Proceedings of the Seventh International Conference on Hydroscience and Engineering, Philadelphia, PA, September 2006.  http://hdl.handle.net/1860/732Accidental river pollution is a severe hazard to all rivers. To mitigate the consequences of a possible
contamination of the river Elbe the contaminant transport model ALAMO (alarm model Elbe) was
developed. This dead-zone-model (DZM) was calibrated and verified by nine dye experiments. The
experimental set-up comprises measurements with in-situ and ex-situ fluorometers and fluorescence
spectrometers. The experiments were carried out for a wide range of discharge conditions. In order
to account for different discharges the model coefficients of longitudinal dispersion and lateral
exchange were parameterized by a power-law relationship depending on the river geometry. A
comparison of the experimentally determined tracer concentration curves with those derived with
ALAMO gave good agreement. The error of the time of travel, the width and the asymmetry of the
tracer cloud amounts to 8 %, 10 % and 12 % at a maximum

Barjenbruch, Ulrich

Lippert, Dieter

Mai, Stephan

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Proceedings of the 7th International Conference on HydroScience and Engineering 
Philadelphia, USA September 10-13, 2006 (ICHE 2006) 
ISBN: 0977447405 
 
Drexel University 
College of Engineering 
 
 
 
 
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The 7th Int.  Conf. on Hydroscience and Engineering (ICHE-2006),Sep 10 Sep 13,Philadelphia,USA 1 
 
 
 
 
 
 
STUDIES OF TRACER TRANSPORT IN THE RIVER ELBE 
 
 
Stephan Mai1, Dieter Lippert2 and Ulrich Barjenbruch3 
 
 
ABSTRACT 
 
Accidental river pollution is a severe hazard to all rivers. To mitigate the consequences of a possible 
contamination of the river Elbe the contaminant transport model ALAMO (alarm model Elbe) was 
developed. This dead-zone-model (DZM) was calibrated and verified by nine dye experiments. The 
experimental set-up comprises measurements with in-situ and ex-situ fluorometers and fluorescence 
spectrometers. The experiments were carried out for a wide range of discharge conditions. In order 
to account for different discharges the model coefficients of longitudinal dispersion and lateral 
exchange were parameterized by a power-law relationship depending on the river geometry. A 
comparison of the experimentally determined tracer concentration curves with those derived with 
ALAMO gave good agreement. The error of the time of travel, the width and the asymmetry of the 
tracer cloud amounts to 8 %, 10 % and 12 % at a maximum. 
 
 
1. INTRODUCTION 
 
The European Water Directive 2000/60/EC (article 11 (3) l) (European Parliament 2000) requires 
measures to reduce the impact of accidental pollution incidents for each river basin district. 
Therefore the International Commission for the Protection of the River Elbe (IKSE), working group 
H - Accidental River Pollution, worked out the International Alarm Plan Elbe (2004). 
The Alarm Plan Elbe regulates the messaging in case of accidental river pollution including 
the forecast of the contaminant transport. This forecast of the contaminant transport is based on the 
numerical model ALAMO, i.e. alarm model Elbe (Mai et al. 2006). ALAMO was developed by the 
German Federal Institute of Hydrology in cooperation with the Leichtweiss Institute and the Czech 
institutes Povodi Labe, CHMU and VUV. The model covers the whole stretch of the not tidally 
influenced river Elbe. Figure 1 gives a sketch of the model area with the Czech part from Jaromer to 
Schöna and the German part from Schöna to Geesthacht. The model covers a total length of 900 km. 
The basic idea of the model ALAMO was given by Taylor (1953) describing the dispersion of 
contaminants along the river. This concept of ALAMO was extended by Hays et al. (1966) to 
account for the exchange of contaminants between the main stream of the river and the still water 
zones near the river banks. For the calibration of the model ALAMO nine dye studies were carried 
out from 1997 to 2005. Both, modeling concept and dye studies, are described in the following. 
                                                 
1 Research Associate, Department of Hydrometry and Hydrological Survey, Federal Institute of Hydrology, Am Mainzer 
Tor 1, 56068 Koblenz, Germany (mai @ bafg.de) 
2 Research Assistant, Department of Hydrometry and Hydrological Survey, Federal Institute of Hydrology, Am Mainzer 
Tor 1, 56068 Koblenz, Germany (lippert @ bafg.de)  
3 Head of Department, Department of Hydrometry and Hydrological Survey, Federal Institute of Hydrology, Am 
Mainzer Tor 1, 56068 Koblenz, Germany (barjenbruch @ bafg.de) 
  2 
 
 
Figure 1 River Elbe form Jaromer to Geesthacht - extend of the model Alamo. 
 
 
 
2. MODELING CONCEPT 
 
ALAMO includes the physical processes of advection, dispersion, diffusion in the main stream, the 
exchange between the main stream and the still water zone, as well as the degradation of pollutants 
in main stream and still water zones. These processes are described by the following fundamental 
set of differential equation  
 
 c k)sc(D 
x
cD
x
cv
t
c
S2
2
L −−ε−∂
∂
+
∂
∂
−=
∂
∂  (1) 
 
 ( ) s kscD
t
s
s −−=∂
∂  (2) 
 
with the contaminant concentration in the main stream c and in the still water zone s, the flow 
velocity in the main stream v, the coefficient of decay k, the relative area of the dead-water zone ε, 
the longitudinal dispersion coefficient DL, and the exchange coefficient DS between main stream and 
dead-water zone. The set of coupled differential equations is solved using the Rosenbrock-Wanner 
method as given by Rentrop and Steinebach (1997). 
The parameters v, ε, DS and DL of the differential equations (1) and (2) are parameterized with 
the river discharge measured at the gauges given in Figure 1, i.e. 
 
 ε⋅=ε ε
bQa  (3) 
 
 vbv Qav ⋅=  (4) 
 
 LbLL QaD ⋅=  (5) 
 
 SbSS QaD ⋅=  (6) 
 
with the tunable coefficients a and b for each of the parameters.   
  3 
The determination of the coefficients av and bv is based on the results obtained from one-
dimensional numerical modeling described by Drewes et al. (2001) while the determination of the 
coefficients aL, bL, aS, bS, aε and bε is carried out using tracer experiments as described in the 
following chapter. For the longitudinal dispersion coefficient DL and the exchange coefficient DS the 
parameterization is given in Figure 2. Both coefficients increase with increasing river discharge. 
Besides of the river discharge the coefficients are influenced by the geometric properties of a river 
section. An increase in the longitudinal dispersion coefficient and a decrease in the lateral exchange 
coefficient are found for increasing river width as well as for increasing river curvature. As found 
also in laboratory experiments by Weitbrecht (2004), a decrease in the distance of groins or an 
increase of the length of groins lead to a decrease of the lateral exchange coefficient DS. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2 Influence of the river discharge on the longitudinal dispersion coefficient (top right) and the 
lateral exchange coefficient (bottom right) for two different locations at the river Elbe (left). 
 
3. DYE STUDIES 
 
Although first steps to use the geometric properties of a river section for a parameterization of the 
coefficients of longitudinal dispersion and lateral exchange based on results of laboratory 
experiments were undertaken, in-situ dye studies are still essential. For the calibration of ALAMO 
nine dye studies were carried out so far.  
 
Table 1 Tracer experiments for the calibration and verification of ALAMO.  
Date location  
of input 
station 
 
[km] 
mass of 
tracer 
[kg] 
Discharge
Q 
[m³/s] 
mean low 
water 
[m³/s] 
mean high
water 
[m³/s] 
Reference 
29/11/99 Němčice -249,2 2,0 16 12 309 Dostál et al. (2000) 
02/05/05 Němčice -249,2 8,0 52 12 309   
26/04/99 Mělník -104,8 24,0 255 76 1324 Dostál et al. (1999) 
30/11/97 Ústí -37,0 12,1 130 91 1430 Dostál et al. (1998) 
15/07/97 Schmilka 4,1 33,5 330 102 1480 Hanisch et al. (1997) 
29/03/01 Schmilka 4,1 75,8 912 102 1480 Hanisch et al. (2004) 
06/10/04 Mauken 184,5 20,0 136 114 1380   
11/10/99 Elster 200,4 26,0 160 130 1490 Hanisch et al. (2004) 
27/10/98 Elster 200,4 26,4 265 130 1490 Hanisch et al. (2004) 
0
400
800
1200
1600
lo
ng
itu
di
na
l d
is
pe
rs
io
n 
[m
/s
²]
W ittenberg (km 214)
W ittenberge (km 434)
0 400 800 1200 1600 2000
river discharge  [m³/s]
0.40
0.50
0.60
0.70
0.80
ex
ch
an
ge
 c
oe
ff
ic
ien
t  
[1
/h
]
Wittenberg (km 214)
Wittenberge (km 434)
 
 
Wittenberge (km 434)
 Wittenberg (km 214)
  4 
 
 
Figure 3 Locations of dye input along the river Elbe. 
 
 
 
Figure 4 Fluorescence spectrum of the tracer Red Dye (measured with the laser fluorescence 
spectrometer OPTIMOS) 
 
 
 
Figure 5 Input of the tracer Red Dye near Němčice, Czech Republic 
 
  5 
Table 1 characterizes the tracer experiments by the conditions of river discharge prevailing 
during the experiment, the mass of dye and the location of its discharge (see Figure 3). For the 
experiments the non eco-toxic tracer Red Dye (Sulforhodamine G) was used. The fluorescence 
spectrum of Red Dye is given in Figure 4. The spectrum is single peaked with a maximum for the 
wavelength of 554 nm. In case of pulsed excitation the half-life period of the fluorescence intensity 
equals approximately 7 ns.  
 
   
 
Figure 6 In-Situ measurements of dye concentration.  
 
   
 
Figure 7 Sampling and ex-situ quantification of dye concentration. 
 
 
 
Figure 8 Time-series of tracer concentration at eight locations downstream of Mauken in 2004.  
  6 
To enhance mixing in the main stream right at the location of tracer input the dye was 
discharged from a boat traveling across the river (Figure 5). The dye concentration in the 
mainstream and in the still water zones downstream of the location of tracer input is measured using 
in-situ fluorometers and fluorescence spectrometers (Figure 6). The measurements were 
supplemented by automatic sampling and ex-situ fluorescence spectroscopy (Figure 7). 
Using spectrometers it was possible to account for a varying background fluorescence in the 
water body caused by organic matter. However only very little deviations of the tracer 
concentrations derived by fluorometers or by fluorescence spectrometers are found. An example of 
the time concentration curves is given in Figure 8. For the given experiment the tracer cloud travels 
about 2.5 km/h (see also Figure 10). Due to dispersion and storage of tracer in the still water zones 
the peak concentration of the tracer cloud decreases, while its width and asymmetry increases (see 
also Figure 11 and 12). 
 
 
4. VERIFICATION OF NUMERICAL MODELLING 
 
The tracer experiments, listed in Table 1, were recalculated with ALAMO. The model results were 
analyzed at the locations of the measuring devices deployed during the experiments. Figure 9 shows 
a comparison of the measured time-concentration curves and those predicted by ALAMO. Both, 
measured and modeled results, agree quite well. This is also found when analyzing the time of travel 
as well as the width and asymmetry of the tracer cloud. 
 
 
 
Figure 9 Comparison of measured time-concentration curves with those acquired from ALAMO.  
 
The time of travel, which is related to the time tp of the peak tracer concentration, is given in 
Figure 10. The general trend is approximated correctly by ALAMO. This is a sign of a good 
parameterization of the flow velocity (see eq. 4). The maximum deviation of measured and modeled 
time of travel amounts to less than 9 hours, i.e. less than 8 %. The time of travel increases linearly 
with the distance from the location of tracer input. 
The width of the tracer cloud, which relates to the time lack between the end and the 
beginning of tracer passage, i.e. Δt = te - tb, is given in Figure 11. Right after the tracer input the 
width of the tracer cloud increases strongly. However with an increasing time of travel the increase 
of the width becomes smaller. The maximum deviation between modeled and measured width is 
equal to 3 hours, i.e. the deviation is less than 10 %. This indicates an adequate parameterization of 
the longitudinal dispersion coefficient (see eq. 5). 
The asymmetry of the tracer cloud, being defined as the ratio of the time with decreasing and 
the time with increasing tracer concentrations, i.e. Δte / Δtb = (te  tp ) / (te - tb ), is given in Figure 12. 
  7 
The general dependence of the asymmetry of the tracer cloud on the location along the river is met 
indicating the quality of the parameterization of the lateral exchange coefficient (see eq. 6).  
 
 
 
Figure 10 Traveling time of the tracer cloud  measurement vs. ALAMO.  
 
 
 
Figure 11 Width of the tracer cloud  measurement vs. ALAMO.  
 
 
 
Figure 12 Asymmetry of the tracer cloud  measurement vs. ALAMO.  
  8 
5. CONCLUSION 
 
The applicability of the model ALAMO for the prediction of pollutant transport in the river Elbe has 
been shown by comparison with tracer experiments. It is possible to model dispersion using Taylors 
concept. The exchange between main stream and still water zones is modeled adequately using the 
dead-zone concept of Hays et al. It is proofed that the geometry of the river strongly influences the 
processes of longitudinal dispersion and lateral exchange. It is planned to use information on river 
geometry for the parameterization of dispersion and lateral exchange. However dye studies will be 
still necessary for verification. 
 
 
ACKNOWLEDGEMENTS 
 
The authors gratefully acknowledge the cooperative work with the International Commission for the 
Protection of the River Elbe (IKSE) and the very good collaboration with the Czech institutions 
Povodi Labe, CHMU and VUV as well as the Leichtweiss Institute, Germany.  
Special thanks are addressed to the colleagues at the local waterways and shipping offices 
(WSA) in Dresden, Magdeburg and Lauenburg who helped to carry out the tracer experiments in 
2004. 
 
 
REFERENCES 
 
Dostál K., Koza V., Rederer L. (1998) Tracer experiment in the river Elbe (original in Czech: 
Zpráva o testovacím pocusu na Labi), report, Povodi Labe, Hradec Králové, Czech Republic.  
Dostál K., Koza V., Rederer L. (1999) 2nd Tracer experiment in the river Elbe (original in Czech: 
Zpráva o 2. testovacím pocusu na Labi), report, Povodi Labe, Hradec Králové, Czech 
Republic.  
Dostál K., Koza V., Rederer L. (2000) 3rd Tracer experiment in the river Elbe (original in Czech: 
Zpráva o 3. testovacím pocusu na Labi), report, Povodi Labe, Hradec Králové, Czech 
Republic.  
Drewes, U., Ettmer, B. Mende, M. (2001) Hydraulic calculations of the river Elbe from Nemcice to 
the German-Czech border (original in German: Hydraulische Berechnungen von Nemcice bis 
zur deutsch-tschechischen Grenze), report, Leichtweiss Institute, no. 869, Braunschweig. 
European Parliament and the Council of the European Union (2000) Directive 2000/60/EC of the 
European Parliament and of the Council establishing a framework for the Community action 
in the field of water policy (short title: EU Water Framework Directive (WFD)), Official 
Journal of the European Communities, L327/1. 
Hanisch H.-H., Dostál K., Trejtnar K., Vosika S., Specht F.-J., Eidner R. (1998) Tracer 
experiments in the river Elbe (original in German: Traceruntersuchungen in der Elbe), Proc. 
of the 8th Seminar on inland water protection (original German title: Magdeburger 
Gewässerschutzseminar), Magdeburg, Germany, pp 29-32. 
Hanisch, H.H., Mende, M., Ettmer, B. (2002) Operational Prediction of Contaminant Transport 
with the Alarm Model Elbe (in German), 10th Seminar on Water Protection, Magdeburg, 
Teubner, Stuttgart, Germany, pp. 337-338. 
Hanisch, H., Dostál, K., Rederer, L., Specht, F.-J., Mende, M., Stahl, K. (2004) Tracer experiments 
in the river Elbe (original in German: Tracerversuche Elbe), report, German Federal Institute 
of Hydrology, Koblenz, Germany. 
Hays, J.R., Krenkel, P.A., Schnelle, K.B. (1966) Mass Transport Mechanisms in Open-Channel 
Flow, Technical Report 8, Vanderbilt University, Nashvilee Tennessee. 
  9 
IKSE (International commission for the protection of the river Elbe) (2004) International alarm 
plan of the river Elbe (original in German: Internationaler Warn- und Alarmplan Elbe), 
report, Magdeburg, Germany, pp. 1-23. 
Mai, S., Lippert, D. and Barjenbruch, U. (2006) Operational Modeling of Contaminant Transport in 
the River Elbe, Proc. of the 7th Int. Conf on Hydroinformatics, Nice, France, Vol. 1, pp. 16-
23. 
Rentrop, P., Steinebach, G. (1997) Model and numerical techniques for the alarm system of river 
Rhine, Surveys on Mathematics for Industry, Vol. 6, pp. 245-265.   
Taylor, G.I: (1953), Dispersion of Soluble Matter in Solvent Flowing Slowly Through a Tube, 
Proc. R. Soc. London, Ser. A 219, pp. 186-203. 
Weitbrecht, V. (2004) Influence of dead-water zones on the dispersive mass transport in rivers, 
Universitätsverlag Karlsruhe, Germany.   
 


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