© [Institute of Urban Water Management and Landscape Water Engineering](https://www.sww.tugraz.at), [Graz University of Technology](https://www.tugraz.at/home/) and [Markus Pichler](mailto:markus.pichler@tugraz.at)
# Intensity duration frequency analysis (based on KOSTRA)
[](https://github.com/MarkusPic/intensity_duration_frequency_analysis/blob/master/LICENSE)
[](https://pypi.python.org/pypi/idf-analysis)
[](https://zenodo.org/doi/10.5281/zenodo.10559991)
[](https://pypi.python.org/pypi/idf-analysis)
[](https://pypi.python.org/pypi/idf-analysis)
[](https://pypi.python.org/pypi/idf-analysis)
Heavy rainfall intensity as a function of duration and return period acc. to [DWA-A 531 (2012)](http://www.dwa.de/dwa/shop/shop.nsf/Produktanzeige?openform&produktid=P-DWAA-8XMUY2).
This program reads the measurement data of the rainfall
and calculates the distribution of the design rainfall as a function of the return period and the duration
for duration steps up to 12 hours (and more) and return period in a range of '0.5a ≤ T_n ≤ 100a'.
The guideline was used in the application [KOSTRA-DWD](https://www.dwd.de/DE/leistungen/kostra_dwd_rasterwerte/kostra_dwd_rasterwerte.html).
----
> Heavy rainfall data are among the most important planning parameters in water management and hydraulic engineering practice. In urban areas, for example, they are required as initial parameters for the design of rainwater drainage systems and in watercourses for the dimensioning of hydraulic structures. The accuracy of the target values of the corresponding calculation methods and models depends crucially on their accuracy. Their overestimation can lead to considerable additional costs in the structural implementation, their underestimation to an unacceptable, excessive residual risk of failure during the operation of water management and hydraulic engineering facilities. Despite the area-wide availability of heavy rainfall data through "Coordinated Heavy Rainfall Regionalisation Analyses" (KOSTRA), there is still a need for local station analyses, e.g. to evaluate the now extended data series, to evaluate recent developments or to classify local peculiarities in comparison to the KOSTRA data. However, this is only possible without restrictions if the methodological approach recommended in the worksheet is followed.
**[DWA-A 531 (2012)](http://www.dwa.de/dwa/shop/shop.nsf/Produktanzeige?openform&produktid=P-DWAA-8XMUY2) Translated with www.DeepL.com/Translator**
----
> An intensity-duration-frequency (IDF) curve is a mathematical function that relates the rainfall intensity with its duration and frequency of occurrence. These curves are commonly used in hydrology for flood forecasting and civil engineering for urban drainage design. However, the IDF curves are also analysed in hydrometeorology because of the interest in the time concentration or time-structure of the rainfall.
**[Wikipedia](https://en.wikipedia.org/wiki/Intensity-duration-frequency_curve)**
----
This package was developed by [Markus Pichler](mailto:markus.pichler@tugraz.at) during his bachelor thesis and finalised it in the course of his employment at the [Institute of Urban Water Management and Landscape Water Engineering](https://www.sww.tugraz.at).
## Documentation
Read the docs [here 📖](https://markuspic.github.io/intensity_duration_frequency_analysis).
## Please cite as
Pichler, M. (2024). idf_analysis: Intensity duration frequency analysis with python based on KOSTRA (v0.2.4). Zenodo. https://doi.org/10.5281/zenodo.10559992
## Installation
This package is written in Python3. (use a version > 3.5)
```
pip install idf-analysis
```
Add the following tags to the command for special options:
- ```--user```: To install the package only for the local user account (no admin rights needed)
- ```--upgrade```: To update the package
### Windows
You have to install python first (i.e. the original python from the [website](https://www.python.org/downloads/)).
To use the command-line-tool, it is advisable to add the path to your Python binary to the environment variables [^path1].
There is also an option during the installation to add python to the PATH automatically. [^path2]
[^path1]: https://geek-university.com/python/add-python-to-the-windows-path/
[^path2]: https://datatofish.com/add-python-to-windows-path/
### Linux/Unix
Python is pre-installed on most operating systems (as you probably knew).
### Dependencies
Packages required for this program will be installed with pip during the installation process and can be seen
in the [`requirements.txt`](https://github.com/MarkusPic/intensity_duration_frequency_analysis/blob/master/requirements.txt) file.
## Usage
The documentation of the python-API can be found [here](https://markuspic.github.io/intensity_duration_frequency_analysis/api.html).
One basic usage could be:
```python
import pandas as pd
from idf_analysis import IntensityDurationFrequencyAnalyse
from idf_analysis.definitions import *
# initialize of the analysis class
idf = IntensityDurationFrequencyAnalyse(series_kind=SERIES.PARTIAL, worksheet=METHOD.KOSTRA, extended_durations=True)
series = pd.Series(index=pd.DatetimeIndex(...), data=...)
# setting the series for the analysis
idf.set_series(series)
# auto-save the calculated parameter so save time for a later use, as the parameters doesn't have to be calculated again.
idf.auto_save_parameters('idf_parameters.yaml')
```
If you only want to analyse an already existing IDF-table
```python
import pandas as pd
from idf_analysis import IntensityDurationFrequencyAnalyse
idf_table = pd.DataFrame(...)
# index: Duration Steps in minutes as int or float
# columns: Return Periods in years as int or float
# values: rainfall height in mm
idf = IntensityDurationFrequencyAnalyse.from_idf_table(idf_table)
```
## Commandline tool
The following commands show the usage for Linux/Unix systems.
To use these features on Windows you have to add ```python -m``` before each command.
To start the script use following commands in the terminal/Prompt
```idf_analysis```
> ```idf_analysis -h```
```
usage: __main__.py [-h] -i INPUT
[-ws {ATV-A_121,DWA-A_531,DWA-A_531_advektiv}]
[-kind {partial,annual}] [-t {>= 0.5 a and <= 100 a}]
[-d {>= 5 min and <= 8640 min}] [-r {>= 0 L/s*ha}]
[-h_N {>= 0 mm}] [--r_720_1] [--plot] [--export_table]
heavy rain as a function of the duration and the return period acc. to DWA-A
531 (2012) All files will be saved in the same directory of the input file but
in a subfolder called like the inputfile + "_idf_data". Inside this folder a
file called "idf_parameter.yaml"-file will be saved and contains interim-
calculation-results and will be automatically reloaded on the next call.
optional arguments:
-h, --help show this help message and exit
-i INPUT, --input INPUT
input file with the rain time-series (csv or parquet)
-ws {ATV-A_121,DWA-A_531,DWA-A_531_advektiv}, --worksheet {ATV-A_121,DWA-A_531,DWA-A_531_advektiv}
From which worksheet the recommendations for
calculating the parameters should be taken.
-kind {partial,annual}, --series_kind {partial,annual}
The kind of series used for the calculation.
(Calculation with partial series is more precise and
recommended.)
-t {>= 0.5 a and <= 100 a}, --return_period {>= 0.5 a and <= 100 a}
return period in years (If two of the three variables
(rainfall (height or flow-rate), duration, return
period) are given, the third variable is calculated.)
-d {>= 5 min and <= 8640 min}, --duration {>= 5 min and <= 8640 min}
duration in minutes (If two of the three variables
(rainfall (height or flow-rate), duration, return
period) are given, the third variable is calculated.)
-r {>= 0 L/(s*ha)}, --flow_rate_of_rainfall {>= 0 L/(s*ha)}
rainfall in Liter/(s * ha) (If two of the three
variables (rainfall (height or flow-rate), duration,
return period) are given, the third variable is
calculated.)
-h_N {>= 0 mm}, --height_of_rainfall {>= 0 mm}
rainfall in mm or Liter/m^2 (If two of the three
variables (rainfall (height or flow-rate), duration,
return period) are given, the third variable is
calculated.)
--r_720_1 design rainfall with a duration of 720 minutes (=12 h)
and a return period of 1 year
--plot get a plot of the idf relationship
--export_table get a table of the most frequent used values
```
## Example
[Example Jupyter notebook for the commandline](examples/example_commandline.ipynb)
[Example Jupyter notebook for the python api](examples/example_python_api.ipynb)
[Example python skript](examples/example_python_api.py)
### Example Files
[Interim Results of the idf analysis](examples/ehyd_112086_idf_data/idf_parameters.yaml)
### Example Plot
### Example IDF table
[IDF-Table](examples/ehyd_112086_idf_data/idf_table_UNIX.csv)
| return period in a<br>duration in min | 1 | 2 | 3 | 5 | 10 | 20 | 25 | 30 | 50 | 75 | 100 |
|--------------------------------------:|------:|-------:|-------:|-------:|-------:|-------:|-------:|-------:|-------:|-------:|-------:|
| 5 | 9.39 | 10.97 | 11.89 | 13.04 | 14.61 | 16.19 | 16.69 | 17.11 | 18.26 | 19.18 | 19.83 |
| 10 | 15.15 | 17.62 | 19.06 | 20.88 | 23.35 | 25.82 | 26.62 | 27.27 | 29.09 | 30.54 | 31.56 |
| 15 | 19.03 | 22.25 | 24.13 | 26.51 | 29.72 | 32.94 | 33.98 | 34.83 | 37.20 | 39.08 | 40.42 |
| 20 | 21.83 | 25.71 | 27.99 | 30.85 | 34.73 | 38.62 | 39.87 | 40.89 | 43.75 | 46.02 | 47.63 |
| 30 | 25.60 | 30.66 | 33.62 | 37.35 | 42.41 | 47.47 | 49.10 | 50.43 | 54.16 | 57.12 | 59.22 |
| 45 | 28.92 | 35.51 | 39.37 | 44.23 | 50.83 | 57.42 | 59.54 | 61.28 | 66.14 | 69.99 | 72.73 |
| 60 | 30.93 | 38.89 | 43.54 | 49.40 | 57.36 | 65.31 | 67.88 | 69.97 | 75.83 | 80.49 | 83.79 |
| 90 | 33.37 | 41.74 | 46.64 | 52.80 | 61.17 | 69.54 | 72.23 | 74.43 | 80.60 | 85.49 | 88.96 |
| 180 | 38.01 | 47.13 | 52.46 | 59.18 | 68.30 | 77.42 | 80.36 | 82.76 | 89.48 | 94.81 | 98.60 |
| 270 | 41.01 | 50.60 | 56.21 | 63.28 | 72.87 | 82.46 | 85.55 | 88.07 | 95.14 | 100.75 | 104.73 |
| 360 | 43.29 | 53.23 | 59.04 | 66.37 | 76.31 | 86.25 | 89.45 | 92.06 | 99.39 | 105.20 | 109.33 |
| 450 | 45.14 | 55.36 | 61.33 | 68.87 | 79.08 | 89.30 | 92.59 | 95.28 | 102.81 | 108.79 | 113.03 |
| 600 | 47.64 | 58.23 | 64.43 | 72.23 | 82.82 | 93.41 | 96.82 | 99.61 | 107.42 | 113.61 | 118.01 |
| 720 | 49.29 | 60.13 | 66.47 | 74.45 | 85.29 | 96.12 | 99.61 | 102.46 | 110.44 | 116.78 | 121.28 |
| 1080 | 54.41 | 64.97 | 71.15 | 78.94 | 89.50 | 100.06 | 103.46 | 106.24 | 114.02 | 120.20 | 124.58 |
| 1440 | 58.02 | 67.72 | 73.39 | 80.54 | 90.24 | 99.93 | 103.05 | 105.61 | 112.75 | 118.42 | 122.45 |
| 2880 | 66.70 | 77.41 | 83.68 | 91.57 | 102.29 | 113.00 | 116.45 | 119.26 | 127.16 | 133.42 | 137.87 |
| 4320 | 71.93 | 85.72 | 93.78 | 103.95 | 117.73 | 131.52 | 135.96 | 139.58 | 149.75 | 157.81 | 163.53 |
| 5760 | 78.95 | 95.65 | 105.42 | 117.72 | 134.43 | 151.13 | 156.50 | 160.89 | 173.20 | 182.97 | 189.90 |
| 7200 | 83.53 | 101.38 | 111.82 | 124.98 | 142.83 | 160.68 | 166.43 | 171.12 | 184.28 | 194.72 | 202.13 |
| 8640 | 85.38 | 104.95 | 116.40 | 130.82 | 150.38 | 169.95 | 176.25 | 181.40 | 195.82 | 207.27 | 215.39 |
## Background
Pseudocode for the parameter calculation.
```
For every duration step
calculating event sums
if using annual event series: # only recommeded for measurements longer than 20 year
converting every max event sum per year to a series
calculating parameters u and w using the gumbel distribution
elif using partial event series:
converting the n (approximatly 2.72 x measurement duration in years) biggest event sums to a series
calculating parameters u and w using the exponential distribution
Splitting IDF curve formulation in to several duration ranges
For each duration range:
For each parameter (u and w):
balancing the parameter over all duation steps (in the range) using a given formulation (creating parameters a and b)
# one-folded-logaritmic | two-folded-logarithmic | hyperbolic
u(D) = f(a_u, b_u, D)
w(D) = f(a_w, b_w, D)
h(D,Tn) = u(D) + w(D) * ln(Tn)
```
Raw data
{
"_id": null,
"home_page": null,
"name": "idf-analysis",
"maintainer": null,
"docs_url": null,
"requires_python": ">=3.7",
"maintainer_email": null,
"keywords": "duration, analysis, rainfall, dwd, idf, measurement-data, precipitation, kostra, dwa, heavy-rain, intensity-duration-frequency, design-rainfall, duration-steps, return-period, dwa-a-531",
"author": null,
"author_email": "Markus Pichler <markus.pichler@tugraz.at>",
"download_url": "https://files.pythonhosted.org/packages/2e/5c/4c0ea9da6131b0065ef7bc4ec09b558664b1ae0dff7b5b707b685d49cb4e/idf_analysis-0.3.0.tar.gz",
"platform": null,
"description": "\u00a9 [Institute of Urban Water Management and Landscape Water Engineering](https://www.sww.tugraz.at), [Graz University of Technology](https://www.tugraz.at/home/) and [Markus Pichler](mailto:markus.pichler@tugraz.at)\n\n\n# Intensity duration frequency analysis (based on KOSTRA)\n\n\n[](https://github.com/MarkusPic/intensity_duration_frequency_analysis/blob/master/LICENSE)\n[](https://pypi.python.org/pypi/idf-analysis)\n[](https://zenodo.org/doi/10.5281/zenodo.10559991)\n\n[](https://pypi.python.org/pypi/idf-analysis)\n[](https://pypi.python.org/pypi/idf-analysis)\n[](https://pypi.python.org/pypi/idf-analysis)\n\n\nHeavy rainfall intensity as a function of duration and return period acc. to [DWA-A 531 (2012)](http://www.dwa.de/dwa/shop/shop.nsf/Produktanzeige?openform&produktid=P-DWAA-8XMUY2).\nThis program reads the measurement data of the rainfall\nand calculates the distribution of the design rainfall as a function of the return period and the duration\nfor duration steps up to 12 hours (and more) and return period in a range of '0.5a ≤ T_n ≤ 100a'.\n\nThe guideline was used in the application [KOSTRA-DWD](https://www.dwd.de/DE/leistungen/kostra_dwd_rasterwerte/kostra_dwd_rasterwerte.html).\n\n----\n\n> Heavy rainfall data are among the most important planning parameters in water management and hydraulic engineering practice. In urban areas, for example, they are required as initial parameters for the design of rainwater drainage systems and in watercourses for the dimensioning of hydraulic structures. The accuracy of the target values of the corresponding calculation methods and models depends crucially on their accuracy. Their overestimation can lead to considerable additional costs in the structural implementation, their underestimation to an unacceptable, excessive residual risk of failure during the operation of water management and hydraulic engineering facilities. Despite the area-wide availability of heavy rainfall data through \"Coordinated Heavy Rainfall Regionalisation Analyses\" (KOSTRA), there is still a need for local station analyses, e.g. to evaluate the now extended data series, to evaluate recent developments or to classify local peculiarities in comparison to the KOSTRA data. However, this is only possible without restrictions if the methodological approach recommended in the worksheet is followed. \n\n**[DWA-A 531 (2012)](http://www.dwa.de/dwa/shop/shop.nsf/Produktanzeige?openform&produktid=P-DWAA-8XMUY2) Translated with www.DeepL.com/Translator**\n\n----\n\n> An intensity-duration-frequency (IDF) curve is a mathematical function that relates the rainfall intensity with its duration and frequency of occurrence. These curves are commonly used in hydrology for flood forecasting and civil engineering for urban drainage design. However, the IDF curves are also analysed in hydrometeorology because of the interest in the time concentration or time-structure of the rainfall.\n\n**[Wikipedia](https://en.wikipedia.org/wiki/Intensity-duration-frequency_curve)**\n\n----\n\nThis package was developed by [Markus Pichler](mailto:markus.pichler@tugraz.at) during his bachelor thesis and finalised it in the course of his employment at the [Institute of Urban Water Management and Landscape Water Engineering](https://www.sww.tugraz.at).\n\n## Documentation\n\nRead the docs [here \ud83d\udcd6](https://markuspic.github.io/intensity_duration_frequency_analysis).\n\n## Please cite as\n\nPichler, M. (2024). idf_analysis: Intensity duration frequency analysis with python based on KOSTRA (v0.2.4). Zenodo. https://doi.org/10.5281/zenodo.10559992\n\n## Installation\n\nThis package is written in Python3. (use a version > 3.5)\n\n```\npip install idf-analysis\n```\n\nAdd the following tags to the command for special options:\n\n- ```--user```: To install the package only for the local user account (no admin rights needed)\n- ```--upgrade```: To update the package\n\n### Windows\n\nYou have to install python first (i.e. the original python from the [website](https://www.python.org/downloads/)).\n\nTo use the command-line-tool, it is advisable to add the path to your Python binary to the environment variables [^path1].\nThere is also an option during the installation to add python to the PATH automatically. [^path2]\n\n[^path1]: https://geek-university.com/python/add-python-to-the-windows-path/\n[^path2]: https://datatofish.com/add-python-to-windows-path/\n\n\n### Linux/Unix\n\nPython is pre-installed on most operating systems (as you probably knew).\n\n### Dependencies\n\nPackages required for this program will be installed with pip during the installation process and can be seen \nin the [`requirements.txt`](https://github.com/MarkusPic/intensity_duration_frequency_analysis/blob/master/requirements.txt) file.\n\n## Usage\n\nThe documentation of the python-API can be found [here](https://markuspic.github.io/intensity_duration_frequency_analysis/api.html).\n\nOne basic usage could be:\n\n```python\nimport pandas as pd\nfrom idf_analysis import IntensityDurationFrequencyAnalyse\nfrom idf_analysis.definitions import *\n\n# initialize of the analysis class\nidf = IntensityDurationFrequencyAnalyse(series_kind=SERIES.PARTIAL, worksheet=METHOD.KOSTRA, extended_durations=True)\n\nseries = pd.Series(index=pd.DatetimeIndex(...), data=...)\n\n# setting the series for the analysis\nidf.set_series(series)\n# auto-save the calculated parameter so save time for a later use, as the parameters doesn't have to be calculated again.\nidf.auto_save_parameters('idf_parameters.yaml')\n```\n\nIf you only want to analyse an already existing IDF-table\n\n```python\nimport pandas as pd\nfrom idf_analysis import IntensityDurationFrequencyAnalyse\n\nidf_table = pd.DataFrame(...)\n# index: Duration Steps in minutes as int or float\n# columns: Return Periods in years as int or float\n# values: rainfall height in mm\nidf = IntensityDurationFrequencyAnalyse.from_idf_table(idf_table)\n```\n\n## Commandline tool\n\nThe following commands show the usage for Linux/Unix systems.\nTo use these features on Windows you have to add ```python -m``` before each command.\n\nTo start the script use following commands in the terminal/Prompt\n\n```idf_analysis```\n\n> ```idf_analysis -h```\n\n```\nusage: __main__.py [-h] -i INPUT\n [-ws {ATV-A_121,DWA-A_531,DWA-A_531_advektiv}]\n [-kind {partial,annual}] [-t {>= 0.5 a and <= 100 a}]\n [-d {>= 5 min and <= 8640 min}] [-r {>= 0 L/s*ha}]\n [-h_N {>= 0 mm}] [--r_720_1] [--plot] [--export_table]\n\nheavy rain as a function of the duration and the return period acc. to DWA-A\n531 (2012) All files will be saved in the same directory of the input file but\nin a subfolder called like the inputfile + \"_idf_data\". Inside this folder a\nfile called \"idf_parameter.yaml\"-file will be saved and contains interim-\ncalculation-results and will be automatically reloaded on the next call.\n\noptional arguments:\n -h, --help show this help message and exit\n -i INPUT, --input INPUT\n input file with the rain time-series (csv or parquet)\n -ws {ATV-A_121,DWA-A_531,DWA-A_531_advektiv}, --worksheet {ATV-A_121,DWA-A_531,DWA-A_531_advektiv}\n From which worksheet the recommendations for\n calculating the parameters should be taken.\n -kind {partial,annual}, --series_kind {partial,annual}\n The kind of series used for the calculation.\n (Calculation with partial series is more precise and\n recommended.)\n -t {>= 0.5 a and <= 100 a}, --return_period {>= 0.5 a and <= 100 a}\n return period in years (If two of the three variables\n (rainfall (height or flow-rate), duration, return\n period) are given, the third variable is calculated.)\n -d {>= 5 min and <= 8640 min}, --duration {>= 5 min and <= 8640 min}\n duration in minutes (If two of the three variables\n (rainfall (height or flow-rate), duration, return\n period) are given, the third variable is calculated.)\n -r {>= 0 L/(s*ha)}, --flow_rate_of_rainfall {>= 0 L/(s*ha)}\n rainfall in Liter/(s * ha) (If two of the three\n variables (rainfall (height or flow-rate), duration,\n return period) are given, the third variable is\n calculated.)\n -h_N {>= 0 mm}, --height_of_rainfall {>= 0 mm}\n rainfall in mm or Liter/m^2 (If two of the three\n variables (rainfall (height or flow-rate), duration,\n return period) are given, the third variable is\n calculated.)\n --r_720_1 design rainfall with a duration of 720 minutes (=12 h)\n and a return period of 1 year\n --plot get a plot of the idf relationship\n --export_table get a table of the most frequent used values\n```\n\n## Example\n\n[Example Jupyter notebook for the commandline](examples/example_commandline.ipynb)\n\n[Example Jupyter notebook for the python api](examples/example_python_api.ipynb)\n\n[Example python skript](examples/example_python_api.py)\n\n\n### Example Files\n\n[Interim Results of the idf analysis](examples/ehyd_112086_idf_data/idf_parameters.yaml)\n\n### Example Plot\n\n\n\n### Example IDF table\n\n[IDF-Table](examples/ehyd_112086_idf_data/idf_table_UNIX.csv)\n\n\n| return period in a<br>duration in min | 1 | 2 | 3 | 5 | 10 | 20 | 25 | 30 | 50 | 75 | 100 |\n|--------------------------------------:|------:|-------:|-------:|-------:|-------:|-------:|-------:|-------:|-------:|-------:|-------:|\n| 5 | 9.39 | 10.97 | 11.89 | 13.04 | 14.61 | 16.19 | 16.69 | 17.11 | 18.26 | 19.18 | 19.83 |\n| 10 | 15.15 | 17.62 | 19.06 | 20.88 | 23.35 | 25.82 | 26.62 | 27.27 | 29.09 | 30.54 | 31.56 |\n| 15 | 19.03 | 22.25 | 24.13 | 26.51 | 29.72 | 32.94 | 33.98 | 34.83 | 37.20 | 39.08 | 40.42 |\n| 20 | 21.83 | 25.71 | 27.99 | 30.85 | 34.73 | 38.62 | 39.87 | 40.89 | 43.75 | 46.02 | 47.63 |\n| 30 | 25.60 | 30.66 | 33.62 | 37.35 | 42.41 | 47.47 | 49.10 | 50.43 | 54.16 | 57.12 | 59.22 |\n| 45 | 28.92 | 35.51 | 39.37 | 44.23 | 50.83 | 57.42 | 59.54 | 61.28 | 66.14 | 69.99 | 72.73 |\n| 60 | 30.93 | 38.89 | 43.54 | 49.40 | 57.36 | 65.31 | 67.88 | 69.97 | 75.83 | 80.49 | 83.79 |\n| 90 | 33.37 | 41.74 | 46.64 | 52.80 | 61.17 | 69.54 | 72.23 | 74.43 | 80.60 | 85.49 | 88.96 |\n| 180 | 38.01 | 47.13 | 52.46 | 59.18 | 68.30 | 77.42 | 80.36 | 82.76 | 89.48 | 94.81 | 98.60 |\n| 270 | 41.01 | 50.60 | 56.21 | 63.28 | 72.87 | 82.46 | 85.55 | 88.07 | 95.14 | 100.75 | 104.73 |\n| 360 | 43.29 | 53.23 | 59.04 | 66.37 | 76.31 | 86.25 | 89.45 | 92.06 | 99.39 | 105.20 | 109.33 |\n| 450 | 45.14 | 55.36 | 61.33 | 68.87 | 79.08 | 89.30 | 92.59 | 95.28 | 102.81 | 108.79 | 113.03 |\n| 600 | 47.64 | 58.23 | 64.43 | 72.23 | 82.82 | 93.41 | 96.82 | 99.61 | 107.42 | 113.61 | 118.01 |\n| 720 | 49.29 | 60.13 | 66.47 | 74.45 | 85.29 | 96.12 | 99.61 | 102.46 | 110.44 | 116.78 | 121.28 |\n| 1080 | 54.41 | 64.97 | 71.15 | 78.94 | 89.50 | 100.06 | 103.46 | 106.24 | 114.02 | 120.20 | 124.58 |\n| 1440 | 58.02 | 67.72 | 73.39 | 80.54 | 90.24 | 99.93 | 103.05 | 105.61 | 112.75 | 118.42 | 122.45 |\n| 2880 | 66.70 | 77.41 | 83.68 | 91.57 | 102.29 | 113.00 | 116.45 | 119.26 | 127.16 | 133.42 | 137.87 |\n| 4320 | 71.93 | 85.72 | 93.78 | 103.95 | 117.73 | 131.52 | 135.96 | 139.58 | 149.75 | 157.81 | 163.53 |\n| 5760 | 78.95 | 95.65 | 105.42 | 117.72 | 134.43 | 151.13 | 156.50 | 160.89 | 173.20 | 182.97 | 189.90 |\n| 7200 | 83.53 | 101.38 | 111.82 | 124.98 | 142.83 | 160.68 | 166.43 | 171.12 | 184.28 | 194.72 | 202.13 |\n| 8640 | 85.38 | 104.95 | 116.40 | 130.82 | 150.38 | 169.95 | 176.25 | 181.40 | 195.82 | 207.27 | 215.39 |\n\n## Background\n\nPseudocode for the parameter calculation.\n\n```\nFor every duration step\n calculating event sums\n \n if using annual event series: # only recommeded for measurements longer than 20 year\n converting every max event sum per year to a series\n calculating parameters u and w using the gumbel distribution\n \n elif using partial event series:\n converting the n (approximatly 2.72 x measurement duration in years) biggest event sums to a series\n calculating parameters u and w using the exponential distribution\n \nSplitting IDF curve formulation in to several duration ranges\nFor each duration range:\n For each parameter (u and w):\n balancing the parameter over all duation steps (in the range) using a given formulation (creating parameters a and b)\n # one-folded-logaritmic | two-folded-logarithmic | hyperbolic\n\nu(D) = f(a_u, b_u, D)\nw(D) = f(a_w, b_w, D)\n\nh(D,Tn) = u(D) + w(D) * ln(Tn)\n```\n",
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