## Characteristic Numbers of Eff. Bed Shear Stress (independent of tides)

### From BAWiki

A graphic sketch for the definition of the various tidal characteristic numbers of eff. bed shear stress is not available. Due to the fact that they are defined in complete analogy to salinity we do refer here to the respective graphical representations of the characteristic numbers of salinity (independent of tides) for further insight.

## Contents

- 1 Motivation
- 2 Definitions for the tide-independent characteristic numbers of salinity
- 2.1 Analysis Program NCANALYSE
- 2.1.1 Maximum eff. Bed Shear Stress
- 2.1.2 Residual eff. Bed Shear Stress
- 2.1.3 Mean Magnitude of eff. Bed Shear Stress
- 2.1.4 Standard Deviation of eff. Bed Shear Stress
- 2.1.5 Variance of eff. Bed Shear Stress
- 2.1.6 Duration of eff. Bed Shear Stress
- 2.1.7 Duration of eff. Bed Shear Stress
- 2.1.8 Relative Frequency Distribution of eff. Bed Shear Stress
- 2.1.9 Cumulative Frequency Distribution of eff. Bed Shear Stress
- 2.1.10 Exceedance Frequency of eff. Bed Shear Stress Limits
- 2.1.11 Underflow Frequency of eff. Bed Shear Stress Limits
- 2.1.12 Quantiles of eff. Bed Shear Stress

- 2.2 Program LZKSF
- 2.2.1 Maximum Value of Eff. Bed Shear Stress
- 2.2.2 Minimum Value of Eff. Bed Shear Stress
- 2.2.3 Mean Value of Eff. Bed Shear Stress
- 2.2.4 Maximum Eff. Bed Shear Stress Difference
- 2.2.5 Maximum (Rate of) Increase of Eff. Bed Shear Stress
- 2.2.6 Maximum (Rate of) Decrease of Eff. Bed Shear Stress
- 2.2.7 Standard Deviation of Eff. Bed Shear Stress
- 2.2.8 Variance of Eff. Bed Shear Stress
- 2.2.9 Duration of High Eff. Bed Shear Stress
- 2.2.10 Duration of Low Eff. Bed Shear Stress

- 2.1 Analysis Program NCANALYSE

## Motivation

Calculation and graphic display of several tide-independent characteristic numbers of eff. bed shear stress can yield additional insight into eff. bed shear stress related phenomena of natural coastal and/or inland waters. In contrast to the computation of the tidal characteristic numbers of eff. bed shear stress the tide-independent numbers can be preferable used for

- natural waters which are not dominated by the tides, e.g. like the coastal waters and estuaries along the Baltic Sea coast of Germany, or in
- extreme situations, like for example periods of high or low fresh water runoff, when eff. bed shear stress may deviate strongly from the average (tide-dominated) conditions, as well as for the
- determination of characteristic values of eff. bed shear stress for an arbitrary long (or short) period of time.

In particular there are several useful applications possible for this type of data analysis:

- In addition to informations about the highest and lowest eff. bed shear stress values which occur during an arbitrary period one can calculate also the maximum eff. bed shear stress difference for this time span. This is a good indicator for the natural variability of eff. bed shear stress.
- Maximum values for the (rate of) increase and (rate of) decrease of eff. bed shear stress are eventually also of some interest in various situations.
- From the computed times for the duration of high eff. bed shear stress and the duration of low eff. bed shear stress one can draw conclusions with respect to the impact of eff. bed shear stress on the bottom sediments as well as on organisms living at the bottom.
- The variance of the time-dependent eff. bed shear stress evolution with respect to mean eff. bed shear stress can be used as an indicator for the dynamics of a natural water system.

**An automatic analysis of all tide-independent characteristic numbers of eff. bed shear stress is carried through by the computer programs LZKSF and NCANALYSE.**

## Definitions for the tide-independent characteristic numbers of salinity

### Analysis Program NCANALYSE

#### Maximum eff. Bed Shear Stress

Highest (local) value of eff. bed shear stress (vector) within the period of data analysis.

No example figure available so far.

Data analysis: NCANALYSE.

#### Residual eff. Bed Shear Stress

Residual value of eff. bed shear stress (computed from addition of vectors) within the period of data analysis.

No example figure available so far.

Data analysis: NCANALYSE.

#### Mean Magnitude of eff. Bed Shear Stress

Mean magnitude of eff. bed shear stress (scalar) within the period of data analysis.

No example figure available so far.

Data analysis: NCANALYSE.

#### Standard Deviation of eff. Bed Shear Stress

Standard deviation of eff. bed shear stress within the period of data analysis.

No example figure available so far.

Data analysis: NCANALYSE.

#### Variance of eff. Bed Shear Stress

Variance of eff. Bed Shear Stress within the period of data analysis.

No example figure available so far.

Data analysis: NCANALYSE.

#### Duration of eff. Bed Shear Stress

Period of the time during which local eff. bed shear stress lies above a given stress limit.

No example figure available so far.

Data analysis: NCANALYSE.

#### Duration of eff. Bed Shear Stress

Period of the time during which local eff. bed shear stress lies below a given stress limit.

No example figure available so far.

Data analysis: NCANALYSE.

#### Relative Frequency Distribution of eff. Bed Shear Stress

Relative frequency of eff. bed shear stress for given stress intervals.

No example figure available so far.

Data analysis: NCANALYSE.

#### Cumulative Frequency Distribution of eff. Bed Shear Stress

Cumulative frequency of eff. bed shear stress for given stress intervals.

No example figure available so far.

Data analysis: NCANALYSE.

#### Exceedance Frequency of eff. Bed Shear Stress Limits

Exceedance frequency of eff. bed shear stress limits within the period of data analysis.

No example figure available so far.

Data analysis: NCANALYSE.

#### Underflow Frequency of eff. Bed Shear Stress Limits

Underflow frequency of eff. bed shear stress limits within the period of data analysis.

No example figure available so far.

Data analysis: NCANALYSE.

#### Quantiles of eff. Bed Shear Stress

Eff. bed shear stress for a time serie which is not exceeded by a certain percentage of eff. bed shear stress values.

No example figure available so far.

Data analysis: NCANALYSE.

### Program LZKSF

#### Maximum Value of Eff. Bed Shear Stress

Highest value of eff. bed shear stress within an arbitrary period of time.

Example: not available.

#### Minimum Value of Eff. Bed Shear Stress

Lowest value of eff. bed shear stress within an arbitrary period of time.

Example: not available.

#### Mean Value of Eff. Bed Shear Stress

Arithmetic mean of eff. bed shear stress for an arbitrary period of time.

Example: not available.

#### Maximum Eff. Bed Shear Stress Difference

Difference in eff. bed shear stress between highest and lowest eff. bed shear stress for an arbitrary period of time.

Example: not available.

#### Maximum (Rate of) Increase of Eff. Bed Shear Stress

Maximum increase of eff. bed shear stress (within one hour) within an arbitrary period of time.

Example: not available.

#### Maximum (Rate of) Decrease of Eff. Bed Shear Stress

Maximum decrease of eff. bed shear stress (within one hour) within an arbitrary period of time.

Example: not available.

#### Standard Deviation of Eff. Bed Shear Stress

Standard deviation of eff. bed shear stress with respect to the mean value of eff. bed shear stress within an arbitrary period of time.

Example: not available.

#### Variance of Eff. Bed Shear Stress

Variance of eff. bed shear stress with respect to the mean value of eff. bed shear stress within an arbitrary period of time.

Example: not available.

#### Duration of High Eff. Bed Shear Stress

Period of time during which eff. bed shear stress lies above a specific threshold for eff. bed shear stress.

Example: not available.

#### Duration of Low Eff. Bed Shear Stress

Period of time during which eff. bed shear stress lies below a specific threshold for eff. bed shear stress.

Example: not available.

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