The use of a particular model depends on the systems to be modeled and on the
legislation in place in that country. Water Quality Models are usually classified into
subdivision categories based on:
1. Identifying the environment modeled
2. Purpose of the model
3. Consideration of the number of ‘dimensions’
4. Description of the main process
5. The data used are discrete observed measurements or statistical distributions, and
6. Consideration of temporal variability.
A model for diffusive flux can be constructed from the following example.
Consider a one-dimensional system with motion in the X direction only (Fig. 3.7).
An interface B-B
0 separates two regions of different concentration, C1 and C2 ¼ particles/volume on the left and right side of the interface, respectively. The motion of
each particle is a one-dimensional random walk. In each time interval, Δt, each
particle will move a distance Æ ΔX, moving right (+ ΔX) or left (À ΔX) with equal
probability.
Within each time step, any particle within a distance ΔX of the interface B-B
0 has
a 50% probability of crossing over that interface. The number of particles with the
potential to cross B-B
0 from left to right (positive mass flux) is (C1 ΔX A), where A is
the area of interface B-B
0 . On average, half of these take a positive step and cross the
interface in time Δt such that the flux left to right is (0.5 C1 ΔX A). Similarly, the
number of particles crossing right to left in Δt (negative mass flux) will be (0.5 C2
ΔX A). The resulting mass flux, q X , is
Threshold = M
1
u(x,t) =
exp
–x 2
4pDt
4Dt
Fig. 3.7 The formula for distance within which the pheromone is sensed is given by
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
À2 D t:Ln 4M
2 π D:t
À
Á
q
3 Surface Water Quality and Analysis
91
legislation in place in that country. Water Quality Models are usually classified into
subdivision categories based on:
1. Identifying the environment modeled
2. Purpose of the model
3. Consideration of the number of ‘dimensions’
4. Description of the main process
5. The data used are discrete observed measurements or statistical distributions, and
6. Consideration of temporal variability.
A model for diffusive flux can be constructed from the following example.
Consider a one-dimensional system with motion in the X direction only (Fig. 3.7).
An interface B-B
0 separates two regions of different concentration, C1 and C2 ¼ particles/volume on the left and right side of the interface, respectively. The motion of
each particle is a one-dimensional random walk. In each time interval, Δt, each
particle will move a distance Æ ΔX, moving right (+ ΔX) or left (À ΔX) with equal
probability.
Within each time step, any particle within a distance ΔX of the interface B-B
0 has
a 50% probability of crossing over that interface. The number of particles with the
potential to cross B-B
0 from left to right (positive mass flux) is (C1 ΔX A), where A is
the area of interface B-B
0 . On average, half of these take a positive step and cross the
interface in time Δt such that the flux left to right is (0.5 C1 ΔX A). Similarly, the
number of particles crossing right to left in Δt (negative mass flux) will be (0.5 C2
ΔX A). The resulting mass flux, q X , is
Threshold = M
1
u(x,t) =
exp
–x 2
4pDt
4Dt
Fig. 3.7 The formula for distance within which the pheromone is sensed is given by
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
À2 D t:Ln 4M
2 π D:t
À
Á
q
3 Surface Water Quality and Analysis
91