ADE & ADZ Models

Question 1

Comment on the accuracy of these ADZ predictions and describe the effect of parameter variations on the values.

Answer 1

Using EA data base to obtain estimates for the velocity and dispersive fraction is the main limitation. EA database is okay if there is no other information available. However, a better estimate of the mean velocity could be obtained from flow formulae (e.g) Manning equation) and estimates of the channel properties (e.g. slope, resistance etc.) are available.

There is a large variation (x/- 0.2 m/s) about the assumed mean velocity. A greater velocity will reduce arrival time and allow less time for spreading. The dispersive fraction, describes spreading.

The dispersive fraction, describes spreading processes similar to the conventional longitudinal dispersion coefficient. Some workers believe this has less variation, but Fig.Q4, shows significant scatter. A larger value of Df would increase spreading, reducing arrival time and peak concentration and increasing exposure time.

Question 2

Describe deconvolution, its limitations and application

Answer 2

Techniques like ADE and ADZ assume a model with a Gaussian distribution, time delay and exponential decay. However, these models do not fit well with the observed data. Deconvolution is used to generate a transfer function which fits the output (downstream profile).
Limitations:
You cannot generally determine an analytical solution.
It tends to be based on numerical, algorithmic approaches using data collected for the known variables.
Applications;
River mixing/solute transport
Seismology
Optics/Imaging

Question 3

What is ADE and ADZ?

Answer 3

Advection Dispersion Equation and Aggregated Dead Zone modelling are techniques used to predict a downstream temporal concentration distribution from a known upstream distribution.
The main advantages of ADZ model over ADE model are:
1. Simplicity of solution
2. Prediction of skewness

Both models are based on theoretical/ mathematical modelling of physical processes. Under idealised conditions, such as laminar flow in a pipe, the dispersion coefficient and travel time can be predicted theoretically, through consideration of the velocity profile and diffusion. Such theoretical prediction is not possible with the ADZ model. The parameters must be found through data fitting or from previous data with similar conditions