Instantaneous release problems in natural rivers ... - MANHAZ

Instantaneous release problems in
natural rivers: experiments and
alarm models.
Paweł M. Rowiński
Institute of Geophysics
Polish Academy of
Sciences
Warsaw, Poland
orkshop on Modelling of pollutant transport in water bodies for decision making
ay 30 - 31, 2005, Centre of Excellence MANHAZ

Natural Rivers – Plan View
• Straight
• Sinuous
• Meandering
•Braided
• Anabranching
• Anastomosing
Morphology

Riverine wetlands
• Riverine wetlands form as linear strips,
generally paralleling river & stream
channels.
• They are found at lower elevations in a
floodplain and tend to be more frequently
inundated and for a longer duration than
areas at slightly higher elevation.

Cleaning or
Filtering pollutants
From surface waters
Riverine Wetlands
Accumulation of harmful substances
May become disastrous
Habitat for wildlife &
plants
e.g. wildlife
mortality!

AIMS
• understanding of the mechanisms governing
pollution transport in the river wandering
through a wetland area.
• creation of respective mathematical models
of the pollution transport in the stream as a
starting point

AIMS -CONTINUATION
CONTINUATION
• Evaluation of the threats by an accidental
release of the pollutants at the downstream
locations in a complex multi-channel river
system.
• Particular aim: determination of
concentration pattern of accidental inputs of
toxic materials within the Narew National
Park.

The Upper Narew River
within
the Narew National Park
Legend
Kurowo
Radule
Waniewo
Kruszewo
Łupianka Stara
boundary of NNP protective zone
river
boundary of Narew National Park
0 2 050 4 100 8 200
Meters
Rzędziany
Izbiszcze
Łapy
Bokiny
Uhowo
Topilec
Choroszcz
Baciuty
Suraż

Narew – anastomosing river
In case of the Upper Narew we
deal with the multi-channel system
on a flood plain but in contrast to
the typical braided rivers, they are
represented by relatively small
slopes.
Anastomosing multichannel streams
evelop when vegetation has stabilized the
ream banks and the channel.

There are islands between
various channels seen at normal
stages of water but from time
to time they are flooded for
the period of days and weeks.

Methods
• Tracer study in which a known mass of a
conservative solute (Rhodamine WT) is released
into the stream.
• Study consists in the examination of the
concentration versus time of the artificially
released dye at downstream stations and fitting
appropriate models.
• DEVELOPMENT OF MATHEMATICAL
MODEL

Hydrological Survey
• A precondition for a proper understanding
of the physical processes that occur in a
river (and among them the processes
governing the transport of pollutants) is a
detailed recognition of hydrological and
morphometric state within the river channel
and possibly on the floodplains.

Hydrological Survey urvey (NNP)
• Description of channel network
• Streamwise velocity field
• Discharges at selected cross-sections
• Water surface slopes (along whole river
reach and local) and bed slope
• Hydraulic and topographic characteristics

GPS SURVEY
RESULTS

Geodesy

Terrain diversity

Velocity measurements

Example of velocity distribution

x 1
Hydraulics computations
h 1
z v 1 (x,y)
x
y
Q
z
x 2
x
h 2
v 2 (x,y)
y
x

Cross-section Cross section survey layout
LEGEND
HG44
G43
HG42
HG41
0 330 660 1 320
Meters
HG40
Floodplain limits
HG39
HG38
HG37
Cross-section

elevation [m a.sl.]
124
123
122
121
120
119
118
117
116
115
The generated, obtained from a field survey,
and simplified G5 cross-section
cross section
G6
generated
measured
simplified
0 200 400 600 800 1000 1200 140
distance [m]

Flood wave routing through the
Narew river - computations

Unsteady flow routing
through the main channel

Dynamic wave model for synthetic hydrograph
Qt ( ) = Q + Qexp( −( t−T) /( T −T))(
t/ T)
discharge [m3/s]
35
30
25
20
15
10
5
0
b 0
p g p p
HG0
HG18
HG27
G33
HG37
HG44
0 100 200 300 400 500 600 700 800 900 1000 1100 1200
( T /( T −T
))
p g p

discharge [m3/s]
50
40
30
20
10
0
Flood wave – spring 2004
HG0
HG18
HG27
G33
HG37
HG44
0 100 200 300 400 500 600 700 800 900 1000

Unsteady flow routing of
overbank flows

water level [m a.s.l.]
117
116.5
116
115.5
115
114.5
114
113.5
Recorded and simulated water elevations
at Bokiny village cross-section
cross section
measured
simulated
0 1000 2000 3000 4000 5000
time [h]

Maximum water levels at the cross-sections cross sections HG18
120
118
116
Elevation [m above sea level]
maximum water level
1980a
1978
1980b
1981
1979
114
0.00 206.75 413.50 620.25 827.00
HG18
Distance [m]

looded area maps for
e typical
lood ood wave recorded in 1978
LEGEND
1978
0 500 1 000 2 000
!
HG27
!
G24
!
!
G28
G23
!
HG44
HG22
!
!
G21
!
!
G43 HG41
!
!
!
!
!
HG42 HG40
HG42
!
HG38
! HG31
G29 G30
HG18
!
!
!
!
HG16
!
G15
G14
HG11
!
G10
!
!
!
G9
G8
G33
!
G7
!
!
!
G6
HG5
HG36
HG34
!
!
HG37
G3 !
G2
!

Dye tracer test
• The method of instantaneous injection of the
tracer was applied
• The dye release consisted of 20 liters of 20%
solution of Rhodamine WT at the cross-section
just downstream of the bridge at Suraż.
• Concentrations were measured at six transects
(3.62 km, 8.34 km, 9.01 km, 9.23 km, 13.58 km,
and 16.83 km). First cross-section was established
at a distance at which 1D conditions were
supposed to be achieved.

o gain more understanding
recognition of hydraulics
conditions is needed
Tracer test

Spreading of Rhodamine WT at the early stage
where lateral mixing occurs

The stage where the tracer is mixed across

Variation of concentration with time at the
cross-sections cross sections downstream of the injection
c(t)
800
700
600
500
400
300
200
100
0
2-N
3-N
5-N
6-N
7-N
0 5 10 15 20 25 30 35 40
time [hours]

Why the mathematical
treatment of pollution transport
offers so many difficulties?

50
45
40
35
30
25
20
15
10
5
0
U [cm/s]
Vertical 13 y = 4 cm
Firstly:
River flow turbulence
Test 2 U = 19.4 cm/s
Test 3 U = 6.1 cm/s
Test 1 U = 38.5 cm/s
0 20 40 60 80 100 120 140 160 180
t [s]

Secondly:
Extremely complex geometry
especially in wetland areas

Modeling concept

Flow Q
Lateral
inflow
Main channel
Exchange due to
transient storage
Transient
storage
Small rivers
Main channel
wetlands
Transient storage
Side pockets,
hyporheis stratum,
bed irregularities
Downstream
transport
Advection and
dispersion
Outflow

Storage zone

Models of pollution transport
Steady and uniform flow conditions
2
∂C ∂C ∂ C ε
+ U − D = C 2
D −C
∂t ∂x ∂x
T
Steady but non-uniform flow conditions
Transient storage
zones
Main channel
∂C ∂C
1 ∂ ⎛ ∂C
⎞ ε
+ u − ⎜ DA ⎟ =
∂t
∂x
A ∂x
⎝ ∂x
⎠ T
∂C 1
=
∂t
T
( C − )
D CD
( )
( C C)
D −

Schematic representation of the solution
method – splitting technique
TRANSPORT
input output
input
advection
output
advection dispersion storage zone
advection
advection -
dispersion
output
upwind
scheme
dispersion
Crank - Nicholson
scheme
storage
zones
Runge – Kutta
method
output

Identification of model
parameters

Optimization Procedure 1 – based on frequency
response function
⎡ 2 2 3
U x 2 4DεTω 4 D( T ω + ω+ εω)
⎤
H( x, iω) = exp⎢ x− U + + i
2 2 2 2 ⎥
⎢⎣ 2D 2D T ω + 1 T ω + 1 ⎥⎦
Optimization procedure on the reach by reach basis
with specially designed objective function comparing
the reverse of Fourier transformation of function H and
the measured concentrations.

Another formulation of optimization problem
Criterion for parameters derivation
[ ] ( ) ( ) 2
TH
⎧ K
⎪ ⎫⎪
min ⎨FuD , , ε,
T = ∑ ∫ ⎡⎣Cx, t −Cx,
t⎤⎦ dt⎬
⎩ ⎭
m k k
uD , , ε , T
⎪ k = 2 0
⎪
Constraints for the
problem
Water continuity equation
( )
X ≤ X x ≤ X
min max
Q= uA

Control Random Search
Start of computations – set of points
Determination of the best xL and
the worst xH from the given set
Formation of a simplex containing x L
xn+1 - result: new point xW Reflection of the last point from simplex
Replacement of x H by x W
Stop criterion
F − F x
sr
( L ) < ε
x 1
constant values of objective function
optimum
simplex 3
simplex 2
simplex 1
The searching rule for the domain
of the objective function by means
of simplex method
x 2

Dead-zone Dead zone model parameters –
E L [km 2 /h]
ε
T[h]
U a [km/h]
Parameters
[0-N,2-N]
0.0027
0.0920
0.4530
0.5200
Upper Narew
[2-N,3-N]
0.0220
0.0120
0.6550
1.8400
[3-N,5-N]
0.0051
0.7920
11.2570
0.4880
Sections
[5-N,6-N]
0.0338
0.3690
7.0706
1.6200
[6-N,7-N]
0.0034
0.2260
0.9030
0.7800
[0-N,7-N]
0.0120
0.1020
1.440
0.9190

Examples of measured and dead-zone dead zone
model results
0,40
0,35
0,30
0,25
0,20
0,15
0,10
0,05
0,00
Dimensionless concentration
10 15 20 25 30 35 40
time [hours]
experimental data
model

Continuation of studies
• Computations under flood conditions, also
when the entire floodplain is inundated.
• The above requires a very good recognition
of the topography of the entire valley
• Flow computations based on CCHE models
– currently conducted

Concluding remarks
• It is shown that because of the asymmetric nature
of all the observed breakthrough curves, the
temporary storage of the admixture plays a crucial
role in the analyses of the pattern of its spread in
the multi-thread river system. This reflects the
interactions with the adjacent wetland areas (high
values of ε
in the model)

Concluding remarks -cont cont
• A tracer test definitely facilitates the analyses and
quantification of the hydrodynamic and also
chemical processes in surface waters, particularly
in such complex environment as the Upper Narew.
Because of its complete safeness for the
environment such method is recommended as a
tool for the recognition of the system behavior.

THANK YOU FOR
YOUR ATTENTION