water
Article
Long-Term Impact of Sediment Deposition and
Erosion on Water Surface Profiles in the Ner River
Tomasz Dysarz *, Ewelina Szałkiewicz and Joanna Wicher-Dysarz
Department of Hydraulic and Sanitary Engineering, Poznan University of Life Sciences, ul. Wojska Polskiego 28,
60-637 Poznan, Poland; [email protected] (E.S.); [email protected] (J.W.-D.)
* Correspondence: [email protected]; Tel.: +48-61-846-6586, Fax: +48-61-848-7726
Academic Editor: Karl-Erich Lindenschmidt
Received: 2 December 2016; Accepted: 22 February 2017; Published: 27 February 2017
Abstract: The purpose of the paper is to test forecasting of the sediment transport process, taking
into account two main uncertainties involved in sediment transport modeling. These are: the lack of
knowledge regarding future flows, and the uncertainty with respect to which sediment transport
formula should be chosen for simulations. The river reach chosen for study is the outlet part of the
Ner River, located in the central part of Poland. The main characteristic of the river is the presence of
an intensive morphodynamic process, increasing flooding frequency. The approach proposed here
is based on simulations with a sediment-routing model and assessment of the hydraulic condition
changes on the basis of hydrodynamic calculations for the chosen characteristic flows. The data used
include Digital Terrain Models (DTMs), cross-section measurements, and hydrological observations
from the Dabie gauge station. The sediment and hydrodynamic calculations are performed using
program HEC-RAS 5.0. Twenty inflow scenarios are of a 10-year duration and are composed on the
basis of historical data. Meyer-Peter and Müller and Engelund-Hansen formulae are applied for the
calculation of sediment transport intensity. The methodology presented here seems to be a good
tool for the prediction of long-term impacts on water surface profiles caused by sediment deposition
and erosion.
Keywords: sediment routing; deposition forecasting; numerical simulations; the Ner River
1. Introduction
The ideas presented here are related to sediment transport impact on changes in bed and water
surface profiles. The purpose of the paper is to find the most reliable method for forecasting this process,
taking into account two main uncertainties involved in sediment transport modeling. These are the lack
of knowledge regarding future flows, and uncertainty with respect to sediment transport formulae that
should be chosen for simulations. The methodology applied enables the assessment of the sediment
accumulation influence on flood hazards and other phenomena depending on channel capacity.
Sediment transport and the processes of sedimentation and erosion have become a very popular
area of scientific investigation (see, for example, References [1–8]). Taking into account the spatial scale
of the problem, the complexity of channel networks, and processes analyzed, mathematical models
are frequently used in such research. Because the areas of sediment transport and sediment modeling
are not yet well known, the models have to be completed with a number of empirical assumptions
(see, for example, References [9–13]). Successful modeling is strongly dependent on the choice of
sediment transport formula determining the transport intensity. Hence, it is one of the most important
uncertainty sources in the forecasting of this process and its consequences [2,14]. The second source
is more common in any forecasting of flow phenomena. There is no or incomplete knowledge about
the future inflows to the river, reservoir, or any other water system. In the case of sediment transport,
characterized by slow changes and long duration, this problem is of real significance. Forecasting
Water 2017, 9, 168; doi:10.3390/w9030168
www.mdpi.com/journal/water
Water 2017, 9, 168
2 of 14
water system. In the case of sediment transport, characterized by slow changes and long duration,
2 of 14
this problem is of real significance. Forecasting of flows in the time frame necessary for modeling of
sediment transport is impossible. Hence, only hypothetical scenarios can be analyzed and
statistically
processed.
of
flows in the
time frame necessary for modeling of sediment transport is impossible. Hence, only
Anotherscenarios
important
of the research
presented
here is the impact of the deposition and
hypothetical
canaspect
be analyzed
and statistically
processed.
erosion
on flow
processaspect
and important
hydraulic
parameters
a natural
river,
References
Another
important
of the research
presented
here isinthe
impact of
the e.g.,
deposition
and
[2,15]. The
sediment
transport
changeshydraulic
the capacity
of the river
Frome.g.,
a water
management
erosion
on flow
process
and important
parameters
in achannel.
natural river,
References
[2,15].
point
of view,transport
the mostchanges
important
may be water
surface
elevations
inundation
areas. point
They
The
sediment
the capacity
of the river
channel.
Fromand
a water
management
depend
on channel
capacity,
butbe
this
dependence
is not direct.
prediction
of thedepend
described
of
view, the
most important
may
water
surface elevations
and Hence,
inundation
areas. They
on
process capacity,
with its but
entire
the application
of sophisticated
mathematical
models
channel
thiscomplexity
dependencerequires
is not direct.
Hence, prediction
of the described
process with
its
with several
empirical
or the
subjective
assumptions
[10,12,16,17],
which models
may bewith
additional
of
entire
complexity
requires
application
of sophisticated
mathematical
severalsources
empirical
uncertainty.
or
subjective assumptions [10,12,16,17], which may be additional sources of uncertainty.
In Poland,
Poland,the
theproblem
problem
discussed
here
analyzed
the context
presented
In
discussed
here
hashas
not not
oftenoften
beenbeen
analyzed
in thein
context
presented
above.
above.
In the scientific
literature,
are relatively
few analyses,
which
linkchanges
natural changes
in the
In
the scientific
literature,
there arethere
relatively
few analyses,
which link
natural
in the channel
channel conveyance
with elements
determining
thethe
useriver,
of the
river,
e.g.,
flood hazard,
shipping,
conveyance
with elements
determining
the use of
e.g.,
flood
hazard,
shipping,
etc. Thisetc.
is
Thisofisthe
onereasons
of the reasons
we decided
to address
the problem.
one
why wewhy
decided
to address
the problem.
Water 2017, 9, 168
2.
2. Study
Study Site
Site Description
Description
The
is situated
in the
Greater
PolandPoland
and Central
Poland climatic
regions.
The Ner
NerBasin
Basinarea
area
is situated
in Central
the Central
Greater
and Central
Poland climatic
The
catchment
area andarea
boundaries
are shown
Figurein1Figure
and marked
in orange.
The river
is
regions.
The catchment
and boundaries
arein
shown
1 and marked
in orange.
TheNer
river
aNer
right
to the river
Warta.
rivers,
Nerthe
andNer
the and
Warta,
marked
as blue lines
in
is atributary
right tributary
to the
river Both
Warta.
Both the
rivers,
theare
Warta,
are marked
as blue
2 , while the
Figure
The total
areatotal
of the
Ner
is 1835
length
oflength
the river
is 134
km.isThe
lines in1.Figure
1. The
area
of Basin
the Ner
Basinkm
is 1835
km2, while
the
of the
river
134 Ner
km.
flows
through
voivodships,
namely Greater
Łódzkie.
The sources
the river
The Ner
flowstwo
through
two voivodships,
namelyPoland
Greaterand
Poland
and Łódzkie.
Theofsources
of are
the
located
in
the
town
of
Łódź
in
the
area
of
the
Widzew
District
[18].
The
outlet
is
in
km
444
+
400
of
the
river are located in the town of Łódź in the area of the Widzew District [18]. The outlet is in km 444 +
Warta
nearRiver,
the village
of Majdany
The reach
thereach
Ner River
forselected
the presented
400 of River,
the Warta
near the
village of[19].
Majdany
[19]. of
The
of the selected
Ner River
for the
analyses
is analyses
marked with
a pinkwith
polygon
in polygon
Figure 1.in Figure 1.
presented
is marked
a pink
Figure 1.
1. Location of the Ner
Ner River
River basin
basin and
and selected
selected reach
reach of
of the
the channel.
channel.
Figure
According to
to the
the physico-geographic
physico-geographic division
division proposed
proposed by
by Kondracki
Kondracki [20],
[20], the
the Ner
Ner Basin
Basin area
area
According
is situated
situated in
in the
the following
following macroregions:
macroregions: Acclivity
Acclivity of
of Southern
Southern Masovia,
Masovia, the
the lowlands
lowlands of
of Southern
Southern
is
Greater
Poland,
and
the
lowlands
of
Central
Masovia.
The
area
has
a
“lowland”
character.
The
Greater Poland, and the lowlands of Central Masovia. The area has a “lowland” character. The absolute
absolute altitudes of the terrain vary from 92.50 to 279.8 m a.s.l. The mean slope of the basin is 1.17%.
altitudes of the terrain vary from 92.50 to 279.8 m a.s.l. The mean slope of the basin is 1.17%. The area
The area is mainly covered by arable land, which occupies 63.35% of the total basin area. The other
is mainly covered by arable land, which occupies 63.35% of the total basin area. The other forms of
forms of land use are forests (14.2%), greenery (10.8%), and urbanized land (11.4%). The total area of
land use are forests (14.2%), greenery (10.8%), and urbanized land (11.4%). The total area of the lakes
the lakes is 4.5 km2, which, with respect to the total basin area, gives a lake index of 0.25%. The
is 4.5 km2 , which, with respect to the total basin area, gives a lake index of 0.25%. The density of the
density of the river network is 1.59 km∙km−2.
river network is 1.59 km·km−2 .
The graphs presented in Figure 2 characterize the variability of flow in the Ner River. They are
composed on the basis of data from the Dabie gauge station. The first graph (Figure 2a) presents
Water 2017, 9, 168
3 of 14
Water 2017, 9, 168
3 of 14
discharge (m3/s)
The graphs presented in Figure 2 characterize the variability of flow in the Ner River. They are
composed on the basis of data from the Dabie gauge station. The first graph (Figure 2a) presents
annual
flows
over
the the
period
of 1964–2013.
TheyThey
are denoted
as green
annual minimum,
minimum,mean,
mean,and
andmaximum
maximum
flows
over
period
of 1964–2013.
are denoted
as
squares,
blue lines,
redand
dots,
The greatest
floods observed
in this time
are time
denoted
green squares,
blueand
lines,
redrespectively.
dots, respectively.
The greatest
floods observed
in this
are
additionally
by year ofby
occurrence
(in red). The
graph
(Figure
2b)(Figure
presents
denoted additionally
year of occurrence
(in second
red). The
second
graph
2b)ordinary
presentsvariability
ordinary
of
flow within
a year.
Thisa plot
alsoplot
prepared
the basis
data
for of
thedata
period
of 1964–2013.
variability
of flow
within
year.isThis
is alsoon
prepared
onofthe
basis
for the
period of
The
green, blue,
redblue,
bars represent
averages
of minimum,
mean,
and maximum
flows
in
1964–2013.
The and
green,
and red bars
represent
averages
of minimum,
mean,
andobserved
maximum
particular
months,
Additionally,
the extreme
values for these
characteristics,
flows observed
inrespectively.
particular months,
respectively.
Additionally,
the extreme
values minimum
for these
and
maximum, minimum
are shown and
as confidence
intervals
in theasform
of dashed
lines. The
floods
presented
in
characteristics,
maximum,
are shown
confidence
intervals
in the
form
of dashed
Figure
2a are
alsopresented
denoted in
lines. The
floods
inFigure
Figure2b.
2a are also denoted in Figure 2b.
100
90
80
70
60
50
40
30
20
10
0
1960
1979
1982
1970
1980
1985
2010
1999
1990
2000
2010
years
mean
min
2020
max
discharge (m3/s)
(a)
100
90
80
70
60
50
40
30
20
10
0
1979
1982
NOV DEC
JAN
average of min
2010
FEB
MAR APR MAY
months
average of mean
1999
JUN
JUL
1985
AUG
SEP
OCT
average of max
(b)
Figure 2. Characteristics of flow variability in the Dabie gauge station for the period of 1964–2013.
Figure 2. Characteristics of flow variability in the Dabie gauge station for the period of 1964–2013.
(a) annual minimum, mean, and maximum flows; (b) monthly averages of minimum, mean, and
(a) annual minimum, mean, and maximum flows; (b) monthly averages of minimum, mean, and
maximum
flows with
with extremes.
extremes.
maximum flows
The Ner River is characterized by snow and rain regime of supply, with a single maximum
The Ner River is characterized by snow and rain regime of supply, with a single maximum (March,
(March, April) and a single minimum (July–September) in a year. The annual mean flow of the Ner
April) and a single minimum (July–September) in a year. The annual mean
flow of the Ner River in
River in the Dabie profile, in the period of 1961–2013 [21], was3 10.93
m3∙s−1, with a minimum of
0.7
−
1
the
Dabie profile, in the period of
[21], was 10.93 m ·s , with a minimum of 0.7 m3 ·s−1
3∙s1961–2013
−1. The extreme
m3∙s−1 and a maximum of 86.0
m
floods
may
occur
all
year,
as
shown
in
Figure
2b.
and
a maximum
86.0
m3 ·s−1 .ofThe
floodsinmay
occur allwhen
year,the
as shown
in Figure
2b.
In the
past, there of
was
a period
veryextreme
large floods
1979–1985,
three biggest
floods
In
the
past,
there
was
a
period
of
very
large
floods
in
1979–1985,
when
the
three
biggest
floods
occurred. The estimated values of the maximum flows came to 86.0 m3∙s−1 in 1979, 73.0 m3∙s−1 in 1982,
occurred. The estimated values of the maximum flows came to 86.0 m3 ·s−1 in 1979, 73.0 m3 ·s−1 in 1982,
and 70.6 m3∙s−1 in 1985. Similar floods were observed in 1999 and 2010, when the maximum flows
reached values of 65.5 m3∙s−1 and 70.8 m3∙s−1, respectively.
Earlier observations of this system indicated intensive sediment transport and deposition
(Figure 3) [22]. The selected river reach was regulated by construction works, aimed at improving
Water 2017, 9, 168
4 of 14
channel capacity (in 1983). The design of the regulated bed in 1983 is very simple. It was assumed
that the river reach would have a single slope and regular shape. In Figure 3, this bed is presented as
a black
line.
The
designfloods
was were
implemented
it isand
not 2010,
known
how
theflows
final
and
70.6 straight
m3 ·s−1 in
1985.
Similar
observedbut
in 1999
when
theaccurate
maximum
3
−
1
3
−
1
regulation
was of
in 65.5
comparison
with70.8
them
design.
However, it is assumed that the uncertainty is small
reached
values
m ·s and
·s , respectively.
enough
to
make
the
qualitative
comparisons
necessary
to explain
thetransport
essence of
problem
Earlier observations of this system indicated
intensive
sediment
andthe
deposition
analyzed.
AfterThe
20 selected
years, inriver
2003,
the was
capacity
of thebychannel
was almost
completely
reduced
(Figure
3) [22].
reach
regulated
construction
works, aimed
at improving
comparing
with the
of The
the channel
inthe
1983
year. Changes
bediselevation
reached
a magnitude
channel
capacity
(instate
1983).
design of
regulated
bed inin
1983
very simple.
It was
assumed
of about
1 mreach
and would
were uniformly
distributed
along
theshape.
channel.
In 2007,
the bed
riveris reach
was
that
the river
have a single
slope and
regular
In Figure
3, this
presented
regulated
again
andThe
hydraulic
were restored.
In not
Figure
3, the
bedaccurate
profiles for
as
a black once
straight
line.
design conditions
was implemented
but it is
known
how
the these
final
three
characteristic
moments
are
compared.
The
data
used
to
compose
the
presented
graph
are
taken
regulation was in comparison with the design. However, it is assumed that the uncertainty is small
from past
river regulations
and documents
reporting
inanalyzed.
the river
enough
to designs
make theofqualitative
comparisons
necessary to
explain the
the hydraulic
essence of conditions
the problem
[22]. The
data are
not georeferenced,
therefore,
it isalmost
difficult
to adopt them
in current
research.
After
20 years,
in 2003,
the capacity ofand,
the channel
was
completely
reduced
comparing
with
However,
the
comparison
well
shows
the
problem
in
this
river
reach.
the state of the channel in 1983 year. Changes in bed elevation reached a magnitude of about 1 m
The graph
in Figure
3 shows
huge
elevations
1983again
and
and were
uniformly
distributed
along
thedifferences
channel. Inbetween
2007, thebed
river
reach wasmeasured
regulatedinonce
2003.hydraulic
The changes
inducedwere
by sediment
are
In some
separated
and
conditions
restored.transport
In Figure
3,not
theuniform.
bed profiles
for these
threecross-sections,
characteristic
erosion may
noticed, The
but,data
in general,
sediment
is about
m. Itfrom
is also
important
to
moments
are be
compared.
used tothe
compose
the deposition
presented graph
are 1taken
past
designs of
indicate
that the and
changes
are rather
uniformly
distributed.
Takingininto
account
length
of this
river
regulations
documents
reporting
the hydraulic
conditions
the river
[22].the
The
data are
not
period
(20
years),
and
the
uncertainty
related
to
the
lack
of
other
observations,
we
may
expect
the
georeferenced, and, therefore, it is difficult to adopt them in current research. However, the comparison
bottom
to
rise
about
0.5–1.0
m
over
a
10-year
period.
well shows the problem in this river reach.
Figure 3. Comparison of bottom and water surface profiles observed in 1983, 2003, and
and 2007.
2007.
It is graph
also important
note that
numerous
environment
protection
zones
are present
inand
the
The
in Figure to
3 shows
huge
differences
between bed
elevations
measured
in 1983
vicinity
of
the
selected
river
reach.
Some
of
them
are
the
Nature
2000
areas.
In
the
Ner
Valley,
there
2003. The changes induced by sediment transport are not uniform. In some separated cross-sections,
are two may
kinds
such zones,
Protection
Area
Area of
erosion
beof
noticed,
but, innamely
general,the
theSpecial
sediment
deposition
is (SPA)
about 1and
m. the
It isSpecial
also important
Conservations
(SAC).
Another
protection
zone
is
the
Ecological
Corridors
of
the
Warta
and
the
to indicate that the changes are rather uniformly distributed. Taking into account the length ofNida
this
Valleys.
period (20 years), and the uncertainty related to the lack of other observations, we may expect the
bottom to rise about 0.5–1.0 m over a 10-year period.
3. Materials and Methods
It is also important to note that numerous environment protection zones are present in the vicinity
of theInselected
river reach.
of them
the Nature
2000data
areas.analyses;
In the Ner
there are
twoa
the research,
threeSome
methods
areare
used:
(1) spatial
(2)Valley,
simulation
with
kinds
of such zones,
namely
thestatistical
Special Protection
(SPA) andand
the tools
Special
of Conservations
hydrodynamic
model;
and (3)
analyses. Area
The methods
forArea
spatial
data analyses
(SAC).
Another protection
zonepreparation
is the Ecological
of theare
Warta
and used
the Nida
Valleys.
are implemented
during the
of theCorridors
model; they
mainly
for processing
the
geometry of the river reach and the topography of the river valley. Such an approach requires that
3. Materials and Methods
In the research, three methods are used: (1) spatial data analyses; (2) simulation with a
hydrodynamic model; and (3) statistical analyses. The methods and tools for spatial data analyses
are implemented during the preparation of the model; they are mainly used for processing the
Water 2017, 9, 168
5 of 14
Water 2017, 9, 168
5 of 14
geometry of the river reach and the topography of the river valley. Such an approach requires that
the bathymetry of the river channel, determined on the basis of ISOK measurements [23] (Polish:
the bathymetry of the river channel, determined on the basis of ISOK measurements [23] (Polish:
ISOK = Informatyczny System Osłony Kraju przed nadzwyczajnymi zagrożeniami, English: IT
ISOK = Informatyczny System Osłony Kraju przed nadzwyczajnymi zagrożeniami, English: IT
system of the Country’s Protection Against Extreme Harazds), is linked with DTM obtained from
system of the Country’s Protection Against Extreme Harazds), is linked with DTM obtained from
CODGiK [24] (Polish: CODGiK = Centralny Ośrodek Dokumentacji Geodezyjnej i Kartograficznej,
CODGiK [24] (Polish: CODGiK = Centralny Ośrodek Dokumentacji Geodezyjnej i Kartograficznej,
English: Main Documentation Centre of Geodesy and Cartography). For this purpose, the standard
English: Main Documentation Centre of Geodesy and Cartography). For this purpose, the standard
ArcGIS software [25] is used with the free extension GeoRAS [26]. Some of the work is also done
ArcGIS software [25] is used with the free extension GeoRAS [26]. Some of the work is also done
with the help of RAS Mapper, which is a part of the HEC-RAS package [27]. At this stage, the basic
with the help of RAS Mapper, which is a part of the HEC-RAS package [27]. At this stage, the basic
techniques of spatial data editing are used, as well as advanced spatial interpolations methods
techniques of spatial data editing are used, as well as advanced spatial interpolations methods available
available in the ArcGIS module, Spatial Analyst.
in the ArcGIS module, Spatial Analyst.
In the next steps, several vector data layers have to be prepared (Figure 4). These layers include
In the next steps, several vector data layers have to be prepared (Figure 4). These layers include
information such as the course of the main stream, bank positions, approximated direction of flows
information such as the course of the main stream, bank positions, approximated direction of flows in
in the floodplains, and location of cross-sections. The model prepared reconstructs 18,906.29 m of the
the floodplains, and location of cross-sections. The model prepared reconstructs 18,906.29 m of the
river course. The geometry is represented by 99 cross-sections. The average distance between cross
river course. The geometry is represented by 99 cross-sections. The average distance between cross
sections is about 250–300 m. The distances of cross sections are smaller near bridges and structures.
sections is about 250–300 m. The distances of cross sections are smaller near bridges and structures.
(a)
(b)
Figure 4. The river and the model cross-sections shown in (a) Digital Terrain Model (DTM) and (b)
Figure 4. The river and the model cross-sections shown in (a) Digital Terrain Model (DTM) and
ortophotomap.
(b) ortophotomap.
Simulations of flow and sediment transport were realized using HEC-RAS 5.0.1. The geometry
Simulations
of flow and
sediment transport
were realized
using HEC-RAS
5.0.1. Thetogeometry
of
of the model, including
cross-sections
of the riverbed
and floodplains,
is imported
HEC-RAS
the
model,
including
cross-sections
of
the
riverbed
and
floodplains,
is
imported
to
HEC-RAS
using
using standard SDF files (English: SDF = Standard Data Format). Such files are generated by the
standard
SDF files (English:
= Standard
Such files
aredescribed
generatedearlier.
by the The
GeoRAS
GeoRAS extension
of ArcGISSDF
on the
basis of Data
DTM Format).
and the vector
layers
flow
extension
of
ArcGIS
on
the
basis
of
DTM
and
the
vector
layers
described
earlier.
The
flow
module
module of the model is initially calibrated implementing (1) water surface elevations from the flood
of
the model
calibrated
(1) water flows
surface
elevations
from
the flood
hazard
hazard
mapsisofinitially
the ISOK
project implementing
[23] and (2) maximum
obtained
from
IMGW
PIB (Polish:
maps
of
the
ISOK
project
[23]
and
(2)
maximum
flows
obtained
from
IMGW
PIB
(Polish:
IMGW
IMGW PIB = Instytut Meteorologii i Gospodarki Wodnej—Państwowy Instytut Badawczy, English:
PIB
= Instytut
Meteorologii i and
Gospodarki
ństwowy Instytut
Badawczy,
English:The
Institute
of
Institute
of Meteorology
Water Wodnej—Pa
Management—National
Research
Institute).
set of
Meteorology
and
Water
Management—National
Research
Institute).
The
set
of
maximum
flows
tested
maximum flows tested include 10-, 100- and 500-year floods. Such a set of flows was taken as the
include
and
500-year
a setcommon
of flows in
wasscientific
taken asworks
the basis
of the
ISOK
project [23]
basis of10-,
the 100ISOK
project
[23]floods.
and itSuch
is very
[28].
They
correspond
to
and
it
is
very
common
in
scientific
works
[28].
They
correspond
to
probabilities
of
exceedance
of1,10%,
probabilities of exceedance of 10%, 1%, and 0.2%, respectively. Hence, they are denoted Q10, Q
and
1%,
0.2%,
Hence,the
they
are denoted
Q10 , Q1is, and
Q0.2
(Table
1). Duringiscalibration,
Q0.2 and
(Table
1). respectively.
During calibration,
steady
flow module
used.
Such
an approach
consistent
the
steady
flow
module
is
used.
Such
an
approach
is
consistent
with
the
main
assumptions
behind
with the main assumptions behind the derivation of the equations describing the dynamics
of
the
derivation
of
the
equations
describing
the
dynamics
of
channel
flow
[16].
The
changes
in
flow
channel flow [16]. The changes in flow resulting from increase in the catchment area are also taken
resulting
fromThe
increase
theapplied
catchment
are also taken
into account.
The
mainthat
ideathe
applied
is to
into account.
main in
idea
is toarea
set roughness
coefficients
in such
a way
computed
set
roughness
coefficients
in such a taken
way that
thethe
computed
water elevations
fit the
elevations
taken
water
elevations
fit the elevations
from
ISOK project.
The measures
used
to assess
the
from
the
ISOK
project.
The
measures
used
to
assess
the
calibration
quality
are
as
follows:
calibration quality are as follows:
Average
absolute
difference:
Average
absolute
difference:
1
Mmod = 1
= N
Average square difference:
∑||WSsim −−WS ISOK | |
(1)
(1)
Water 2017, 9, 168
6 of 14
Average square difference:
Msq
1
=
N
q
∑(WSsim − WS ISOK )2
(2)
Maximum absolute difference:
Mmax = max |WSsim − WS ISOK |
(3)
where WSsim —is the simulated water surface elevations, WSISOK —the water surface elevations
obtained from flood hazard maps. The marching form of the algorithm for steady flow computations
implemented in HEC-RAS [17] enables decomposition of the problem. The roughness coefficients
search for reaches between the locations of ISOK values of water elevation, from downstream
to upstream.
Table 1. Measures of calibration quality.
Measures of Calibration Quality (cm)
Q10 (10 Year)
Q1 (100 Year)
Q0.2 (500 Year)
−average absolute difference
−average square difference
−maximum absolute difference
13.2
2.7
39.0
22.0
4.2
53.0
24.7
4.6
62.0
The obtained fitting of simulated surface elevation, and those taken from flood hazard maps, are
presented in Table 1. The results obtained are in agreement with reasonable expectations regarding the
quality of the simulation model. The values of selected measures vary relatively slightly, if we take the
complexity of real data used in the analyses into account. The values of average square differences
(Msq ), which is the most popular indicator of model quality, vary from 2.7 to 4.6 cm. The values of
average absolute difference (Mmod ) are greater, from 13.2 to 24.7 cm. The maximum absolute differences
(Mmax ) are used here for control and they vary from 39.0 to 62.0 cm. The values of calibrated roughness
coefficients vary from 0.012 to 0.035 s·m−1/3 in the river channel, and from 0.045 to 0.050 s·m−1/3
in floodplains.
The main simulation model is constructed on the basis of sediment transport module available
in the HEC-RAS package. Simulation of morphodynamic changes in the riverbed consists of a few
basic elements. These are: (a) calculation of quasi-unsteady flow; (b) numerical solution of the Exner
equation implemented for particular fractions of sediment; and (c) proper sediment transport formulae
enabling calculation of transport intensity. This module also includes several additional elements, e.g.,
an algorithm for updating bed elevations, procedures for the generation of resulting geometry, etc.
The fundamental element of the quasi-unsteady flow simulation is the solution of Bernoulli’s
equation [16,29,30] in the form presented by Brunner [17]. The equation has a simple mathematical
form of mechanical energy balance in fluid flow including: (1) potential energy; (2) work of pressure
force; (3) kinetic energy; and (4) energy losses due to friction and cross-section contraction or expansion.
In the form applied in HEC-RAS, the effects related to floodplains and compound shape of the channel
are also taken into account. More detailed description of Equation (4) may be found in Brunner [17].
This concept enables determination of hydraulic parameters for steady flow conditions such as depth,
average velocity, etc. There is one main assumption in the modeling of the quasi-unsteady flow with
sediment transport. The hydraulic parameters are considered constant in some finite time intervals.
This assumption enables the calculation of flow in the same way as for steady flow conditions. This
approach means that we assume abrupt equalization of flow along the river reach. There is no
flow propagation along a channel, which is the opposite to the modeling of unsteady flow with full
St. Venant equations.
The sediment transport phenomena are modeled with Exner’s equation [10,12,17]. The equation
consists of two elements: (1) bed elevation changes and (2) gradient of total volumetric intensity of
Water 2017, 9, 168
7 of 14
sediment transport. The second value is calculated with empirical formulae chosen for each sediment
fraction separately.
Due to the fact that there is a lack of sufficient data for robust calibration of the sediment transport
module, the approach based on sensitivity/uncertainty analysis is applied. The factors identified as
most uncertain and affecting potential results are (1) empirical formula for sediment transport intensity;
(2) grain size distribution, which is the main parameter of sediment transport formula. The third
uncertain element in the entire predictive procedure is (3) future flow scenario. Hence, the approach
applied here selects several forms of each factor and runs the model. The selection of the representative
elements for uncertain factors is governed by statistical laws. The results obtained are also processed
and presented as statistics.
Two empirical formulae for calculation of sediment transport are used: (1) the Meyer-Peter
and Müller (MPM) formula; (2) Engelund-Hanasen (EH) formula. The first of them is a general
relationship derived on the basis of laboratory experiments for coarse sediments like coarse sands and
gravel [9,10,13,31]. Because of that, the MPM formula provides quite good results under mountainous
conditions. However, its dimensionless form may suggest broader implementation. Some research on
lowland rivers shows a satisfactory fit of the MPM formula with observations [13,32].
The second formula used, the Engelund-Hansen formula [9,10,13,33,34], is addressed for rivers
with sandy beds. The estimated characteristics of sediments in the analyzed Ner River reach fit
this requirement.
The reference grain size distribution was selected as the approximate sieve curve reflecting a
sandy bed, which is a typical kind of bed in the region where the Ner flows. Then several grain size
distributions were generated as regular deviations from the reference one. During the preliminary tests,
it occurred that the uncertainty of grain sizes is less important than two other factors, namely sediment
transport formula and flow scenario. Hence, this element is neglected in further considerations.
The methods of statistical analysis used in this study [35,36] are implemented at the stage of the
data preparation as well as for post-processing of results. The statistical and probabilistic methods
are used for the construction of flow scenarios, analysis of flow frequency, and their duration. For the
simulation of sediment transport phenomena, 20 scenarios of a 10-year duration are constructed.
The flow hydrographs are randomly selected from historical data for each scenario. At the stage of
post-processing, the calculation of mean values, standard deviations, and scatter are crucial for proper
interpretation of obtained results and uncertainty of formulated forecasts.
To take into account the uncertainty of the problem the computations are prepared in the way
presented in Figure 5. The basic data, determined with satisfactory precision, are initial channel
geometry and calibrated values of roughness coefficients. It is assumed that uncertainty of the
forecast is mainly related to no possibility of knowing future flows, not knowing a proper formula for
calculation of sediment transport intensity and incomplete information about grain size distribution.
As previously mentioned, the last element occurred to be less important than the first two.
The uncertainty of the future inflows is reconstructed by the selection of 20 scenarios of a 10-year
duration. The uncertainty related to the calculation of sediment transport intensity is modeled by
testing the two formulae described above, MPM and EH. All these elements with synthetic samples
of sediments are used for the configuration of the simulation model. The model reconstructs the
process of sediment transport with accumulation and erosion in the selected river reach. As the “inlet”
boundary condition for Exner’s equation the inflow of sediments in equilibrium conditions is imposed.
The results are 41 bed profiles. The first represents the initial bed; the rest include two sets of 20
profiles, which represent the final bed. Each set represents the effect of one sediment transport formula.
Hence, a single result, the bed profile, depends on the implemented formula and flow scenario.
The bed profiles with flow frequency curves, maximum flows, and characteristic flows are used
for configuration of the steady flow model. This model enables determination of water surface profiles
and distribution along the channel of such hydraulic parameters as depth and flow velocity. The results
depend mainly on the channel geometry and discharge. Such elements as roughness coefficients and
Water 2017, 9, 168
Water 2017, 9, 168
8 of 14
8 of 14
UNCERTAINTY
initial bottom of
the river channel
hydrographs
20 x 10 years
simulation model
sediment
transport
formula:
MPM, EH
steady flow
analysis
grain sizes
PARAMETERS
roughness
coefficients
BASIC DATA
outflow boundary
condition
are treated
as known.
The
is roughness
determined
the basison
of
coefficients
and outflow
boundary
condition
are treated
asroughness
known. The
is on
determined
previous
simplified
calibration
of
flow
model.
The
boundary
condition
is
imposed
as
free
outflow
the basis of previous simplified calibration of flow model. The boundary condition is imposed as
(i.e.,outflow
normal (i.e.,
flow).normal flow).
free
2 x 20 profiles of
the river bottom
SIMULATION RESULTS
water surface profiles
min flows
min flows
mean flows
forecast of
sediment impact
mean flows
max flows
max flows
FINAL RESULTS
assessment of
forecast uncertainty
Figure
Figure 5.
5. The
Thebasic
basicidea
idea of
of simulations.
simulations.
The results of steady flow computations are water surface profiles corresponding to the
The results of steady flow computations are water surface profiles corresponding to the minimum,
minimum, mean, and maximum flows of the Ner River. These profiles are determined for each of the
mean, and maximum flows of the Ner River. These profiles are determined for each of the 41 beds
41 beds obtained from sediment simulations. On the basis of these profiles, a comparison of initial
obtained from sediment simulations. On the basis of these profiles, a comparison of initial and
and final simulated conditions can be made. The number of simulations and the analyzed variation
final simulated conditions can be made. The number of simulations and the analyzed variation of
of parameters enabled determination of the forecast uncertainty. The results may be also presented
parameters enabled determination of the forecast uncertainty. The results may be also presented in the
in the form of expected inundation frequency and its uncertainty. On this basis, flood hazard maps
form of expected inundation frequency and its uncertainty. On this basis, flood hazard maps may also
may also be produced, including expectations and possible deviations.
be produced, including expectations and possible deviations.
4. Results and Discussion
4. Results and Discussion
The first results are presented as longitudinal profiles of riverbed and water surface (Figures 6
The first results are presented as longitudinal profiles of riverbed and water surface (Figures 6
and 7). There are initial and final results presented in each graph. The final geometry is the effect of
and 7). There are initial and final results presented in each graph. The final geometry is the effect
averaging over results of simulations. The results of simulations are generated on the basis of
of averaging over results of simulations. The results of simulations are generated on the basis of
10-year flow scenarios. The averaging is performed for each sediment transport formula separately.
10-year flow scenarios. The averaging is performed for each sediment transport formula separately.
The presented profiles are obtained for the average of mean flow determined for the period
The presented profiles are obtained for the average of mean flow determined for the period 1964–2013.
1964–2013. The continuous lines represent the initial geometry. The dashed lines show the results for
The continuous lines represent the initial geometry. The dashed lines show the results for the final
the final geometry. The black lines are bottoms and the blue ones are water surfaces.
geometry. The black lines are bottoms and the blue ones are water surfaces.
In the case of the MPM formula (Figure 6), it is well seen that the sediments are accumulated
In the case of the MPM formula (Figure 6), it is well seen that the sediments are accumulated
mainly in the upper part of the channel. Completely different results are shown for the bed
mainly in the upper part of the channel. Completely different results are shown for the bed downstream
downstream of the bridge in the town of Dabie. There is relatively little or no accumulation. The
of the bridge in the town of Dabie. There is relatively little or no accumulation. The changes in water
changes in water surface follow the variation in bed positions. In the upper reach, the water surface is
surface follow the variation in bed positions. In the upper reach, the water surface is significantly
significantly increased. In the downstream reach, the water surface did not shift much from initial
increased. In the downstream reach, the water surface did not shift much from initial elevations.
elevations.
The results obtained from simulation with the EH formula (Figure 7) are different.
The accumulation of sediments is observed along the whole channel reach. The distribution of
sediments is more uniform. The average increase in bottom elevations is about 1 m. The changes in
water surface elevations are similarly uniform. However, the changes in water surface are smaller than
the rise in the bed. It may be noted that such uniform distribution of accumulated material is more
compatible with earlier observations of bed changes in this river reach. Comparing with the results
elevations (m a.s.l.)
98
96
94
Water 2017, 9, 168
9 of 14
92
90
presented in0 Figure 3 and discussion
the results obtained15000
with the EH formula
seem to be
5000 in Section 2;10000
20000
Water 2017,
9, 168
9 of 14
closer
to real
observations.
distance (m)
elevations (m a.s.l.)
initial bed
simulated bed
initial WS
simulated WS
98
Figure 6. The averaged longitudinal profiles for mean flow in the Ner River calculated with the
96
Meyer-Peter and Müller formula.
94
The results
obtained from simulation with the EH formula (Figure 7) are different. The
92
accumulation of sediments is observed along the whole channel reach. The distribution of sediments
90
is more uniform. The average increase in bottom elevations is about 1 m. The changes in water
0
5000
10000
15000
20000
surface elevations are similarly uniform. However, the changes in water surface are smaller than the
distance (m)
rise in the bed. It may be noted that such uniform distribution of accumulated material is more
initial bed
simulated bed
initial WS
simulated WS
compatible with earlier observations of bed changes in this river reach. Comparing with the results
Figure
The averaged
averaged
longitudinal
profiles 2;
forthe
mean
flowobtained
in the
the Ner
Ner
River
calculated
withseem
the to
presented
in6.6.
Figure
3 and discussion
in Section
results
with
thecalculated
EH formula
Figure
The
longitudinal
profiles
for
mean
flow
in
River
with
the
Meyer-Peter
andMüller
Müllerformula.
formula.
be closer
to real observations.
Meyer-Peter
and
elevations (m a.s.l.)
The98results obtained from simulation with the EH formula (Figure 7) are different. The
accumulation of sediments is observed along the whole channel reach. The distribution of sediments
96
is more uniform. The average increase in bottom elevations is about 1 m. The changes in water
94
surface elevations
are similarly uniform. However, the changes in water surface are smaller than the
rise in the
92 bed. It may be noted that such uniform distribution of accumulated material is more
compatible with earlier observations of bed changes in this river reach. Comparing with the results
90in Figure 3 and discussion in Section 2; the results obtained with the EH formula seem to
presented
0
5000
10000
15000
20000
be closer to real observations.
elevations (m a.s.l.)
distance (m)
98
initial bed
simulated bed
initial WS
simulated WS
Figure96
Theaveraged
averagedlongitudinal
longitudinalprofiles
profilesfor
formean
meanflow
flowininthe
theNer
NerRiver
Rivercalculated
calculatedwith
withthe
the
Figure
7.7. The
Engelund-Hansen
formula.
Engelund-Hansen
formula.
94
92
The
Thestatistics
statisticsofofthe
thesediment
sedimenttransport
transportintensity
intensityininthe
theinlet
inletcross-section
cross-sectionare
areshown
shownininFigure
Figure8.8.
90
This
graph
characterizes
the
equilibrium
load
condition
imposed
as
upstream
boundary
condition
This graph characterizes the equilibrium load condition imposed as upstream boundary condition
0 transport
5000The
15000obtained
20000
for
forthe
thesediment
sediment
transportequation.
equation.
Thered
redcolor
coloris10000
isused
usedtotodenote
denoteresults
results
obtainedwith
withthe
theMPM
MPM
distanceaxis
(m)represents
formula.
formula.The
Theblue—for
blue—forthe
theEH
EHformula.
formula.The
Thehorizontal
horizontal
axis
representsscenarios
scenarioslabeled
labeledwith
withroman
roman
numbers.
bars, red
redand
and
blue,
show
the
values
of median
intensity
of transport
during
each
initial
bedblue,
simulated
bed
initial
WS
simulated
WSscenario.
numbers. The
The bars,
show
the
values
of median
intensity
of transport
during
each
scenario.
The variability
of thisismeasure
huge
but the distribution
values
in each
scenario
is not
The variability
of this measure
huge butisthe
distribution
of values inofeach
scenario
is not
symmetrical.
Figure
7.
The averaged
profiles
mean
flow
in the Ner
calculated
with the
symmetrical.
Hence,
the
0.1used
and
0.9characterize
arefor
used
to the
characterize
the
variability.
value
of0.1
theis
Hence,
the quantiles
0.1 quantiles
andlongitudinal
0.9 are
to
variability.
ARiver
value
of theAquantile
Engelund-Hansen
formula.
quantile
0.1
is
too
small
to
be
visible
in
Figure
8.
Only
the
second
value
is
present,
showing
the
too small to be visible in Figure 8. Only the second value is present, showing the practical range of
practical
range
variability.
is clear that
vary
in the ranges
0.60–0.80
variability.
It isofclear
that theItmedians
varythe
in medians
the ranges
of 0.60–0.80
and of
0.94–1.80
kgand
·s−10.94–1.80
for MPM
The
statistics
of
the
sediment
transport
intensity
in
the
inlet
cross-section
are
shown
in
Figure
8.
−1 for MPM and EH, respectively. The quantiles estimated and the variability of calculated
kg∙s
and EH, respectively. The quantiles estimated and the variability of calculated transport with
EH
Thisgreater
graph
characterizes
thethan
equilibrium
load
condition
imposed
as
condition
transport
with
EHthose
are greater
those
obtained
with
When
theupstream
values
of boundary
quantile
for
the
are
than
obtained
with
MPM.
When
theMPM.
values
of quantile
0.9 for
the
latter0.9
are
below
for
the
sediment
transport
equation.
The
red
color
is
used
to
denote
results
obtained
with
the MPM
−1
−1
−
1
−
1
latter
5 kg∙s
, thefor
same
former
10 kg∙s
in many scenarios.
5 kg·are
s ,below
the same
values
the values
former for
arethe
beyond
10 are
kg·sbeyond
in many
scenarios.
formula.
The blue—for
the EH
formula.
axis
represents
scenarios
labeled
with roman
The graphs
presented
in Figures
9 The
and horizontal
10 show the
changes
in bed
elevations
obtained
from
numbers.
The
bars,
red
and
blue,
show
the
values
of
median
intensity
of
transport
during
each
simulations and their scatter, indicating the difference between maximum and minimum increments.
scenario.
The
variability
of
this
measure
is
huge
but
the
distribution
of
values
in
each
scenario
is
not
The positive values indicate accumulation, negative—erosion. The averaged increments are presented
symmetrical.
thelines
quantiles
and 0.9
are used
characterize
variability.isAdenoted
value ofasthe
as
a blue line. Hence,
The black
show 0.1
extreme
values.
Theto
scatter
for eachthe
cross-section
a
quantile
0.1
is
too
small
to
be
visible
in
Figure
8.
Only
the
second
value
is
present,
showing
the
red error bar. The dashed green line represents zero, what means no changes. Figure 9 shows results
practical range
It is clear
that
the medians
vary in the ranges of 0.60–0.80 and 0.94–1.80
calculated
with of
thevariability.
MPM formula,
Figure
10—the
EH formula.
−1
kg∙s for MPM and EH, respectively. The quantiles estimated and the variability of calculated
transport with EH are greater than those obtained with MPM. When the values of quantile 0.9 for the
latter are below 5 kg∙s−1, the same values for the former are beyond 10 kg∙s−1 in many scenarios.
inflow scenario
median for
for MPM
MPM
median
quantile 0.9
0.9 for
for MPM
MPM
quantile
median for
for EH
EH
median
quantile
0.9
for EH
EH
quantile 0.9 for
Figure 8.
8. The
The statistics
statistics of
of sediment
sediment transport
transport intensity
intensity in
in the
the inlet
inlet cross-section
cross-section for
for both
both applied
applied
Figure
formulae.
Water formulae.
2017,
9, 168
Water 2017, 9, 168
10 of 14
10 of 14
changes of bed elev. (m)
changes
changesofofbed
bedelev.
elev.(m)
(m)
XX
XIX
XVIII
XVII
XVI
XV
XIV
XIII
XII
XI
X
IX
VIII
VII
VI
V
IV
III
II
I
changes
changesofofbed
bedelev.
elev.(m)
(m)
statistics of transport
in the inlet (kg/s)
The graphs
graphs presented
presented in
in Figures
Figures 99 and
and 10
10 show
show the
the changes
changes in
in bed
bed elevations
elevations obtained
obtained from
from
The
15
simulations and
and their
their scatter,
scatter, indicating
indicating the
the difference
difference between
between maximum
maximum and
and minimum
minimum
simulations
increments.
The
positive
values
indicate
accumulation,
negative—erosion.
The
averaged
increments
increments. The
10 positive values indicate accumulation, negative—erosion. The averaged increments
are presented
presented as
as aa blue
blue line.
line. The
The black
black lines
lines show
show extreme
extreme values.
values. The
The scatter
scatter for
for each
each cross-section
cross-section is
is
are
denoted as
as aa red
error bar.
bar. The
The dashed
dashed green
green line
line represents
represents zero,
zero, what
what means
means no
no changes.
changes. Figure
Figure 99
5red error
denoted
shows
results
calculated
with
the
MPM
formula,
Figure
10—the
EH
formula.
shows results calculated with the MPM formula, Figure 10—the EH formula.
0 in Figure 9, the scatter of values obtained with the MPM formula is quite
As shown
shown
As
in Figure 9, the scatter of values obtained with the MPM formula is quite
considerable.
In
the
upper reach
reach itit is
is about
about 5–6
5–6 m.
m. In
In the
the low
low part,
part, downstream
downstream of
of the
the bridge
bridge in
in the
the
considerable. In the upper
town
of
Dabie,
the
scatter
is
smaller,
varying
from
one
to
two
meters.
inflow
town of Dabie, the scatter is smaller, varying from
onescenario
to two meters.
Different
tendencies
are
seen
in
the
results
obtained
withmedian
the EH
EHforformula
formula
(Figure 10).
10). The
The
median
for MPM
EH
Different tendencies are seen
in the
results obtained with
the
(Figure
scatter
of
the
values
is
significantly
smaller
and
oscillates
near
half
a
meter.
In
the
extreme
case
quantile
0.9 for
scatter of the values is significantly
smaller
and
oscillates near half
a meter.
InEH
the extreme case itit
quantile
0.9 for
MPM
reaches
one
meter.
It
is
important
to
indicate
that
all
results
show
accumulation
of the
the sediments
sediments
reaches one meter. It is important to indicate that all results show accumulation of
alongFigure
the whole
whole
analyzed
reach.
This result
result
is consistent
consistent
with
previous
observations.
These
results
8.
statistics
of
sediment
transport
intensity
inwith
theininlet
for bothThese
applied
8. The
The
statistics
of sediment
transport
intensity
thecross-section
inletobservations.
cross-section
for
both
along
the
analyzed
reach.
This
is
previous
results
permit
making
a
more
stable
forecast.
The
subsequent
simulations
produce
channel
beds,
which
are
formulae.
applied
formulae.
permit making a more stable forecast. The subsequent simulations produce channel beds, which are
more
similar
to
others
than
when
they
were
observed
in
the
computations
with
MPM.
more similar to others than when they were observed in the computations with MPM.
The graphs presented in Figures 9 and 10 show the changes in bed elevations obtained from
2.0
simulations2.0
and their scatter, indicating the difference between maximum and minimum
increments. 0.0
The positive values indicate accumulation, negative—erosion. The averaged increments
0.0
are presented
-2.0as a blue line. The black lines show extreme values. The scatter for each cross-section is
denoted as-2.0
a red error bar. The dashed green line represents zero, what means no changes. Figure 9
-4.0
-4.0 calculated with the MPM formula, Figure 10—the EH formula.
shows results
-6.0 in Figure 9, the scatter of values obtained with the MPM formula is quite
As shown
-6.0
0
5000
10000
15000
20000
15000
considerable. In0 the upper reach5000
it is about 5–6 m.10000
In the low part, downstream
of the20000
bridge in the
distance (m)
distance
(m)
town of Dabie, the scatter is smaller, varying from one to two meters.
lower limit
upper limit
average
upper limitwith the EH formula
average (Figure 10). The
Different tendencies arelower
seenlimit
in the results obtained
scatter
of the
values
is significantly
smaller
and
oscillates
half
aof
InRiver
the
extreme
case it
Figure
9.The
Thechanges
changes
inthe
the
average
bottom
elevation
innear
the
reach
ofmeter.
the River
Ner
River
calculated
Figure
9.
inin
average
bottom
elevation
in the
reach
of the
Ner
calculated
with
Figure
9.
The
changes
the
average
bottom
elevation
in
the
reach
the
Ner
calculated
reaches
meter.
is important
to indicate that all results show accumulation of the sediments
withone
Meyer-Peter
and
Müller
formula.
Meyer-Peter
and It
Müller
formula.
with
Meyer-Peter
and
Müller
formula.
along the whole analyzed reach. This result is consistent with previous observations. These results
2.0
2.0 a more stable forecast. The subsequent simulations produce channel beds, which are
permit making
0.0
more similar0.0
to others than when they were observed in the computations with MPM.
-2.0
-2.0
2.0
-4.0
-4.0
0.0
-6.0
-6.0
-2.0 0
0
-4.0
-6.0
5000
5000
lower limit
lower limit
10000
10000
distance (m)
distance (m)
upper limit
upper limit
15000
15000
20000
20000
average
average
0 changes of average
5000 bottom elevation
10000
20000with
Figure 10.
10. The
The
in the
the reach of
of 15000
the Ner River
River calculated
calculated
Figure
in
with
Figure 10.
The changes
changes of
of average
average bottom
bottom elevation
elevation
in
the reach
reach of the
the Ner
Ner River calculated
with
distance
(m)
Engelund-Hansen formula.
formula.
Engelund-Hansen
Engelund-Hansen formula.
lower limit
upper limit
average
Figure 9. The changes in the average bottom elevation in the reach of the Ner River calculated
changes of bed elev. (m)
As shown in Figure 9, the scatter of values obtained with the MPM formula is quite considerable.
with Meyer-Peter and Müller formula.
In the upper reach it is about 5–6 m. In the low part, downstream of the bridge in the town of Dabie,
the scatter is 2.0
smaller, varying from one to two meters.
Different tendencies are seen in the results obtained with the EH formula (Figure 10). The scatter
0.0
of the values is significantly smaller and oscillates near half a meter. In the extreme case it reaches one
-2.0
meter. It is important
to indicate that all results show accumulation of the sediments along the whole
-4.0 This result is consistent with previous observations. These results permit making a
analyzed reach.
more stable forecast.
The subsequent simulations produce channel beds, which are more similar to
-6.0
5000 in the computations
10000
15000
20000
others than when0 they were observed
with MPM.
distance
(m)
Changes in water surface elevations determined for the mean flow are shown in Figures 11 and 12.
lower limit
upper limit assuming the
average
The first graph consists of results
of simulations performed
MPM formula, and the
Figure 10. The changes of average bottom elevation in the reach of the Ner River calculated with
Engelund-Hansen formula.
changesofofWS
WS(m)
(m)
changes
Changes in water surface elevations determined for the mean flow are shown in Figures 11 and
12. The first graph consists of results of simulations performed assuming the MPM formula, and the
12. The first graph consists of results of simulations performed assuming the MPM formula, and the
second with the EH formula. As previously mentioned, the blue line represents average changes and
second with the EH formula. As previously mentioned, the blue line represents average changes and
the black lines are extreme values, minimum and maximum. As expected, the changes in bottom
the black lines are extreme values, minimum and maximum. As expected, the changes in bottom
elevations are not the same as those in the water surface elevations. The relationship between these
elevations are not the same as those in the water surface elevations. The relationship between these
two
is indirect. The changes in the water surface elevations depend, not only on11local
Watercharacteristics
2017, 9, 168
of 14
two
characteristics
is indirect. The changes in the water surface elevations depend, not only on local
increase or decrease in the bed, but also on the entire profile of the bed along the channel reach.
increase or decrease in the bed, but also on the entire profile of the bed along the channel reach.
Hence, the changes in the bed, downstream or upstream of a particular cross-section, may also affect
Hence,
the bed,As
downstream
upstreamthe
of ablue
particular
cross-section,
may
also affect
second the
withchanges
the EHin
formula.
previously or
mentioned,
line represents
average
changes
and
the local water surface.
the
the local
blackwater
lines surface.
are extreme values, minimum and maximum. As expected, the changes in bottom
When the calculations are made with the MPM formula, the highest changes are clearly visible
When are
the not
calculations
madein
with
MPM
formula,
the highest
changes are between
clearly visible
elevations
the same are
as those
the the
water
surface
elevations.
The relationship
these
in the upper part of the reach. In this zone, the maximum increase in the water surface reaches one
in
the
upper
part
of
the
reach.
In
this
zone,
the
maximum
increase
in
the
water
surface
reaches
one
two characteristics is indirect. The changes in the water surface elevations depend, not only
on local
meter. In the downstream part, the maximum changes are about 30–40 cm. It is important to note
meter.
downstream
part,but
thealso
maximum
changes
areofabout
30–40
cm.
is important
note
increaseInorthe
decrease
in the bed,
on the entire
profile
the bed
along
theItchannel
reach.to
Hence,
that the scatter of the results is small. Such results contrast with those representing the changes in the
that
the
scatter
of
the
results
is
small.
Such
results
contrast
with
those
representing
the
changes
in
the
the changes in the bed, downstream or upstream of a particular cross-section, may also affect the local
bed profile.
bed
profile.
water surface.
1.2
1.2
0.9
0.9
0.6
0.6
0.3
0.3
0.0
0.0
0
0
5000
5000
lower limit
lower limit
10000
10000
distance (m)
distance (m)
upper limit
upper limit
15000
15000
20000
20000
average
average
changesofofWS
WS(m)
(m)
changes
Figure
The
water surface
along the Ner River calculated
Figure 11.
The changes
changes in
in the
surface elevations
elevations for
for mean
mean flow
calculated
Figure
11. The
changes
in
the water surface
elevations
for
mean
flow along the Ner River calculated
with the Meyer-Peter and Müller (MPM) formula.
with the Meyer-Peter and Müller (MPM) formula.
1.2
1.2
0.9
0.9
0.6
0.6
0.3
0.3
0.0
0.0
0
0
5000
5000
lower limit
lower limit
10000
10000
distance (m)
distance (m)
upper limit
upper limit
15000
15000
20000
20000
average
average
Figure 12.
12. The
The changes
changes in
in the
the water
water surface
surface elevations
elevations for
for mean
mean flow
flow along
along the
the Ner
Ner River
River calculated
calculated
Figure
Figure
The changes in the
water
surface elevations for mean flow along the Ner River calculated
with the12.
Engelund-Hansen
(EH)
formula.
with the Engelund-Hansen (EH) formula.
with the Engelund-Hansen (EH) formula.
When the calculations
made with
formula,
the
highest
changes
visible
According
to the resultsare
obtained
withthe
theMPM
EH formula,
the
highest
changes
in are
the clearly
water surface
According to the results obtained with the EH formula, the highest changes in the water surface
in the upper
of the reach.
this zone, the
increase
theabout
water90surface
reaches one
elevations
arepart
observed
in the In
downstream
partmaximum
of the reach.
Theyin
are
cm. However,
the
elevations are observed in the downstream part of the reach. They are about 90 cm. However, the
meter. In the
downstream
part, the
arethe
about
30–40 cm.and
It isupstream
important
to note
differences
between
the increases
inmaximum
the water changes
surface in
downstream
parts
are
differences between the increases in the water surface in the downstream and upstream parts are
that the scatter
of theobserved
results isfor
small.
results contrast
with
those
representing
changes
in the
the
smaller
than those
the Such
calculations
with the
MPM
formula.
In thethe
upper
part,
smaller than those observed for the calculations with the MPM formula. In the upper part, the
bed profile.
average
increments are about 50 cm. It should be pointed out that the scatters, marked as red error
average increments are about 50 cm. It should be pointed out that the scatters, marked as red error
to the results
with
the EH formula,
highest changes
waterformula.
surface
bars, According
are significantly
higher obtained
than those
following
from thethe
implementation
of in
thethe
MPM
bars, are significantly higher than those following from the implementation of the MPM formula.
elevations
are observed
in downstream
the downstream
part about
of the30reach.
are about
90 cm. However,
They
are about
50 cm in the
part and
cm in They
the upstream
one.
They are about 50 cm in the downstream part and about 30 cm in the upstream one.
the differences
increases
in impact
the water
surface inaccumulation
the downstream
and upstream
parts are
The resultsbetween
obtainedthe
show
that the
of sediment
on water
surface elevation
The results obtained show that the impact of sediment accumulation on water surface elevation
smaller
thanflow
thosemay
observed
for the
withisthe
MPM formula.
theimpact
upper part,
the average
with
mean
be about
0.5calculations
m. This value
comparable
withInthe
of other
factors
with mean flow may be about 0.5 m. This value is comparable with the impact of other factors
incrementsinare
about 50such
cm. It
pointed impact
out thaton
themaximum
scatters, marked
as red
error bars,
are
described
literature,
asshould
climatebechange’s
flows and
maximum
water
described in literature, such as climate change’s impact on maximum flows and maximum water
significantly higher than those following from the implementation of the MPM formula. They are
about 50 cm in the downstream part and about 30 cm in the upstream one.
The results obtained show that the impact of sediment accumulation on water surface elevation
with mean flow may be about 0.5 m. This value is comparable with the impact of other factors described
in literature, such as climate change’s impact on maximum flows and maximum water stages [37–39],
inaccuracies in the DEM causing errors in the generation of flood hazard zones [40,41], etc.
Water 2017, 9, 168
12 of 14
It should also be indicated that the stability of the obtained averaged elevations are satisfactory
in both cases. The only doubts are related to relatively huge scatters obtained with the EH formula;
the reason for this is supposedly the influence of the boundary conditions.
5. Conclusions
The applied model of the Ner River including flow and sediment processes is prepared on the
basis of commonly available data. It is undoubtedly a great advantage of the presented methodology.
The methodology applied is based on GIS, simulation models, and statistical analysis. Its main
elements are a sediment routing model and hydrodynamic calculations. The main concept is to
formulate a 10-year forecast of sediment deposition and erosion in the selected reach of the Ner River.
The approach discussed takes into account uncertainty related to (1) unknown inflows and (2) the
form of formula for calculation of sediment intensity. To cope with the problem of unknown inflows,
20 scenarios of 10-year duration are composed on the basis of historical hydrographs. The problem
of proper calculation of sediment transport intensity is solved by testing of two formulae, namely
(1) Meyer-Peter and Müller (MPM) and (2) Engelund-Hansen (EH). The bed geometries resulting
from sediment transport simulations are then used for the calculation of hydraulic conditions for the
average of annual mean flow. Finally, the results are compared. On this basis, the validity of the results
is estimated and the possible impacts of the sedimentation on water surface profiles are assessed.
There are significant differences in the obtained results related mainly to the type of formula
chosen for the calculation of sediment transport intensity. In both cases the deposition is the dominant
process in the selected reach of the Ner River. According to the simulations with the MPM formula, the
material is non-uniformly distributed along the channel. The uncertainty related to the inflow scenario
is higher in this case. The simulations with the EH formula provided much more stable results, as the
distribution of the deposits was more uniform. Such results are more compatible with the earlier
observations of sedimentation process in the Ner River. Although the changes in the bed elevations
also have an impact on the water surface profiles, the relation between these two characteristics is
not obvious. The results of hydraulic computations on the basis of bed geometries resulting from
sediment simulations are a little bit confusing. Greater non-uniformity of changes follow from the
tests with MPM. The changes in the water surface elevations are more uniform when assuming the
EH formula. However, the results obtained with MPM seem to be more stable than those with EH,
taking into account only water surface. This observation is very interesting and opens ways for
further investigation.
Taking into account the uncertainty of available data, the presented methodology enables
assessment of potential impact of sedimentation on the magnitude and distribution of water stages.
It also enables estimation of sedimentation and channel capacity changes, and their influence on flood
hazard and other threats. It seems to be really important to consider the impact of such processes as
sediment accumulation and removal in long-term water management of rivers.
Author Contributions: Tomasz Dysarz, Ewelina Szałkiewicz and Joanna Wicher-Dysarz contributed equally in
the work and in the production of the present manuscript.
Conflicts of Interest: The authors declare no conflicts of interest.
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