[](https://zenodo.org/badge/latestdoi/388610692)
# doublemanning
## Package contents
This package contains two command-line utilities
* `doublemanning-fit` inverts stage—discharge data to generate a rating curve and the associated double-Manning-equation parameters:
* A Manning's-equation relationships for an approximately rectangular channel
* A generalized Manning's equation (power-law) relationship for flows across the floodplain
* `doublemanning-calc` uses this fit to perform forward computations:
* Stage → discharge
* Flow depth → discharge
* Discharge → stage
* Discharge → flow depth
## Installation
### From PyPI using Pip
This command will install the most recent stable release of `doublemanning`.
```bash
pip install doublemanning
```
### Editable, from a local directory
These instructions allow you to use the most recent version of `doublemanning` and to make your own edits.
These instructions assume that you have the GitHub CLI installed. If you do not, just change the repository-cloning line to a standard `git` command.
```bash
gh repo clone MNiMORPH/doublemanning
cd doublemanning
pip install -e .
```
## Running the double-Manning software
You should be able to run both commands by simply typing their names on the command line.
Here we provide the outputs form the "`-h`" help flag.
Such outputs are also provided if you enter the commands with no arguments.
### `doublemanning-fit`
**Note:** Although many command-line options exist to fit the data, I recommend using the `YAML` configuration-file option alone. This will allow you to access the full functionality of `doublemanning-fit` (the command-line options include only a smaller subset) and will self-document your work.
```bash
>> doublemanning-fit -h
usage: doublemanning-fit [-h] [-y CONFIGFILE] [-f DATAFILE]
[--delimiter DELIMITER] [-b CHANNEL_WIDTH]
[-H CHANNEL_DEPTH] [-s SLOPE] [-o OUTFILE]
[--use_depth] [--us_units] [--plot] [-v]
Pass channel and flow characteristics to obtain a "Double Manning" --
Manning\'s Equation (channel) + generic power-law (floodplain) stage--discharge
-- relationship.
options:
-h, --help show this help message and exit
-y CONFIGFILE, --configfile CONFIGFILE
YAML file from which all inputs are read.
-f DATAFILE, --datafile DATAFILE
file with two columns: Discharge, Stage
--delimiter DELIMITER
"tab", "comma", or "semicolon"
-b CHANNEL_WIDTH, --channel_width CHANNEL_WIDTH
river-channel width
-H CHANNEL_DEPTH, --channel_depth CHANNEL_DEPTH
river-channel depth (not flow depth)
-s SLOPE, --slope SLOPE
channel slope
-o OUTFILE, --outfile OUTFILE
Stores fit parameters.
--use_depth Use flow depth instead of hydraulic radius.
--us_units Convert imported data from cfs and feet
--plot Plot stage-discharge relationship
-v, --verbose Plot stage-discharge relationship
```
### `doublemanning-calc`
The `doublemanning-calc` program returns a scalar value to `stdout`.
```bash
>> doublemanning-calc -h
usage: doublemanning-calc [-h] [-p PARAMFILE] [-zQ STAGE_DISCHARGE]
[-hQ DEPTH_DISCHARGE] [-Qz DISCHARGE_STAGE]
[-Qh DISCHARGE_DEPTH]
Return stage or discharge based on a double-Manning fit. All values are SI
(mks).
options:
-h, --help show this help message and exit
-p PARAMFILE, --paramfile PARAMFILE
CSV file for double-Manning parameters.
-zQ STAGE_DISCHARGE, --stage_discharge STAGE_DISCHARGE
Calculate discharge from this stage.
-hQ DEPTH_DISCHARGE, --depth_discharge DEPTH_DISCHARGE
Calculate discharge from this flow depth.
-Qz DISCHARGE_STAGE, --discharge_stage DISCHARGE_STAGE
Calculate stage from this discharge.
-Qh DISCHARGE_DEPTH, --discharge_depth DISCHARGE_DEPTH
Calculate flow depth from this discharge.
```
## Physical and mathematical basis
### Core equation
The double-Manning approach applies the following combination of Manning's equation for in-channel flows (left of the $+$ sign) and a power-law equation for overbank flow (right of the $+$ sign):
$$Q = \frac{b}{n_\mathrm{ch}} h R_h^{2/3} S^{1/2} + k_\mathrm{fp} \left(h - h_\beta \right)^{P_\mathrm{fp}}$$
### Variables
| **Variable** | **Description** | **Units [SI]** |
|-----------------|--------------------------------------------------------------------------------------------------------|-------------------------------------------------|
| $Q$ | Discharge | m$\mathrm{m}^3 \text{ s}^{-1}$ |
| $b$ | Channel width | m |
| $B$ | Valley-bottom width | m |
| $B-b$ | Floodplain width | m |
| $z_b$ | River-bed elevation (compared to an arbitrary datum) | m |
| $z_s$ | River stage: water-surface elevation (compared to the same arbitrary datum) | m |
| $h$ | Flow depth: $h = z_s - z_b$ | m |
| $h_b$ | Channel-bank height | m |
| $R_h$ | Hydraulic radius; for the assumed rectangular channel, $R_h = b \cdot h / (b + 2 (h \wedge h_\beta) )$ | m |
| $n_\mathrm{ch}$ | Manning's roughness coefficient within the channel | m |
| $S$ | River-channel slope | — |
| $k_\mathrm{fp}$ | Floodplain-flow coefficient | $\mathrm{m}^{3 - P_\mathrm{fp}} \text{ s}^{-1}$ |
| $P_\mathrm{fp}$ | Floodplain-flow exponent | — |
## Example
Because playing a game is usually quicker and more fun than reading the rules, we provide data and a YAML configuration file for the [Minnesota River near Jordan, MN, USA](examples/MinnesotaJordan), USGS gauge [05330000](https://waterdata.usgs.gov/monitoring-location/05330000/). `config.yaml` is commented and hopefully self-documented well enough; please open an "Issue" if you need some clarification.
### Running `doublemanning-fit`: obtaining the coefficients and plotting the result
`cd` to the `examples/MinnesotaJordan` directory.
```bash
doublemanning-fit -y config.yaml
```
#### `config.yaml`
This is the same `config.yaml` file [from the example](examples/MinnesotaJordan/config.yaml).
```yaml
river: Minnesota
station: Jordan
author: Andy Wickert
data:
# Filename expected with columns "Q", "Stage"
filename: 'MinnesotaJordan.tsv'
# tab, space, or comma
delimiter: 'tab'
# If data set uses US cfs (Q) and feet (Stage), converts these to metric.
us-units: True
channel:
# meters; if ommitted, will be solved for as a free variable
width: 100
# meters; if omitted, will be solved for as a free variable
# depth:
# unitless
slope: 1E-4
# Use depth instead of hydraulic radius for calculations. True/False.
use_depth: False
bounds:
# Uncomment the following to set them different from the defaults
# They should be given in LOWER, UPPER
# Estimated from clast count: 0.365
# Range for mountain streams with gravel + few boulders: 0.03--0.05
mannings_n_bounds:
- 0.025
- 0.06
# Floodplain characteristics:
# * Approximately rectangular
# * 9 m wide (- channel = 6.5 m)
# * 0.8 m high above channel (so 1.6 total) -- but assume infinite
# * Manning's n for heavy timber or med-to-dense brush ~0.1
# k_fp = (B-b)/n * S^(1/2) = 17.9
#floodplain_coeff_bounds:
# - 0
# - 200
floodplain_exponent_bounds:
- 1
- 4
stage_offset_bounds:
# On Google Sheet, I have + 7 cm for 2020 onwards.
# And 10 cm from the start, to which this is now referenced
- -1
- 1
channel_depth_bounds:
- 4
- 10
#channel_width_bounds:
# - 60
# - 100
plotting:
# If this is present, the plot will be saved.
# Format set by file extension.
# Path may be relative or absolute
savepath: 'MinnesotaRiver_Jordan.pdf'
# True/False Boolean flag
show: True
# Optional fixed plotting bounds
stage_min: -0.001
stage_max: 12
#discharge_min:
discharge_max: 3500
# Plot curve even if discharge is negative (nonphysical)
display_negative_rating_curve: False
# Markers and lines for stage offsets and bank heights
stage_offset_hash_bottom: False
stage_offset_hash_top: False
stage_offset_dotted_line: True
bank_height_hash_bottom: False
bank_height_hash_top: False
bank_height_dotted_line: True
output:
# CSV output file name or full path
outfile: 'doublemanning_params_MinnesotaJordan.csv'
# True/False Boolean flag
verbose: True
```
#### Outputs from the double-Manning inversion
`doublemanning-fit` outputs the following table displaying the parameter estimation.
|Manning's n |Floodplain discharge coefficient|Floodplain discharge exponent|Stage at Q = 0 [m] |Bank height [m] |Channel width [m]|Channel slope|SD: Manning's n |SD: Floodplain discharge coefficient|SD: Floodplain discharge exponent|SD: Stage at Q = 0 [m]|SD: Bank height [m] |SD: Channel width [m]|SD: Channel slope|Fit RMSE [m^3/s] |Use flow depth instead of Rh|
|--------------------|--------------------------------|-----------------------------|-------------------|-----------------|-----------------|-------------|---------------------|------------------------------------|---------------------------------|----------------------|---------------------|---------------------|-----------------|------------------|----------------------------|
|0.033831468015063926|138.36638842157538 |1.6166749803210574 |0.47064363991612973|5.797468642861781|100.0 |0.0001 |1.830532636088621e-13|163822.52280191344 |4.139278869596877e-05 |4.002253904290435e-06 |9.715555430266482e-05|0 |0 |44.612476854901466|False |
In addition, `doublemanning-fit` with the provided `config.yaml` outputs a figure. Here, we have altered `config.yaml` from the version provided here in order to output a `svg` instead of a `pdf`.
Here, the data points are in black and the double-Manning rating curve is in thick, solid, gray. The thin vertical dotted gray lines represent (left) the stage at which discharge = 0, corresponding to the river bed in the approximately rectangular channel ($z_b$), and (right) the stage at which flow enters the floodplain, $z_s = z_b + z_\beta$.
### Running `doublemanning-calc`: Obtaining stage or water depth from discharge (and vice versa)
With the parameter-estimation CSV file in hand, you may next perform forward calculations to calculate either water depth (or river stage) from discharge, or compute discharge from river depth (or flow stage).
```bash
# First, let's find discharge based on a provided flow stage
# In this case, let's try 7 meters, which corresponds to an overbank flood.
>> doublemanning-calc -p doublemanning_params_MinnesotaJordan.csv -zQ 7
633.0231625564036
# Next, let's pass this discharge to recover our 7-meter stage.
doublemanning-calc -p doublemanning_params_MinnesotaJordan.csv -Qz 633.0231625564036
7.000000000000001
# Yay!
```
## Acknowledgements
* Campbell Dunn created an early version of the command-line interface to `doublemanning-fit`.
* Jabari Jones assembled the USGS data for the Minnesota River gauge near Jordan.
## Funding
Funding for this project comes from:
* The Alexander von Humboldt-Stiftung through a [Humboldt-Forschungsstipendium](https://www.humboldt-foundation.de/en/apply/sponsorship-programmes/humboldt-research-fellowship) provided to A. Wickert.
* The U.S. National Science foundation via Award [1944782: CAREER: Alluvial river dynamics through watershed networks] to A. Wickert.
<img src="./documentation/funding/AvH_Logo_Support_RGB.svg" alt="Unterstützt von der Alexander von Humboldt Stiftung." width="360px">
<img src="./documentation/funding/logo-NSF.svg" alt="Supported by the U.S. National Science Foundation." width="360px">
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"description": "[](https://zenodo.org/badge/latestdoi/388610692)\n\n# doublemanning\n\n## Package contents\n\nThis package contains two command-line utilities\n* `doublemanning-fit` inverts stage—discharge data to generate a rating curve and the associated double-Manning-equation parameters:\n * A Manning's-equation relationships for an approximately rectangular channel\n * A generalized Manning's equation (power-law) relationship for flows across the floodplain\n* `doublemanning-calc` uses this fit to perform forward computations:\n * Stage → discharge\n * Flow depth → discharge\n * Discharge → stage\n * Discharge → flow depth\n\n## Installation\n\n### From PyPI using Pip\n\nThis command will install the most recent stable release of `doublemanning`.\n\n```bash\npip install doublemanning\n```\n\n### Editable, from a local directory\n\nThese instructions allow you to use the most recent version of `doublemanning` and to make your own edits.\n\nThese instructions assume that you have the GitHub CLI installed. If you do not, just change the repository-cloning line to a standard `git` command.\n\n```bash\ngh repo clone MNiMORPH/doublemanning\ncd doublemanning\npip install -e .\n```\n\n## Running the double-Manning software\n\nYou should be able to run both commands by simply typing their names on the command line.\nHere we provide the outputs form the \"`-h`\" help flag.\nSuch outputs are also provided if you enter the commands with no arguments.\n\n### `doublemanning-fit`\n\n**Note:** Although many command-line options exist to fit the data, I recommend using the `YAML` configuration-file option alone. This will allow you to access the full functionality of `doublemanning-fit` (the command-line options include only a smaller subset) and will self-document your work.\n\n```bash\n>> doublemanning-fit -h\nusage: doublemanning-fit [-h] [-y CONFIGFILE] [-f DATAFILE]\n [--delimiter DELIMITER] [-b CHANNEL_WIDTH]\n [-H CHANNEL_DEPTH] [-s SLOPE] [-o OUTFILE]\n [--use_depth] [--us_units] [--plot] [-v]\n\nPass channel and flow characteristics to obtain a \"Double Manning\" --\nManning\\'s Equation (channel) + generic power-law (floodplain) stage--discharge\n-- relationship.\n\noptions:\n -h, --help show this help message and exit\n -y CONFIGFILE, --configfile CONFIGFILE\n YAML file from which all inputs are read.\n -f DATAFILE, --datafile DATAFILE\n file with two columns: Discharge, Stage\n --delimiter DELIMITER\n \"tab\", \"comma\", or \"semicolon\"\n -b CHANNEL_WIDTH, --channel_width CHANNEL_WIDTH\n river-channel width\n -H CHANNEL_DEPTH, --channel_depth CHANNEL_DEPTH\n river-channel depth (not flow depth)\n -s SLOPE, --slope SLOPE\n channel slope\n -o OUTFILE, --outfile OUTFILE\n Stores fit parameters.\n --use_depth Use flow depth instead of hydraulic radius.\n --us_units Convert imported data from cfs and feet\n --plot Plot stage-discharge relationship\n -v, --verbose Plot stage-discharge relationship\n```\n\n### `doublemanning-calc`\n\nThe `doublemanning-calc` program returns a scalar value to `stdout`.\n\n```bash\n>> doublemanning-calc -h\nusage: doublemanning-calc [-h] [-p PARAMFILE] [-zQ STAGE_DISCHARGE]\n [-hQ DEPTH_DISCHARGE] [-Qz DISCHARGE_STAGE]\n [-Qh DISCHARGE_DEPTH]\n\nReturn stage or discharge based on a double-Manning fit. All values are SI\n(mks).\n\noptions:\n -h, --help show this help message and exit\n -p PARAMFILE, --paramfile PARAMFILE\n CSV file for double-Manning parameters.\n -zQ STAGE_DISCHARGE, --stage_discharge STAGE_DISCHARGE\n Calculate discharge from this stage.\n -hQ DEPTH_DISCHARGE, --depth_discharge DEPTH_DISCHARGE\n Calculate discharge from this flow depth.\n -Qz DISCHARGE_STAGE, --discharge_stage DISCHARGE_STAGE\n Calculate stage from this discharge.\n -Qh DISCHARGE_DEPTH, --discharge_depth DISCHARGE_DEPTH\n Calculate flow depth from this discharge.\n```\n\n## Physical and mathematical basis\n\n### Core equation\n\nThe double-Manning approach applies the following combination of Manning's equation for in-channel flows (left of the $+$ sign) and a power-law equation for overbank flow (right of the $+$ sign):\n\n$$Q = \\frac{b}{n_\\mathrm{ch}} h R_h^{2/3} S^{1/2} + k_\\mathrm{fp} \\left(h - h_\\beta \\right)^{P_\\mathrm{fp}}$$\n\n### Variables\n\n| **Variable** | **Description** | **Units [SI]** |\n|-----------------|--------------------------------------------------------------------------------------------------------|-------------------------------------------------|\n| $Q$ | Discharge | m$\\mathrm{m}^3 \\text{ s}^{-1}$ |\n| $b$ | Channel width | m |\n| $B$ | Valley-bottom width | m |\n| $B-b$ | Floodplain width | m |\n| $z_b$ | River-bed elevation (compared to an arbitrary datum) | m |\n| $z_s$ | River stage: water-surface elevation (compared to the same arbitrary datum) | m |\n| $h$ | Flow depth: $h = z_s - z_b$ | m |\n| $h_b$ | Channel-bank height | m |\n| $R_h$ | Hydraulic radius; for the assumed rectangular channel, $R_h = b \\cdot h / (b + 2 (h \\wedge h_\\beta) )$ | m |\n| $n_\\mathrm{ch}$ | Manning's roughness coefficient within the channel | m |\n| $S$ | River-channel slope | — |\n| $k_\\mathrm{fp}$ | Floodplain-flow coefficient | $\\mathrm{m}^{3 - P_\\mathrm{fp}} \\text{ s}^{-1}$ |\n| $P_\\mathrm{fp}$ | Floodplain-flow exponent | — |\n\n## Example\n\nBecause playing a game is usually quicker and more fun than reading the rules, we provide data and a YAML configuration file for the [Minnesota River near Jordan, MN, USA](examples/MinnesotaJordan), USGS gauge [05330000](https://waterdata.usgs.gov/monitoring-location/05330000/). `config.yaml` is commented and hopefully self-documented well enough; please open an \"Issue\" if you need some clarification.\n\n### Running `doublemanning-fit`: obtaining the coefficients and plotting the result\n\n`cd` to the `examples/MinnesotaJordan` directory.\n\n```bash\ndoublemanning-fit -y config.yaml\n```\n\n#### `config.yaml`\n\nThis is the same `config.yaml` file [from the example](examples/MinnesotaJordan/config.yaml).\n\n```yaml\nriver: Minnesota\nstation: Jordan\n\nauthor: Andy Wickert\n\ndata:\n # Filename expected with columns \"Q\", \"Stage\"\n filename: 'MinnesotaJordan.tsv'\n # tab, space, or comma\n delimiter: 'tab'\n # If data set uses US cfs (Q) and feet (Stage), converts these to metric.\n us-units: True\n\nchannel:\n # meters; if ommitted, will be solved for as a free variable\n width: 100\n # meters; if omitted, will be solved for as a free variable\n # depth:\n # unitless\n slope: 1E-4\n # Use depth instead of hydraulic radius for calculations. True/False.\n use_depth: False\n\nbounds:\n # Uncomment the following to set them different from the defaults\n # They should be given in LOWER, UPPER\n # Estimated from clast count: 0.365\n # Range for mountain streams with gravel + few boulders: 0.03--0.05\n mannings_n_bounds:\n - 0.025\n - 0.06\n # Floodplain characteristics:\n # * Approximately rectangular\n # * 9 m wide (- channel = 6.5 m)\n # * 0.8 m high above channel (so 1.6 total) -- but assume infinite\n # * Manning's n for heavy timber or med-to-dense brush ~0.1\n # k_fp = (B-b)/n * S^(1/2) = 17.9\n #floodplain_coeff_bounds:\n # - 0\n # - 200\n floodplain_exponent_bounds:\n - 1\n - 4\n stage_offset_bounds:\n # On Google Sheet, I have + 7 cm for 2020 onwards.\n # And 10 cm from the start, to which this is now referenced\n - -1\n - 1\n channel_depth_bounds:\n - 4\n - 10\n #channel_width_bounds:\n # - 60\n # - 100\n\nplotting:\n # If this is present, the plot will be saved.\n # Format set by file extension.\n # Path may be relative or absolute\n savepath: 'MinnesotaRiver_Jordan.pdf'\n # True/False Boolean flag\n show: True\n # Optional fixed plotting bounds\n stage_min: -0.001\n stage_max: 12\n #discharge_min:\n discharge_max: 3500\n # Plot curve even if discharge is negative (nonphysical)\n display_negative_rating_curve: False\n # Markers and lines for stage offsets and bank heights\n stage_offset_hash_bottom: False\n stage_offset_hash_top: False\n stage_offset_dotted_line: True\n bank_height_hash_bottom: False\n bank_height_hash_top: False\n bank_height_dotted_line: True\n\noutput:\n # CSV output file name or full path\n outfile: 'doublemanning_params_MinnesotaJordan.csv'\n # True/False Boolean flag\n verbose: True\n```\n\n#### Outputs from the double-Manning inversion\n\n`doublemanning-fit` outputs the following table displaying the parameter estimation.\n\n|Manning's n |Floodplain discharge coefficient|Floodplain discharge exponent|Stage at Q = 0 [m] |Bank height [m] |Channel width [m]|Channel slope|SD: Manning's n |SD: Floodplain discharge coefficient|SD: Floodplain discharge exponent|SD: Stage at Q = 0 [m]|SD: Bank height [m] |SD: Channel width [m]|SD: Channel slope|Fit RMSE [m^3/s] |Use flow depth instead of Rh|\n|--------------------|--------------------------------|-----------------------------|-------------------|-----------------|-----------------|-------------|---------------------|------------------------------------|---------------------------------|----------------------|---------------------|---------------------|-----------------|------------------|----------------------------|\n|0.033831468015063926|138.36638842157538 |1.6166749803210574 |0.47064363991612973|5.797468642861781|100.0 |0.0001 |1.830532636088621e-13|163822.52280191344 |4.139278869596877e-05 |4.002253904290435e-06 |9.715555430266482e-05|0 |0 |44.612476854901466|False |\n\nIn addition, `doublemanning-fit` with the provided `config.yaml` outputs a figure. Here, we have altered `config.yaml` from the version provided here in order to output a `svg` instead of a `pdf`.\n\n\n\nHere, the data points are in black and the double-Manning rating curve is in thick, solid, gray. The thin vertical dotted gray lines represent (left) the stage at which discharge = 0, corresponding to the river bed in the approximately rectangular channel ($z_b$), and (right) the stage at which flow enters the floodplain, $z_s = z_b + z_\\beta$.\n\n### Running `doublemanning-calc`: Obtaining stage or water depth from discharge (and vice versa)\n\nWith the parameter-estimation CSV file in hand, you may next perform forward calculations to calculate either water depth (or river stage) from discharge, or compute discharge from river depth (or flow stage).\n\n```bash\n# First, let's find discharge based on a provided flow stage\n# In this case, let's try 7 meters, which corresponds to an overbank flood.\n>> doublemanning-calc -p doublemanning_params_MinnesotaJordan.csv -zQ 7\n633.0231625564036\n\n# Next, let's pass this discharge to recover our 7-meter stage.\ndoublemanning-calc -p doublemanning_params_MinnesotaJordan.csv -Qz 633.0231625564036\n7.000000000000001\n\n# Yay!\n```\n\n## Acknowledgements\n\n* Campbell Dunn created an early version of the command-line interface to `doublemanning-fit`.\n* Jabari Jones assembled the USGS data for the Minnesota River gauge near Jordan.\n\n## Funding\n\nFunding for this project comes from:\n* The Alexander von Humboldt-Stiftung through a [Humboldt-Forschungsstipendium](https://www.humboldt-foundation.de/en/apply/sponsorship-programmes/humboldt-research-fellowship) provided to A. Wickert.\n* The U.S. National Science foundation via Award [1944782: CAREER: Alluvial river dynamics through watershed networks] to A. Wickert.\n\n<img src=\"./documentation/funding/AvH_Logo_Support_RGB.svg\" alt=\"Unterst\u00fctzt von der Alexander von Humboldt Stiftung.\" width=\"360px\">\n\n<img src=\"./documentation/funding/logo-NSF.svg\" alt=\"Supported by the U.S. National Science Foundation.\" width=\"360px\">\n",
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