#### Estuarine salinity 1D model

##### Joao G. Ferreira ★

This model implements the one-dimensional version of the advection-dispersion equation for an estuary. The equation is:

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (Eq. 1)

Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q

At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:

Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)

Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity

E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.

By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:

QSe=E(b)e,s(Se-Ss) (Eq. 4)

At steady state

E(b)e,s = QSe/(Se-Ss) (Eq 5)

The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.

You can use the upper slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.

The lower slider allows you to simulate a variable river flow, and understand how dispersion compensates for changes in freshwater input.

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (Eq. 1)

Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q

At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:

Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)

Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity

E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.

By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:

QSe=E(b)e,s(Se-Ss) (Eq. 4)

At steady state

E(b)e,s = QSe/(Se-Ss) (Eq 5)

The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.

You can use the upper slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.

The lower slider allows you to simulate a variable river flow, and understand how dispersion compensates for changes in freshwater input.

- 11 months 2 weeks ago

#### Forcing functions (tides and light)

##### Joao G. Ferreira ★

This very simple model generates a tidal curve and a light climate at the sea surface to illustrate the non-linearity of the diel and tidal cycles. This has repercussions on benthic primary (and therefore also secondary) production.

- 1 year 6 months ago

#### Estuarine salinity 1 box model (J. Gomes Ferreira)

##### Andre Simoes

This model implements the one-dimensional version of the advection-dispersion equation for an estuary. The equation is:

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (Eq. 1)

Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q

At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:

Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)

Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity

E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.

By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:

QSe=E(b)e,s(Se-Ss) (Eq. 4)

At steady state

E(b)e,s = QSe/(Se-Ss) (Eq 5)

The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.

You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (Eq. 1)

Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q

At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:

Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)

Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity

E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.

By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:

QSe=E(b)e,s(Se-Ss) (Eq. 4)

At steady state

E(b)e,s = QSe/(Se-Ss) (Eq 5)

The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.

You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.

- 3 years 4 months ago

#### Estuary Salinity 4 Boxes Model

##### Andre Simoes

This model represents the four-dimensional version of the advection-dispersion equation

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx)

Where S: salinity (kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume.For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient (m3 s-1, i.e. a flow, equivalent to Q)

We can rewrite

Q(Sr-S1)=E(b)r,1(Sr-S1)-E(b)1,2(S1-S2)

Where Sr: river salinity (=0), S1: mean estuary salinity for box 1; S2: mean estuary salinity for box 2; E(b)r,1: dispersion coefficient between river and estuary box 1; and E(b)1,2: dispersion coefficient between the estuary boxes 1 and 2.

Because we're at the head of the estuary, E(b)r,1 is zero, wich means: no salt enters the river. Sr is also zero, because the river salinity is zero. Therefore:

QS1=E(b)1,2(S1-S2)

At steady state

E(b)1,2 = QS1/(S1-S2)

**(1)**for an estuary.dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx)

**(1)**Where S: salinity (kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume.For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS

**(2)**EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient (m3 s-1, i.e. a flow, equivalent to Q)

We can rewrite

**(2)**for the first estuarine box as:Q(Sr-S1)=E(b)r,1(Sr-S1)-E(b)1,2(S1-S2)

**(3)**Where Sr: river salinity (=0), S1: mean estuary salinity for box 1; S2: mean estuary salinity for box 2; E(b)r,1: dispersion coefficient between river and estuary box 1; and E(b)1,2: dispersion coefficient between the estuary boxes 1 and 2.

Because we're at the head of the estuary, E(b)r,1 is zero, wich means: no salt enters the river. Sr is also zero, because the river salinity is zero. Therefore:

QS1=E(b)1,2(S1-S2)

**(4)**At steady state

E(b)1,2 = QS1/(S1-S2)

**(5)**- 3 years 4 months ago

#### Estuarine Nitrates 4 boxes model

##### Tiago Gageiro

[ This model represents the four-dimensional version of the advection-dispersion equation (1) for an estuary.

dN/dt = (1/A)d(QN)/dx - (1/A)d(EA)/dx(dN/dx) (1)

Where N: Nitrates (kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume.For a set value of Q, the equation becomes:

VdN/dt = QdN - (d(EA)/dx) dN (2)

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient (m3 s-1, i.e. a flow, equivalent to Q)

We can rewrite (2) for the first estuarine box as:

Q(Nr-N1)=E(b)r,1(Nr-N1)-E(b)1,2(N1-N2) (3)

Where Sn: river nitrates(=5), N1: mean estuary Nitrates for box 1; N2: mean estuary nitrates for box 2; E(b)r,1: dispersion coefficient between river and estuary box 1; and E(b)1,2: dispersion coefficient between the estuary boxes 1 and 2.

Therefore:

QN1=E(b)1,2(N1-N2) (4)

At steady state

E(b)1,2 = QN1/(N1-N2) (5) ]

dN/dt = (1/A)d(QN)/dx - (1/A)d(EA)/dx(dN/dx) (1)

Where N: Nitrates (kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume.For a set value of Q, the equation becomes:

VdN/dt = QdN - (d(EA)/dx) dN (2)

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient (m3 s-1, i.e. a flow, equivalent to Q)

We can rewrite (2) for the first estuarine box as:

Q(Nr-N1)=E(b)r,1(Nr-N1)-E(b)1,2(N1-N2) (3)

Where Sn: river nitrates(=5), N1: mean estuary Nitrates for box 1; N2: mean estuary nitrates for box 2; E(b)r,1: dispersion coefficient between river and estuary box 1; and E(b)1,2: dispersion coefficient between the estuary boxes 1 and 2.

Therefore:

QN1=E(b)1,2(N1-N2) (4)

At steady state

E(b)1,2 = QN1/(N1-N2) (5) ]

- 3 years 4 months ago

#### Estuarine Salinity 4 boxes model

##### Tiago Gageiro

[ This model represents the four-dimensional version of the advection-dispersion equation (1) for an estuary.

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (1) Where S: salinity (kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1). For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes: VdS/dt = QdS - (d(EA)/dx) dS (2) EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient (m3 s-1, i.e. a flow, equivalent to Q) We can rewrite (2) for the first estuarine box as: Q(Sr-S1)=E(b)r,1(Sr-S1)-E(b)1,2(S1-S2) (3) Where Sr: river salinity (=0), S1: mean estuary salinity for box 1; S2: mean estuary salinity for box 2; E(b)r,1: dispersion coefficient between river and estuary box 1; and E(b)1,2: dispersion coefficient between the estuary boxes 1 and 2. Because we're at the head of the estuary, E(b)r,1 is zero, wich means: no salt enters the river. Sr is also zero, because the river salinity is zero. Therefore: QS1=E(b)1,2(S1-S2) (4) At steady state E(b)1,2 = QS1/(S1-S2) (5) ]

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (1) Where S: salinity (kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1). For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes: VdS/dt = QdS - (d(EA)/dx) dS (2) EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient (m3 s-1, i.e. a flow, equivalent to Q) We can rewrite (2) for the first estuarine box as: Q(Sr-S1)=E(b)r,1(Sr-S1)-E(b)1,2(S1-S2) (3) Where Sr: river salinity (=0), S1: mean estuary salinity for box 1; S2: mean estuary salinity for box 2; E(b)r,1: dispersion coefficient between river and estuary box 1; and E(b)1,2: dispersion coefficient between the estuary boxes 1 and 2. Because we're at the head of the estuary, E(b)r,1 is zero, wich means: no salt enters the river. Sr is also zero, because the river salinity is zero. Therefore: QS1=E(b)1,2(S1-S2) (4) At steady state E(b)1,2 = QS1/(S1-S2) (5) ]

- 3 years 4 months ago

#### Clone of Estuarine salinity 1 box model (J. Gomes Ferreira)

##### João Serra

This model implements the one-dimensional version of the advection-dispersion equation for an estuary. The equation is:

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (Eq. 1)

Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q

At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:

Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)

Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity

E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.

By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:

QSe=E(b)e,s(Se-Ss) (Eq. 4)

At steady state

E(b)e,s = QSe/(Se-Ss) (Eq 5)

The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.

You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (Eq. 1)

Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q

At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:

Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)

Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity

E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.

By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:

QSe=E(b)e,s(Se-Ss) (Eq. 4)

At steady state

E(b)e,s = QSe/(Se-Ss) (Eq 5)

The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.

You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.

- 2 years 5 months ago

#### Clone of Estuarine salinity 1 box model (J. Gomes Ferreira)

##### João Serra

This model implements the one-dimensional version of the advection-dispersion equation for an estuary. The equation is:

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (Eq. 1)

Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q

At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:

Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)

Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity

E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.

By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:

QSe=E(b)e,s(Se-Ss) (Eq. 4)

At steady state

E(b)e,s = QSe/(Se-Ss) (Eq 5)

The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.

You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (Eq. 1)

Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q

At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:

Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)

Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity

E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.

By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:

QSe=E(b)e,s(Se-Ss) (Eq. 4)

At steady state

E(b)e,s = QSe/(Se-Ss) (Eq 5)

The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.

You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.

- 2 years 5 months ago

#### Clone of Clone of Estuarine salinity 1 box model (J. Gomes Ferreira)

##### João Serra

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (Eq. 1)

Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q

At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:

Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)

Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity

E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.

By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:

QSe=E(b)e,s(Se-Ss) (Eq. 4)

At steady state

E(b)e,s = QSe/(Se-Ss) (Eq 5)

The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.

You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.

- 2 years 4 months ago

#### Clone of Estuarine salinity 1 box model (J. Gomes Ferreira)

##### João Serra

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (Eq. 1)

Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q

At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:

Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)

Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity

E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.

By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:

QSe=E(b)e,s(Se-Ss) (Eq. 4)

At steady state

E(b)e,s = QSe/(Se-Ss) (Eq 5)

The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.

You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.

- 2 years 5 months ago

#### Clone of Clone of Estuarine salinity 1 box model (J. Gomes Ferreira)

##### João Serra

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (Eq. 1)

Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q

At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:

Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)

Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity

E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.

By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:

QSe=E(b)e,s(Se-Ss) (Eq. 4)

At steady state

E(b)e,s = QSe/(Se-Ss) (Eq 5)

The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.

You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.

- 2 years 4 months ago

#### Clone of Estuarine salinity 1D model

##### João Serra

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (Eq. 1)

Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q

At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:

Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)

Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity

E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.

By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:

QSe=E(b)e,s(Se-Ss) (Eq. 4)

At steady state

E(b)e,s = QSe/(Se-Ss) (Eq 5)

The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.

You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.

- 2 years 4 months ago

#### Clone of Estuary Salinity 4 Boxes Model

##### João Serra

This model represents the four-dimensional version of the advection-dispersion equation

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx)

Where S: salinity (kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume.For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient (m3 s-1, i.e. a flow, equivalent to Q)

We can rewrite

Q(Sr-S1)=E(b)r,1(Sr-S1)-E(b)1,2(S1-S2)

Where Sr: river salinity (=0), S1: mean estuary salinity for box 1; S2: mean estuary salinity for box 2; E(b)r,1: dispersion coefficient between river and estuary box 1; and E(b)1,2: dispersion coefficient between the estuary boxes 1 and 2.

Because we're at the head of the estuary, E(b)r,1 is zero, wich means: no salt enters the river. Sr is also zero, because the river salinity is zero. Therefore:

QS1=E(b)1,2(S1-S2)

At steady state

E(b)1,2 = QS1/(S1-S2)

**(1)**for an estuary.dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx)

**(1)**Where S: salinity (kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume.For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS

**(2)**EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient (m3 s-1, i.e. a flow, equivalent to Q)

We can rewrite

**(2)**for the first estuarine box as:Q(Sr-S1)=E(b)r,1(Sr-S1)-E(b)1,2(S1-S2)

**(3)**Where Sr: river salinity (=0), S1: mean estuary salinity for box 1; S2: mean estuary salinity for box 2; E(b)r,1: dispersion coefficient between river and estuary box 1; and E(b)1,2: dispersion coefficient between the estuary boxes 1 and 2.

Because we're at the head of the estuary, E(b)r,1 is zero, wich means: no salt enters the river. Sr is also zero, because the river salinity is zero. Therefore:

QS1=E(b)1,2(S1-S2)

**(4)**At steady state

E(b)1,2 = QS1/(S1-S2)

**(5)**- 2 years 4 months ago

#### Clone of Estuary Salinity 4 Boxes Model

##### João Serra

This model represents the four-dimensional version of the advection-dispersion equation

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx)

Where S: salinity (kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume.For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient (m3 s-1, i.e. a flow, equivalent to Q)

We can rewrite

Q(Sr-S1)=E(b)r,1(Sr-S1)-E(b)1,2(S1-S2)

Where Sr: river salinity (=0), S1: mean estuary salinity for box 1; S2: mean estuary salinity for box 2; E(b)r,1: dispersion coefficient between river and estuary box 1; and E(b)1,2: dispersion coefficient between the estuary boxes 1 and 2.

Because we're at the head of the estuary, E(b)r,1 is zero, wich means: no salt enters the river. Sr is also zero, because the river salinity is zero. Therefore:

QS1=E(b)1,2(S1-S2)

At steady state

E(b)1,2 = QS1/(S1-S2)

**(1)**for an estuary.dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx)

**(1)**Where S: salinity (kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume.For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS

**(2)**EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient (m3 s-1, i.e. a flow, equivalent to Q)

We can rewrite

**(2)**for the first estuarine box as:Q(Sr-S1)=E(b)r,1(Sr-S1)-E(b)1,2(S1-S2)

**(3)**Where Sr: river salinity (=0), S1: mean estuary salinity for box 1; S2: mean estuary salinity for box 2; E(b)r,1: dispersion coefficient between river and estuary box 1; and E(b)1,2: dispersion coefficient between the estuary boxes 1 and 2.

Because we're at the head of the estuary, E(b)r,1 is zero, wich means: no salt enters the river. Sr is also zero, because the river salinity is zero. Therefore:

QS1=E(b)1,2(S1-S2)

**(4)**At steady state

E(b)1,2 = QS1/(S1-S2)

**(5)**- 2 years 4 months ago

#### Clone of Estuary Salinity 4 Boxes Model

##### João Serra

**(1)**for an estuary.

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx)

**(1)**

Where S: salinity (kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume.For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS

**(2)**

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient (m3 s-1, i.e. a flow, equivalent to Q)

We can rewrite

**(2)**for the first estuarine box as:

Q(Sr-S1)=E(b)r,1(Sr-S1)-E(b)1,2(S1-S2)

**(3)**

Where Sr: river salinity (=0), S1: mean estuary salinity for box 1; S2: mean estuary salinity for box 2; E(b)r,1: dispersion coefficient between river and estuary box 1; and E(b)1,2: dispersion coefficient between the estuary boxes 1 and 2.

Because we're at the head of the estuary, E(b)r,1 is zero, wich means: no salt enters the river. Sr is also zero, because the river salinity is zero. Therefore:

QS1=E(b)1,2(S1-S2)

**(4)**

At steady state

E(b)1,2 = QS1/(S1-S2)

**(5)**

- 2 years 4 months ago

#### Clone of Estuarine salinity 1 box model (J. Gomes Ferreira)

##### João Serra

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (Eq. 1)

Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q

At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:

Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)

Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity

E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.

By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:

QSe=E(b)e,s(Se-Ss) (Eq. 4)

At steady state

E(b)e,s = QSe/(Se-Ss) (Eq 5)

The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.

You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.

- 2 years 4 months ago

#### Clone of Clone of Clone of Estuarine salinity 1 box model (J. Gomes Ferreira)

##### João Serra

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (Eq. 1)

Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q

At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:

Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)

Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity

E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.

By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:

QSe=E(b)e,s(Se-Ss) (Eq. 4)

At steady state

E(b)e,s = QSe/(Se-Ss) (Eq 5)

The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.

You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.

- 2 years 4 months ago

#### Clone of Estuary Salinity 4 Boxes Model

##### João Serra

**(1)**for an estuary.

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx)

**(1)**

Where S: salinity (kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume.For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS

**(2)**

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient (m3 s-1, i.e. a flow, equivalent to Q)

We can rewrite

**(2)**for the first estuarine box as:

Q(Sr-S1)=E(b)r,1(Sr-S1)-E(b)1,2(S1-S2)

**(3)**

Where Sr: river salinity (=0), S1: mean estuary salinity for box 1; S2: mean estuary salinity for box 2; E(b)r,1: dispersion coefficient between river and estuary box 1; and E(b)1,2: dispersion coefficient between the estuary boxes 1 and 2.

Because we're at the head of the estuary, E(b)r,1 is zero, wich means: no salt enters the river. Sr is also zero, because the river salinity is zero. Therefore:

QS1=E(b)1,2(S1-S2)

**(4)**

At steady state

E(b)1,2 = QS1/(S1-S2)

**(5)**

- 2 years 4 months ago

#### Clone of Estuarine salinity 1D model

##### João Serra

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (Eq. 1)

Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q

At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:

Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)

Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity

E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.

By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:

QSe=E(b)e,s(Se-Ss) (Eq. 4)

At steady state

E(b)e,s = QSe/(Se-Ss) (Eq 5)

The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.

You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.

- 2 years 5 months ago

#### Clone of Estuary Salinity 4 Boxes Model

##### João Serra

**(1)**for an estuary.

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx)

**(1)**

Where S: salinity (kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume.For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS

**(2)**

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient (m3 s-1, i.e. a flow, equivalent to Q)

We can rewrite

**(2)**for the first estuarine box as:

Q(Sr-S1)=E(b)r,1(Sr-S1)-E(b)1,2(S1-S2)

**(3)**

Where Sr: river salinity (=0), S1: mean estuary salinity for box 1; S2: mean estuary salinity for box 2; E(b)r,1: dispersion coefficient between river and estuary box 1; and E(b)1,2: dispersion coefficient between the estuary boxes 1 and 2.

Because we're at the head of the estuary, E(b)r,1 is zero, wich means: no salt enters the river. Sr is also zero, because the river salinity is zero. Therefore:

QS1=E(b)1,2(S1-S2)

**(4)**

At steady state

E(b)1,2 = QS1/(S1-S2)

**(5)**

- 2 years 4 months ago

#### Clone of Estuary Salinity 4 Boxes Model

##### João Serra

**(1)**for an estuary.

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx)

**(1)**

Where S: salinity (kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume.For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS

**(2)**

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient (m3 s-1, i.e. a flow, equivalent to Q)

We can rewrite

**(2)**for the first estuarine box as:

Q(Sr-S1)=E(b)r,1(Sr-S1)-E(b)1,2(S1-S2)

**(3)**

Where Sr: river salinity (=0), S1: mean estuary salinity for box 1; S2: mean estuary salinity for box 2; E(b)r,1: dispersion coefficient between river and estuary box 1; and E(b)1,2: dispersion coefficient between the estuary boxes 1 and 2.

Because we're at the head of the estuary, E(b)r,1 is zero, wich means: no salt enters the river. Sr is also zero, because the river salinity is zero. Therefore:

QS1=E(b)1,2(S1-S2)

**(4)**

At steady state

E(b)1,2 = QS1/(S1-S2)

**(5)**

- 2 years 4 months ago

#### Clone of Estuarine salinity 1 box model (J. Gomes Ferreira)

##### João Serra

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (Eq. 1)

Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q

At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:

Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)

Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity

E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.

By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:

QSe=E(b)e,s(Se-Ss) (Eq. 4)

At steady state

E(b)e,s = QSe/(Se-Ss) (Eq 5)

The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.

You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.

- 2 years 5 months ago

#### Clone of Estuarine salinity 1D model

##### João Serra

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (Eq. 1)

Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q

At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:

Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)

Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity

E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.

By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:

QSe=E(b)e,s(Se-Ss) (Eq. 4)

At steady state

E(b)e,s = QSe/(Se-Ss) (Eq 5)

The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.

You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.

- 2 years 4 months ago

#### Clone of Estuary Salinity 4 Boxes Model

##### João Serra

**(1)**for an estuary.

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx)

**(1)**

Where S: salinity (kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume.For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS

**(2)**

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient (m3 s-1, i.e. a flow, equivalent to Q)

We can rewrite

**(2)**for the first estuarine box as:

Q(Sr-S1)=E(b)r,1(Sr-S1)-E(b)1,2(S1-S2)

**(3)**

Where Sr: river salinity (=0), S1: mean estuary salinity for box 1; S2: mean estuary salinity for box 2; E(b)r,1: dispersion coefficient between river and estuary box 1; and E(b)1,2: dispersion coefficient between the estuary boxes 1 and 2.

Because we're at the head of the estuary, E(b)r,1 is zero, wich means: no salt enters the river. Sr is also zero, because the river salinity is zero. Therefore:

QS1=E(b)1,2(S1-S2)

**(4)**

At steady state

E(b)1,2 = QS1/(S1-S2)

**(5)**

- 2 years 4 months ago