd
'R
esca
led
WF
- cas
e 'e
'
Wid
th F
unct
ion
(sm
ooth
ing
win
dow
: 1 h
our)
Sum
mar
y
Sum
mar
yW
F m
axW
F pe
ak ti
me
WF
cent
roid
Max
Dis
char
geM
ax D
isch
arge
(hou
rs)
(hou
rs)
(hou
rs)
(m3 /s
)O
bser
ved
Cas
e 'a
':(m
3 /s)
Mai
dmen
t et a
l. Fo
rmul
a: V
mea
n: 0
.19
m/s
7.08
3.58
2.81
327.
5236
0.61
Cas
e 'b
':ch
anne
l vel
ocity
: 2 m
/s, h
illsl
ope
velo
city
: 0.0
5 m
/s14
.33
3.75
4.92
298.
63C
ase
'c':
chan
nel v
eloc
ity: 1
m/s
, hill
slop
e ve
loci
ty: 0
.05
m/s
17.8
37.
007.
1729
0.19
Cas
e 'd
':ch
anne
l vel
ocity
: 2 m
/s, h
illsl
ope
velo
city
: 0.0
2 m
/s31
.33
3.75
9.08
256.
35C
ase
'e':
chan
nel v
eloc
ity: 1
m/s
, hill
slop
e ve
loci
ty: 0
.02
m/s
34.0
07.
0011
.25
251.
42
Basi
nM
asta
llone
Out
let
Pont
e Fo
lleC
ode
B15
Cel
lsiz
e (m
)20
Prec
isio
nin
tege
rA
rea
(Km
2 )14
9PE
M4P
IT P
aram
eter
s (β
, D, θ
)0.
01, 1
60, 0
.5O
bser
ved
Lag
Tim
e (h
ours
)2.
81
CA
SE
STU
DY
1
0
0.1
0.2
0.3
0.4
010
2030
40T
ime
(hou
rs)
number of cells / total cells
Res
cale
d W
F - c
ase
'a'
Res
cale
d W
F - c
ase
'b'
Res
cale
d W
F - c
ase
'c'R
esca
led
WF
- cas
e 'd
'R
esca
led
WF
- cas
e 'e
'
Wid
th F
unct
ion
(sm
ooth
ing
win
dow
: 1 h
our)
Basi
nLy
sO
utle
tG
ress
oney
St.
Jean
Cod
eB3
3C
ells
ize
(m)
20Pr
ecis
ion
inte
ger
Are
a (K
m2 )
92PE
M4P
IT P
aram
eter
s (β
, D, θ
)0.
01, 1
76, 0
.5O
bser
ved
Lag
Tim
e (h
ours
)3.
96
WF
max
WF
peak
tim
eW
F ce
ntro
idM
ax D
isch
arge
Max
Dis
char
ge(h
ours
)(h
ours
)(h
ours
)(m
3 /s)
Obs
erve
dC
ase
'a':
(m3 /s
)M
aidm
ent e
t al.
Form
ula:
Vm
ean:
0.1
1 m
/s14
.16
3.33
3.96
36.1
437
.01
Cas
e 'b
':ch
anne
l vel
ocity
: 2 m
/s, h
illsl
ope
velo
city
: 0.0
5 m
/s17
.58
2.66
3.75
35.7
2C
ase
'c':
chan
nel v
eloc
ity: 1
m/s
, hill
slop
e ve
loci
ty: 0
.05
m/s
19.9
14.
505.
0835
.17
Cas
e 'd
':ch
anne
l vel
ocity
: 2 m
/s, h
illsl
ope
velo
city
: 0.0
2 m
/s40
.58
4.00
7.16
31.2
9C
ase
'e':
chan
nel v
eloc
ity: 1
m/s
, hill
slop
e ve
loci
ty: 0
.02
m/s
42.8
36.
758.
5830
.59
0
0.1
0.2
0.3
010
2030
4050
Tim
e (h
ours
)
number of cells / total cells
Res
cale
d W
F - c
ase
'a'
Res
cale
d W
F - c
ase
'b'
Res
cale
d W
F - c
ase
'c'R
esca
led
WF
- cas
e 'd
'R
esca
led
WF
- cas
e 'e
'
Wid
th F
unct
ion
(sm
ooth
ing
win
dow
: 1 h
our)
Basi
nIs
orno
Out
let
Pont
etto
Cod
eA
03C
ells
ize
(m)
20Pr
ecis
ion
inte
ger
Are
a (K
m2 )
71PE
M4P
IT P
aram
eter
s (β
, D, θ
)0.
01, 1
65, 0
.5O
bser
ved
Lag
Tim
e (h
ours
)3.
3
Elev
atio
ns a
nd B
lue
Line
0
0.050.1
0.15
010
2030
40T
ime
(hou
rs)
number of cells / total cells
Res
cale
d W
F - c
ase
'a'
Res
cale
d W
F - c
ase
'b'
Res
cale
d W
F - c
ase
'c'R
esca
led
WF
- cas
e 'd
'R
esca
led
WF
- cas
e 'e
'
Wid
th F
unct
ion
(sm
ooth
ing
win
dow
: 0.5
hou
r)
WF
max
WF
peak
tim
eW
F ce
ntro
idM
ax D
isch
arge
Max
Dis
char
ge(h
ours
)(h
ours
)(h
ours
)(m
3 /s)
Obs
erve
dC
ase
'a':
(m3 /s
)M
aidm
ent e
t al.
Form
ula:
Vm
ean:
0.1
4 m
/s8.
333.
583.
3015
0.80
149.
29C
ase
'b':
chan
nel v
eloc
ity: 2
m/s
, hill
slop
e ve
loci
ty: 0
.05
m/s
13.2
53.
003.
8314
2.64
Cas
e 'c'
:ch
anne
l vel
ocity
: 1 m
/s, h
illsl
ope
velo
city
: 0.0
5 m
/s14
.75
5.50
5.75
138.
12C
ase
'd':
chan
nel v
eloc
ity: 2
m/s
, hill
slop
e ve
loci
ty: 0
.02
m/s
31.0
03.
677.
0011
7.24
Cas
e 'e
':ch
anne
l vel
ocity
: 1 m
/s, h
illsl
ope
velo
city
: 0.0
2 m
/s32
.41
6.42
8.75
116.
01
Elev
atio
ns a
nd B
lue
Line
Basi
nBi
senz
ioO
utle
tG
ambe
ram
eC
ode
A04
Cel
lsiz
e (m
)20
Prec
isio
nin
tege
rA
rea
(Km
2 )15
0PE
M4P
IT P
aram
eter
s (β
, D, θ
)0.
01, 1
86, 0
.5O
bser
ved
Lag
Tim
e (h
ours
)7.
08
WF
max
WF
peak
tim
eW
F ce
ntro
idM
ax D
isch
arge
Max
Dis
char
ge(h
ours
)(h
ours
)(h
ours
)(m
3 /s)
Obs
erve
dC
ase
'a':
(m3 /s
)M
aidm
ent e
t al.
Form
ula:
Vm
ean:
0.0
7 m
/s15
.83
6.83
7.08
83.9
261
.66
Cas
e 'b
':ch
anne
l vel
ocity
: 2 m
/s, h
illsl
ope
velo
city
: 0.0
5 m
/s11
.91
3.91
4.25
89.1
6C
ase
'c':
chan
nel v
eloc
ity: 1
m/s
, hill
slop
e ve
loci
ty: 0
.05
m/s
15.3
37.
587.
0083
.39
Cas
e 'd
':ch
anne
l vel
ocity
: 2 m
/s, h
illsl
ope
velo
city
: 0.0
2 m
/s24
.66
3.91
6.50
69.8
9C
ase
'e':
chan
nel v
eloc
ity: 1
m/s
, hill
slop
e ve
loci
ty: 0
.02
m/s
28.0
87.
839.
1664
.11
0
0.1
0.2
010
2030
Tim
e (h
ours
)
number of cells / total cells
Res
cale
d W
F - c
ase
'a'
Res
cale
d W
F - c
ase
'b'
Res
cale
d W
F - c
ase
'c'
Res
cale
d W
F - c
ase
'd'
Res
cale
d W
F - c
ase
'e'
Wid
th F
unct
ion
(sm
ooth
ing
win
dow
: 1 h
our)
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atio
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lue
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ells
ize
(m)
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inte
ger
Are
a (K
m2 )
86PE
M4P
IT P
aram
eter
s (β,
D, θ
)0.
01, 1
82, 0
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bser
ved
Lag
Tim
e (h
ours
)3.
12
Sum
mar
yW
F m
axW
F pe
ak ti
me
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cent
roid
Max
Dis
char
geM
ax D
isch
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(hou
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(hou
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(hou
rs)
(m3 /s
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bser
ved
Cas
e 'a
':(m
3 /s)
Mai
dmen
t et a
l. Fo
rmul
a: V
mea
n: 0
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m/s
7.16
2.66
3.12
71.3
963
.44
Cas
e 'b
':ch
anne
l vel
ocity
: 2 m
/s, h
illsl
ope
velo
city
: 0.0
5 m
/s15
.33
2.66
4.58
48.2
3C
ase
'c':
chan
nel v
eloc
ity: 1
m/s
, hill
slop
e ve
loci
ty: 0
.05
m/s
16.1
64.
665.
7545
.46
Cas
e 'd
':ch
anne
l vel
ocity
: 2 m
/s, h
illsl
ope
velo
city
: 0.0
2 m
/s37
.00
4.50
9.50
35.0
2C
ase
'e':
chan
nel v
eloc
ity: 1
m/s
, hill
slop
e ve
loci
ty: 0
.02
m/s
37.9
15.
7510
.66
34.3
9
0
0.050.
1
010
2030
40Ti
me
(hou
rs)
number of cells / total cells
Res
cale
d W
F - c
ase
'a'
Res
cale
d W
F - c
ase
'b'
Res
cale
d W
F - c
ase
'c'R
esca
led
WF
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e 'd
'R
esca
led
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e 'e
'
Wid
th F
unct
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ooth
ing
win
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: 0.2
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ur)
Elev
atio
ns a
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terv
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04080120
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Discharge (m3/s)
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Rai
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0204060
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Tim
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ours
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Rainfall (mm)
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all
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010203040
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Tim
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ours
)
Discharge (m3/s)
0 5 10 15 20
Rainfall (mm)
Act
ual N
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arge
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Dis
char
ge c
ase
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Net
Dis
char
ge c
ase
'b'
Net
Dis
char
ge c
ase
'c'N
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isch
arge
cas
e 'd
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isch
arge
cas
e 'e
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all
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son
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terv
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020406080
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020
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ime
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rs)
Discharge (m3/s)
0 5 10 15 20
Rainfall (mm)
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ual N
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isch
arge
Net
Dis
char
ge c
ase
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Net
Dis
char
ge c
ase
'b'
Net
Dis
char
ge c
ase
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isch
arge
cas
e 'd
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et D
isch
arge
cas
e 'e
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et R
ainf
all
Hyd
rogr
aphs
com
pari
son
(tim
e in
terv
al: 0
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hour
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Dep
. of H
ydra
ulic
s, R
oadw
ays,
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viro
nmen
tal,
and
Surv
eyin
g En
gine
erin
g
0
100
200
300
400
500
050
100
150
Tim
e (h
ours
)
Discharge (m3/s)
0 20 40 60
Rainfall (mm)
Act
ual N
et D
isch
arge
Net
Dis
char
ge c
ase
'a'
Net
Dis
char
ge c
ase
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Net
Dis
char
ge c
ase
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isch
arge
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e 'd
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isch
arge
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e 'e
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ainf
all
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rogr
aphs
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pari
son
(tim
e in
terv
al: 1
hou
r)
Flow
vel
ocity
w
ith M
aidm
ent e
t al.
(199
6) fo
rmul
aFl
ow v
eloc
ity
with
Mai
dmen
t et a
l. (1
996)
form
ula
CA
SE
STU
DY
4
CA
SE
STU
DY
5
CA
SE
STU
DY
2
CA
SE
STU
DY
3 CA
SE
STU
DY
6
Flow
vel
ocity
w
ith M
aidm
ent e
t al.
(199
6) fo
rmul
aFl
ow v
eloc
ity
with
Mai
dmen
t et a
l. (1
996)
form
ula
Flow
vel
ocity
w
ith M
aidm
ent e
t al.
(199
6) fo
rmul
a
Flow
vel
ocity
w
ith M
aidm
ent e
t al.
(199
6) fo
rmul
a
