## Tidal Characteristic Numbers of Salinity

### From BAWiki

Graphical representation of characteristic numbers of salinity (with German text only). This graphical representation is also available in Encapsulated PostScript format.

Graphical representation of characteristic numbers of advective salt transport (with German text only). This graphical representation is also available in Encapsulated PostScript format.

## Contents

- 1 Motivation
- 2 Definitions for the Tidal Characteristic Numbers of Salinity
- 2.1 Flood Current
- 2.2 Ebb Current
- 2.3 Tidal Cycle (between two subsequent ebb slacks)
- 2.3.1 Maximum Salinity
- 2.3.2 Minimum Salinity
- 2.3.3 Mean Salinity
- 2.3.4 Tidal Variation of Salinity
- 2.3.5 Advective Residual Transport of Salt
- 2.3.6 Diffusive Residual Transport of Salt
- 2.3.7 Advective Tidal Transport of Salt
- 2.3.8 Advective Salt Transport, Flood-Ebb-Ratio
- 2.3.9 Advective Salt Transport, Flood-Tide-Ratio
- 2.3.10 Advective Salt Transport, Ebb-Tide-Ratio
- 2.3.11 Mean Salinity Flood Current : Mean Salinity
- 2.3.12 Mean Salinity Ebb Current : Mean Salinity
- 2.3.13 Mean Salinity Flood Current : Mean Salinity Ebb Current
- 2.3.14 Tidal Variation of Salinity : Mean Salinity
- 2.3.15 Maximum Salinity : Mean Salinity
- 2.3.16 Minimum Salinity : Mean Salinity

- 2.4 Flood
- 2.5 Ebb
- 2.6 Tidal Cycle (between two subsequent tidal low waters)
- 2.6.1 Maximum Salinity
- 2.6.2 Minimum Salinity
- 2.6.3 Mean Salinity
- 2.6.4 Tidal Variation of Salinity
- 2.6.5 Mean Salinity Flood : Mean Salinity
- 2.6.6 Mean Salinity Ebb : Mean Salinity
- 2.6.7 Mean Salinity Flood : Mean Salinity Ebb
- 2.6.8 Tidal Variation of Salinity : Mean Salinity
- 2.6.9 Maximum Salinity : Mean Salinity
- 2.6.10 Minimum Salinity : Mean Salinity

## Motivation

The calculation as well as the graphic visualization of various tidal characteristic numbers of salinity and also for the advective transport of salt contributes to an improved understanding of tidally dominated transport processes in estuaries. Spatial variations of salinity, advective transport of salt by means of flood and ebb currents can be highlighted for areas like coastal seas and estuaries as well (see also animation of tidal variability of salinity in the Außenweser Estuary).

- As the calculations are performed separately for the durations of ebb- and flood-current it can be shown that transport paths can differ significantly for the two tidal phases. From this one can get additional insight with respect to the relevant transport mechanisms dominated by the tidal currents. This can be related to locally varying flood-ebb asymmetries for ebb volume and flood volume. Also the presence of horizontal gradients can contribute to this effect.
- The variation of salinity resulting from the local maximum as well as the local minimum of salinity can be quite large. This is a consequence of fresh water inflow into an estuary. The value for the local salinity variation is mainly the result of the product between the horizontal salinity gradient and the lagrangian drift of a water particle during a complete tidal cycle. Due to the fact that salt is mainly advectively transported by means of the tidal current. The water particles which are passing at a location during a complete tidal cycle do have different regions of origin. Therefore they can also show substantial differences in salinity because estuaries are regions where fresh and sea water is mixed. For organisms which are living at the seabed and which cannot move the tidal variation of salinity is one of the significant natural stress factors (variation of the osmotic pressure due to salinity variations).

Multiple characteristic numbers can be computed also for the duration of flood (not duration of flood current) and the duration of ebb (not ebb current).

**Automatic analyses for all of the above mentioned tidal characteristic numbers of salinity are carried out for 2D- as well as for 3D-data by the programs TDKSF and NCANALYSE** (modes **TDKS** (flood current, ebb current) and **TDWS** (flood, ebb)).

For modes **TDKS** and **TDWS** the periods of analysis and integration are differently defined:

- mode
**TDKS**- flood current: period between ebb slack (or start of flooding) and flood slack;
- ebb current: period between flood slack and ebb slack (or end of flooding);
- tide: period between first ebb slack (or start of flooding) and second ebb slack (or end of flooding).

- mode
**TDWS**- flood: period between tidal low water (or start of flooding) and tidal high water;
- ebb: period between tidal high water and tidal low water (or end of flooding);
- tide: period between first tidal low water (or start of flooding) and second tidal low water (or end of flooding).

## Definitions for the Tidal Characteristic Numbers of Salinity

### Flood Current

#### Advective Flood Transport of Salt

##### Computed from synoptic current velocity and synoptic salinity

salt volume, which is transported by means of flood current through a cross section.

Example: Advective Flood Transport of Salt in the Inner Außenweser.

Data analysis: TDKSF.

##### Computed from integral (salt) volume transport

Exact volume of salt (with exception of roundoff) which passes a certain cross section during flood current due to advection. This quantity makes use of the normal flow of salt only, which is orthogonal to the flow face. Reconstruction of the total vector by means of projection is left to visualization programs (e. g. NCPLOT).

Data analysis: NCANALYSE.

#### Diffusive Flood Transport of Salt

##### Computed from synoptic current velocity and synoptic salinity

Not computed by program TDKSF.

##### Computed from integral (salt) volume transport

Exact volume of salt (with exception of roundoff) which passes a certain cross section during flood current due to (turbulent) diffusion. This quantity makes use of the normal flow of salt only, which is orthogonal to the flow face. Reconstruction of the total vector by means of projection is left to visualization programs (e. g. NCPLOT).

Data analysis: NCANALYSE.

#### Advective Flood Transport-Rate of Salt

##### Computed from synoptic current velocity and synoptic salinity

Not computed by program TDKSF.

##### Computed from integral (salt) volume transport

Exact volume transport rate of salt (with exception of roundoff) which passes a certain cross section during flood current due to advection. This quantity makes use of the normal flow of salt only, which is orthogonal to the flow face. Reconstruction of the total vector by means of projection is left to visualization programs (e. g. NCPLOT). On tidal flats this quantity is computed for the period of inundation only.

Data analysis: NCANALYSE.

#### Diffusive Flood Transport-Rate of Salt

##### Computed from synoptic current velocity and synoptic salinity

Not computed by program TDKSF.

##### Computed from integral (salt) volume transport

Exact volume transport rate of salt (with exception of roundoff) which passes a certain cross section during flood current due to (turbulent) diffusion. This quantity makes use of the normal flow of salt only, which is orthogonal to the flow face. Reconstruction of the total vector by means of projection is left to visualization programs (e. g. NCPLOT). On tidal flats this quanmtity is computed for the period of inundation only.

Data analysis: NCANALYSE.

#### Mean Salinity Flood Current

Mean value of salinity during the flood current duration of a tide.

Example figures: mean salinity flood current.

Data analysis: NCANALYSE.

### Ebb Current

#### Advective Ebb Transport of Salt

##### Computed from synoptic current velocity and synoptic salinity

salt volume, which is transported by means of ebb current through a cross section.

Example: Advective Ebb Transport of Salt in the Inner Außenweser.

Data analysis: TDKSF.

##### Computed from integral (salt) volume transport

Exact volume of salt (with exception of roundoff) which passes a certain cross section during ebb current due to advection. This quantity makes use of the normal flow of salt only, which is orthogonal to the flow face. Reconstruction of the total vector by means of projection is left to visualization programs (e. g. NCPLOT).

Data analysis: NCANALYSE.

#### Diffusive Ebb Transport of Salt

##### Computed from synoptic current velocity and synoptic salinity

Not computed by program TDKSF.

##### Computed from integral (salt) volume transport

Exact volume of salt (with exception of roundoff) which passes a certain cross section during ebb current due to (turbulent) diffusion. This quantity makes use of the normal flow of salt only, which is orthogonal to the flow face. Reconstruction of the total vector by means of projection is left to visualization programs (e. g. NCPLOT).

Data analysis: NCANALYSE.

#### Advective Ebbe Transport-Rate of Salt

##### Computed from synoptic current velocity and synoptic salinity

Not computed by program TDKSF.

##### Computed from integral (salt) volume transport

Exact volume transport rate of salt (with exception of roundoff) which passes a certain cross section during ebb current due to advection. This quantity makes use of the normal flow of salt only, which is orthogonal to the flow face. Reconstruction of the total vector by means of projection is left to visualization programs (e. g. NCPLOT). On tidal flats this quantity is computed for the period of inundation only.

Data analysis: NCANALYSE.

#### Diffusive Ebb Transport-Rate of Salt

##### Computed from synoptic current velocity and synoptic salinity

Not computed by program TDKSF.

##### Computed from integral (salt) volume transport

Exact volume transport rate of salt (with exception of roundoff) which passes a certain cross section during ebb current due to (turbulent) diffusion. This quantity makes use of the normal flow of salt only, which is orthogonal to the flow face. Reconstruction of the total vector by means of projection is left to visualization programs (e. g. NCPLOT). On tidal flats this quantity is computed for the period of inundation only.

Data analysis: NCANALYSE.

#### Mean Salinity Ebb Current

Mean value of salinity during the ebb current duration of a tide.

Example figures: mean salinity ebb current.

Data analysis: NCANALYSE.

### Tidal Cycle (between two subsequent ebb slacks)

#### Maximum Salinity

maximum value of salinity during a complete tidal cycle (period between two subsequent slack water times of ebb current).

Example figures: maximum salinity.

Data analysis: TDKSF and NCANALYSE.

#### Minimum Salinity

minimum value of salinity during a complete tidal cycle (period between two subsequent slack water times of ebb current).

Example figures: minimum salinity.

Data analysis: TDKSF and NCANALYSE.

#### Mean Salinity

average value of salinity during a complete tidal cycle (period between two subsequent slack water times of ebb current).

Example figures: mean salinity.

Data analysis: TDKSF and NCANALYSE.

#### Tidal Variation of Salinity

difference between the extreme values of salinity during a complete tidal cycle (period between two subsequent slack water times of ebb current).

Example figures: tidal variation of salinity.

Data analysis: TDKSF and NCANALYSE.

#### Advective Residual Transport of Salt

residual salt volume which is transported by means of ebb and flood currents through a cross section (the different transport directions are taken into account). If the advective transport by means of flood current is equal but in opposite direction of the ebb current transport this will result in a zero advective residual transport of salt.

##### Computed from synoptic current velocity and synoptic salinity

Example: Advective Residual Transport of Salt in the Inner Außenweser.

Data analysis: TDKSF.

##### Computed from integral (salt) volume transport

Residual based on exact volume of salt (with exception of roundoff) which passes a certain cross section during a tidal cycle (flood current plus ebb current) due to advection. This quantity makes use of the normal flow of salt only, which is orthogonal to the flow face. Reconstruction of the total vector by means of projection is left to visualization programs (e. g. NCPLOT).

Data analysis: NCANALYSE.

#### Diffusive Residual Transport of Salt

residual salt volume which is transported by means of diffusion during ebb and flood current through a cross section (the different transport directions are taken into account). If the diffusive transport for each of the tidal phases is equal but in opposite direction this will result in a zero diffusive residual transport of salt.

##### Computed from synoptic current velocity and synoptic salinity

Not computed by program TDKSF.

##### Computed from integral (salt) volume transport

Residual based on exact volume of salt (with exception of roundoff) which passes a certain cross section during a tidal cycle (flood current plus ebb current) due to diffusion. This quantity makes use of the normal flow of salt only, which is orthogonal to the flow face. Reconstruction of the total vector by means of projection is left to visualization programs (e. g. NCPLOT).

Data analysis: NCANALYSE.

#### Advective Tidal Transport of Salt

total salt volume which is transported by means of advection during ebb and flood current through a cross section (the different transport directions are taken into account). Magnitudes for flood and ebb current transport are added.

##### Computed from synoptic current velocity and synoptic salinity

Not computed by program TDKSF.

##### Computed from integral (salt) volume transport

Sum of individual transports (magnitudes) based on exact volume of salt (with exception of roundoff) which passes a certain cross section during a tidal cycle (flood current plus ebb current) due to advection. This quantity makes use of the normal flow of salt only, which is orthogonal to the flow face.

Data analysis: NCANALYSE.

#### Advective Salt Transport, Flood-Ebb-Ratio

flood to ebb ratio for the salt volumes which are transported by means of flood and ebb currents.

##### Computed from synoptic current velocity and synoptic salinity

Example: Flood-Ebb-Ratio for the Advective Salt Transport in the Inner Außenweser.

Data analysis: TDKSF.

##### Computed from integral (salt) volume transport

Based on exact volume of salt (with exception of roundoff) which passes a certain cross section during a tidal cycle due to advection. Quantity is computed from the (face) normal components only.

Data analysis: NCANALYSE.

#### Advective Salt Transport, Flood-Tide-Ratio

flood to tide ratio for the salt volumes which are transported by means of flood and tide (flood plus ebb) currents.

##### Computed from synoptic current velocity and synoptic salinity

Not computed by program TDKSF.

##### Computed from integral (salt) volume transport

Based on exact volume of salt (with exception of roundoff) which passes a certain cross section due to advection. Quantity is computed from the (face) normal components only.

Data analysis: NCANALYSE.

#### Advective Salt Transport, Ebb-Tide-Ratio

ebb to tide ratio for the salt volumes which are transported by means of ebb and tide (flood plus ebb) currents.

##### Computed from synoptic current velocity and synoptic salinity

Not computed by program TDKSF.

##### Computed from integral (salt) volume transport

Based on exact volume of salt (with exception of roundoff) which passes a certain cross section due to advection. Quantity is computed from the (face) normal components only.

Data analysis: NCANALYSE.

#### Mean Salinity Flood Current : Mean Salinity

Ratio of mean salinity of flood current to mean salinity during the complete tide.

Example figures: mean salinity flood current : mean salinity.

Data analysis: NCANALYSE.

#### Mean Salinity Ebb Current : Mean Salinity

Ratio of mean salinity of ebb current to mean salinity during the complete tide.

Example figures: mean salinity ebb current : mean salinity.

Data analysis: NCANALYSE.

#### Mean Salinity Flood Current : Mean Salinity Ebb Current

Ratio of mean salinity of flood current to mean salinity of ebb current.

Example figures: mean salinity flood current : mean salinity ebb current.

Data analysis: NCANALYSE.

#### Tidal Variation of Salinity : Mean Salinity

Ratio of tidal variation of salinity to mean salinity value of the tide.

Example figures: tidal variation of salinity : mean salinity.

Data analysis: NCANALYSE.

#### Maximum Salinity : Mean Salinity

Ratio of maximum salinity of the tide to mean salinity value of the tide.

Example figures: maximum salinity : mean salinity.

Data analysis: NCANALYSE.

#### Minimum Salinity : Mean Salinity

Ratio of minimum salinity of the tide to mean salinity value of the tide.

Example figures: minimum salinity : mean salinity.

Data analysis: NCANALYSE.

### Flood

#### Mean Salinity Flood

Mean value of salinity during flood duration of a tide. This value is typically lower than the respective mean computed for flood current duration.

Data analysis: NCANALYSE.

### Ebb

#### Mean Salinity Ebb

Mean value of salinity during ebb duration of a tide. This value is typically larger than the respective mean computed for ebb current duration.

Data analysis: NCANALYSE.

### Tidal Cycle (between two subsequent tidal low waters)

#### Maximum Salinity

Maximum value of salinity during a complete tidal cycle (period between two subsequent tidal low waters). This value is typically identical to the respective maximum computed for the period between two subsequent ebb slacks.

Data analysis: NCANALYSE.

#### Minimum Salinity

Minimum value of salinity during a complete tidal cycle (period between two subsequent tidal low waters). This value may differ from the respective minimum computed for the period between two subsequent ebb slacks.

Data analysis: NCANALYSE.

#### Mean Salinity

Average value of salinity during a complete tidal cycle (period between two subsequent tidal low waters). This value is typically comparable to the respective mean computed for the period between two subsequent ebb slacks.

Data analysis: NCANALYSE.

#### Tidal Variation of Salinity

Difference between the extreme values of salinity during a complete tidal cycle (period between two subsequent tidal low waters). This value may differ from the respective value computed for the period between two subsequent ebb slacks.

Data analysis: NCANALYSE.

#### Mean Salinity Flood : Mean Salinity

Ratio of mean salinity of flood to mean salinity during the complete tide (period between two subsequent tidal low waters).

Data analysis: NCANALYSE.

#### Mean Salinity Ebb : Mean Salinity

Ratio of mean salinity of ebb to mean salinity during the complete tide (period between two subsequent tidal low waters).

Data analysis: NCANALYSE.

#### Mean Salinity Flood : Mean Salinity Ebb

Ratio of mean salinity of during flood to mean salinity during ebb.

Data analysis: NCANALYSE.

#### Tidal Variation of Salinity : Mean Salinity

Ratio of tidal variation of salinity to mean salinity value of the tide (period between two subsequent tidal low waters).

Data analysis: NCANALYSE.

#### Maximum Salinity : Mean Salinity

Ratio of maximum salinity of the tide to mean salinity value of the tide (period between two subsequent tidal low waters)..

Data analysis: NCANALYSE.

#### Minimum Salinity : Mean Salinity

Ratio of minimum salinity of the tide to mean salinity value of the tide (period between two subsequent tidal low waters)..

Data analysis: NCANALYSE.

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