**5. Conclusions**

158 Current Issues of Water Management

<sup>2</sup> 0.04 *L x D* Δ

0.05

*<sup>x</sup> <sup>T</sup> D* Δ

*<sup>x</sup> <sup>x</sup> <sup>T</sup> u D*

*L*

0.09

2

*L*

0 400 800 1200 1600 2000

Time in min

Fig. 9. Pulse responses of the hybrid at the end of 3.2 km, 16 km and 26 km for the data

26km

Δ

2

(Ghosh et al., 2004; Muthukrishnavellaisamy K, 2007; Ghosh et al., 2008) as follows:

α

1

Δ

2

/ which should be greater than or equals to 4 and less than 8

= (18)

= (19)

= − (20)

Dash lines (R=1.0) Solid lines (R=2.1)

Peclet number, *P xu D e L* =

0

collected from river Brahmani

0.2

Concentration in mg/L

0.4

0.6

Δ

3.2km

16km

A Hybrid model coupled with hyporheic exchange has been derived by incorporating a time delay factor termed as "retardation factor" with each of the three compartments in the hybrid model to simulate retardation governed pollutant transport in riparian streams or rivers. A linear equilibrium condition between the concentration of pollutants in the hyporheic zone and the mainstream water has been considered. The stagnation or dead or hyporheic zone retards the transport of downstream pollutants. The hybrid model is a fourparameter model representing three time parameters and one constant factor. Theoretical study on non-equilibrium exchange of pollutant has also been done to demonstrate the model.

The unit step response and the unit impulse response functions of the hybrid model have been simulated with synthetic data and limited field data. The characteristics of the concentration-time profiles generated by the hybrid model are comparable to the physical processes of pollutant transport governed by the advection-dispersion-retardation both in equilibrium and non-equilibrium exchanges in a natural stream. This present model can be used to obtain theoretically exact solutions and can be compared with results of ADE model considering with and without retardation of pollutant transport in a stream along with advection and dispersion processes.

Data regarding the influence of the hyporheic zone to pollutant trap in streams are rare due to the absence of simple techniques to get necessary parameters and complexity of the phenomenon. The pollutant exchange between the main channel and the hyporheic zone is very variable and estimation of exchange rate is mostly inaccurate due to channel irregularities and other complexities. In depth analysis and understanding about the hyporheic exchange will over-come the problem in collecting relevant data from natural streams.

It can be concluded that the presented hybrid model for pollutant transport in streams affected by hyporheic exchange is a useful tool in predicting water quality status streams.

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Simulation of non-equilibrium exchange of non-conservative pollutant between main channel and stagnation zone is vital. As we have considered conservative pollutant in this chapter, the maximum concentrations of pollutant at different locations were same due to mass conservation, but the residence times were different. Thus, this study also gives a retrospect for the extension of the model considering non-equilibrium condition of decaying pollutant exchange for natural streams.
