),
Chen-Chien Li
and Bernhard Westrich
Institut für Wasserbau, Universität Stuttgart
Pfaffenwaldring 61, D-70569 Stuttgart, Germany
Tel: +49-(0)711-6854727; Fax: +49-(0)711-6854681;
E-mail: li@iws.uni-stuttgart.de
Abstract:
Due to the interactions of complex processes in a
river system and the variability of the process parameters stochastical concept
has been combined with a deterministic transport model to simulate suspended
sediment transport. Stochastic characteristics of the governing parameters such
as river discharge and concentration of suspended matters are introduced to cope
with the uncertainty of the forecasting calculation results. For a 11 km lock
regulated river section long term simulations were carried out using stochastic
generated discharge data. The water level, sediment erosion volume and river bed
evolution are of interest. A statistical summary plot was made to show the
quantiles of predicted water levels. The impact of flood events on the sediment
transport process with regard to the peak flow rate and flood duration were also
investigated. The result shows that 1750 m3/s will be the maximum
peak flow rate of the possibly coming flood event and a reduction of the deposit
height of about 1.5m will be expected during this period.
Keywords:
stochastic, uncertainty, data generation, water
level, erosion rate, deposit height, sediment mobility, resuspended sediment
mass
Numerical models are widely applied to design hydraulic structures and evaluate alternative strategies of river sediment management. Although numerical models have been improved and refined to reduce the model uncertainty in the description of sediment transport processes in the river, those models based on deterministic concept still have to cope with the variability and uncertainties of the field data used for model calibration. Due to the budget and time limitation, there are only a few field data sampled to execute the model calculation. Therefore, it has become a very important task in engineering practice to cope with and account for the uncertainty of model input data.
In river engineering, uncertainty analysis has been introduced mainly for dike design in recent years. In combination with the method of reliability analysis, first order second moment analysis was used to estimate the dike height for a T years flood (Plate, 1998). Another approach is using parameter statistics inferred from field data to estimate the flow variables (Gates and Al-Zahrani, 1996).
Due to interaction of hydrological , hydrodynamic and sedimentological processes, the spatial and temporal variability of the process parameters suspended sediment transport has to be modeled by a deterministic transport model, in combination with a probabilistic concept. Therefore, stochastic characteristics of the governing parameters such as river discharge, suspended sediment inflow concentration and parameters describing the beginning and rate of erosion and sedimentation, respectively are considered should be regarded as stochastic variables. In this Paper, the influence of the variability of those flow and sediment parameters on the water level, the river bed evolution and sediment erosion volume as well will be investigated to provide a probabilistic information as a base for optimum river sediment management.
A calibrated one dimensional flow and sediment transport model (Kern and Westrich, 1996) is applied to execute long term numerical simulations to predict the highest possible water level and the changes of t on the respective river bed. The numerical compartment model consists of finite-difference sub-models for flow, transport of suspended sediments which is coupled with a sub-model for a sediment layering. The model accounts for the convective and dispersive transport, turbulent mixing at the water-sediment interface, deposition, consolidation, aging and erosion of sediment.
The model was applied to the 11 km long lock-regulated section of the Neckar river near Lauffen located in the south-western Germany. Simulations were carried out using stochastic generated discharge data series (Kern, 1997) with 365000 realizations each. The 10 discharge series were generated from the measured series from 1950 to 1995. The inflow concentration of the suspended sediments was calculated using an experimentally determined power law function (Kern, 1997).The calculated results of each realizations were summarized, sorted and then shown in a statistical summary plot.
The sediment erosion potential of floods in the river section is also studied using the numerical model. Three section from the available discharge date series from 1950 to 1995 were chosen as three different flood hydrographs. The aim is trying to get a general view of the influence of peak flow rate and the flood duration on the resupension of sediment mass. A related subject is the change of river bed due to floods.
All calculation are carried out using
the results of a long term simulation for the period of 01.01.1950 to
30.06.1994. The fall velocity of suspended sediment is 3.2´10-4
m/s (Kern, 1997). The following equation(Kuijper et al. 1989) was introduced for
calculating erosion rate(
),
where M=erosion coefficient, t0=shear stress, tc,E=the critical shear stress for erosion, n=empirical constant. M, tc,E and n are set to be 7.5´10-4kg/m2s, 1.25Pa and 3.2 respectively.
Fig. 1(a) shows the minimum and maximum values, the 16%, 50%, 84% and 99% quantiles of the predicted water level of simulations carried out for all computted realizations. The maximum value could be taken as the requested height of a dike to protect against any possible flood. Because there is a large difference between the 99% quantil and the maximum values the decision should be made after a economical analysis. The irregular points may result from data errors. Another data series was generated from the discharge series from 1978 to 1994 because there were several flood events registered in that period. The statistical plot of the results using these data series (Fig. 1(b)) shows a similar trend. From the statistical view the peak flow rate is the dominating factor no matter the whole discharge data set or a partial data set is used as the base of discharge data generation. If the data series from 1950 to 1994 is still used, the result (Fig. 1(c)) shows that only the calculated maximum water level is lower than in case of Fig. 1(a) and 1(b) because the peak flow rate of this discharge serie set is lower than that of the generated series. It implies the great influence of the peak flow rate again although the occurance probability is small.
Fig. 1 Statistical summary plot of the calculated water level: (a)using discharges generated from the available series from 1950 to 1994; (b) using discharges generated from the available series from 1978 to 1994; (c) using the available discharge series from 1950 to 1994.
Sediment resuspension is an important process caused by floods. Three hydrographs as shown in Fig. 2 (a)-(c) were chosen for the calculation. Fig. 3(a)-(c) depicts the mass balance for the observed reach for each calculation. A reduction of the deposited sediment mass means a resuspension of previously deposited suspended matters. According to the calculation erosion of the sediment will occur if the discharge is greater than 200 m3/s. The hydrograph (a) and (b) have the same effect on sediment resuspension. The change is as similar as to the curve type of the two hydrographs. In case of the hydrograph (a) the sediment mass changes abruptly whereas the sediment mass in case of the hydrograph (b) gradually. The hydrograph (b) has a lower peak flow rate but a longer duration. Although the hydrograph (c) has a peak flow rate about 1000m3/s, the change of deposited sediment mass is smaller by one order.
The extent of the eroded sediment mass will be larger if there is a combined effect of peak flow rate and duration. This is inferred from Fig. 3(d)-(f) resulting from the hyrographs shown in Fig. 2(d)-(f).
Fig. 2 Hydrograph of the chosen floods
Fig. 3 Mass balance of the chosen flood events
The change of the river bed elevation due to flood events was investigated. Because there is no apparent change in the section between km 136.28 and km 130.0. The study was focused on the section between km 130.0 and km 125.1. Again, the hydrographs in Fig.2 were used for the calculations. Only the deposited sediment thickness at the beginning and at the end of the erosion process was depicted for each flood event. The hydrograph (a) and (b) has the same effect on the depopsited sediment thickness downstream of km 129.0. The hydrograph (a) result in no net erosion between km 130.0 and 129.0, and the hydrograph (b) result in no net erosion between km 126.0 and km125.0. The change in case (c) is surprisingly small. Less suspended particulate matters entered and accumulated in the reservoir reach hence, the erosion extent is smaller.
The influence of the duration of a flood event on the sediment erosion depth is illustrated in Fig. 4(a)-(c) as compared with Fig. 4(d)-(f), especially if a flood event has a relatively high peak flow rate, for example hydrograph (d). In this case, local degradation of the river bed about 1.5m was calculated at in cross section km125.2, km 125.4 and km 125.5 .
Fig. 4 Change of the deposited sediment thickness
Fig. 5 Change of the height of the bed deposit(continued)
The concept allows to investigate the effect of the discharge hydrograph on cohesive sediment erosion process. It is also possible to make a probabilistic quantification of relevant design parameters such as water level, erosion volume of sediment to make the predictive simulation compatible with nature. It shows the reliability of results as depending on stochastic input data.
A statistical summary plot shows the exceedance probability for a certain water level. It is an important information for the design of levees. This approach can also applied to investigate the influence of the variability of other model parameters involved in the complex fluvial transport such as the critical erosion shear stress.
Mass balance of the whole investigated reach and the change of river bed provide important information about the suspended sediment transport process during a flood event. The peak flow rate and the duration a flood event are two significant factors for suspended sediment transport. The two factors would amplify the effect when they are joined together. It will be the next task to use bivariable statistic method to estimate the possibility of a predicted coming flood event with a certain duration firstly and to find whether there is a correlation between peak flow rate and duration and the extent of the change of the river bed.
References
Gates, T.K. and Al-Zahrani, M.A. (1996): Spatiotemporal stochastic open channel flow II: Simulation experiments, Journal of hydraulic engineering, Vol. 122, No. 11.
Kern, U. (1997): Transport von Schweb- und Schadstoffen in staugeregelten Fließgewässern am Beispiel des Neckars, Mitteilung des Intituts für Wasserbau, Heft93, Universität Stuttgart (in German).
Kern, U. and Westrich, B. (1996): Mobiltät von Schadstoffen in den Sediment staugeregelter Flüsse- Natur versuche in der Stauhaltung Lauffen, Modellierung und Abschätzung des Remobilisierungsrisikos kontaminierter Altsedimente. Wissenschaftlicher Bericht Nr. 96/23 (HG 237), Institut für Wasserbau, Universität Stuttgart (in German).
Kuijper, C., Cornelisse, J.M. and Winterwerp, J.C.: Research on erosive properties of cohe sive sediments, J. Geophysical Research 94(C10), 1989.
Plate, E.J. (1998): Stochastic Hydraulic Modelling - A Way to Cope with Uncertainty, Proceedings of the 3rd International Conference on Hydro-Science and –Engineering, Cottbus/Berlin, Germany.