## Characteristic Numbers of Temperature (independent of tides)

### From BAWiki

A graphic sketch for the definition of the various tidal characteristic numbers of temperature 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 Temperature
- 2.1 Program NCANALYSE
- 2.1.1 Maximum Value of Temperature
- 2.1.2 Minimum Value of Temperature
- 2.1.3 Mean Value of temperature
- 2.1.4 Maximum Temperature Difference
- 2.1.5 Standard Deviation of Temperature
- 2.1.6 Variance of Temperature
- 2.1.7 Duration of High Temperature
- 2.1.8 Duration of Low Temperature
- 2.1.9 Relative Frequency Distribution of Temperature
- 2.1.10 Cumulative Frequency Distribution of Temperature
- 2.1.11 Exceedance Frequency of Temperature Limits
- 2.1.12 Underflow Frequency of Temperature Limits
- 2.1.13 Quantiles of Temperature

- 2.2 Program LZKSF
- 2.2.1 Maximum Value of Temperature
- 2.2.2 Minimum Value of Temperature
- 2.2.3 Mean Value of Temperature
- 2.2.4 Maximum Emperature Difference
- 2.2.5 Maximum (Rate of) Increase of Temperature
- 2.2.6 Maximum (Rate of) Decrease of Temperature
- 2.2.7 Standard Deviation of Temperature
- 2.2.8 Variance of Temperature
- 2.2.9 Duration of high temperature
- 2.2.10 Duration of low temperature
- 2.2.11 Advective Heat Transport
- 2.2.12 Mean Advective Heat Transport
- 2.2.13 Maximum Advective Heat Transport
- 2.2.14 Minimum Advective Heat Transport

- 2.1 Program NCANALYSE

## Motivation

Calculation and graphic display of several tide-independent characteristic numbers of temperature can yield additional insight into temperature related phenomena of natural coastal and/or inland waters. In contrast to the computation of the tidal characteristic numbers of temperature 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 temperature may deviate strongly from the average (tide-dominated) conditions, as well as for the
- determination of characteristic values of temperature 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 temperature values which occur during an arbitrary period one can calculate also the maximum temperature difference for this time span. This is a good indicator for the natural variability of temperature.
- Maximum values for the (rate of) increase and (rate of) decrease of temperature are an additional measure for the characterization of e.g. extreme runoff situations.
- From the computed times for the duration of high temperature and the duration of low temperature one can draw conclusions with respect to the impact of temperature on organisms living in the water or along the beaches.
- The variance of the time-dependent temperature evolution with respect to mean temperature can be used as an indicator for the dynamics of a natural water system.

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

## Definitions for the Tide-Independent Characteristic Numbers of Temperature

### Program NCANALYSE

#### Maximum Value of Temperature

Highest (local) value of temperature within the period of data analysis.

Data analysis: NCANALYSE.

#### Minimum Value of Temperature

Lowest (local) value of temperature within the period of data analysis.

Data analysis: NCANALYSE.

#### Mean Value of temperature

Mean value of temperature within the period of data analysis.

Data analysis: NCANALYSE.

#### Maximum Temperature Difference

Difference in temperature between maximum and minimum value within the period of data analysis.

Data analysis: NCANALYSE.

#### Standard Deviation of Temperature

Standard deviation of temperature within the period of data analysis.

Computed for permanently flooded areas only.

Data analysis: NCANALYSE.

#### Variance of Temperature

Variance of temperature within the period of data analysis.

Computed for permanently flooded areas only.

Data analysis: NCANALYSE.

#### Duration of High Temperature

Time span for which temperature lies *above* a certain threshold within an arbitrary period of time.

Data analysis: NCANALYSE.

#### Duration of Low Temperature

Time span for which temperature lies *below* a certain threshold within an arbitrary period of time.

Data analysis: NCANALYSE.

#### Relative Frequency Distribution of Temperature

Relative frequency of temperature within given temperature intervals.

Data analysis: NCANALYSE.

#### Cumulative Frequency Distribution of Temperature

Cumulative frequency of temperature within given temperature intervals.

Data analysis: NCANALYSE.

#### Exceedance Frequency of Temperature Limits

Exceedance frequency of temperature limits within the period of data analysis.

Data analysis: NCANALYSE.

#### Underflow Frequency of Temperature Limits

Underflow frequency of temperature limits within the period of data analysis.

Data analysis: NCANALYSE.

#### Quantiles of Temperature

Temperature value of a time series which is not exceeded of a certain percentage of temperature values in the serie.

Computed for permanently flooded areas only.

Data analysis: NCANALYSE.

### Program LZKSF

#### Maximum Value of Temperature

Highest value of temperature within an arbitrary period of time.

Example: not available.

#### Minimum Value of Temperature

Lowest value of temperature within an arbitrary period of time.

Example: not available.

#### Mean Value of Temperature

Arithmetic mean of temperature for an arbitrary period of time.

Example: not available.

#### Maximum Emperature Difference

Difference in temperature between highest and lowest temperature for an arbitrary period of time.

Example: not available.

#### Maximum (Rate of) Increase of Temperature

Maximum increase of temperature (within one hour) within an arbitrary period of time.

Example: not available.

#### Maximum (Rate of) Decrease of Temperature

Maximum decrease of temperature (within one hour) within an arbitrary period of time.

Example: not available.

#### Standard Deviation of Temperature

Standard deviation of temperature with respect to the mean value of temperature within an arbitrary period of time.

Example: not available.

#### Variance of Temperature

Variance of temperature with respect to the mean value of temperature within an arbitrary period of time.

Example: not available.

#### Duration of high temperature

Period of time during which temperature lies above a specific threshold for temperature.

Example: not available.

#### Duration of low temperature

Period of time during which temperature lies below a specific threshold for temperature.

Example: not available.

#### Advective Heat Transport

Amount of heat, which is transported through a cross section over a period of time.

Example: not available.

#### Mean Advective Heat Transport

Mean value of heat transport within a period of time.

Example: not available.

#### Maximum Advective Heat Transport

Highest value of heat transport within a period of time.

Example: not available.

#### Minimum Advective Heat Transport

Lowest value of heat transport within a period of time.

Example: not available.

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