NIVAFjord
This is auto-generated documentation based on the model code in models/nivafjord_simplycnp_model.txt . Since the modules can be dynamically loaded with different arguments, this documentation does not necessarily reflect all use cases of the modules.
See the note on notation.
The file was generated at 2024-05-29 12:40:58.
NIVAFjord dimensions
Version: 0.0.0
File: modules/nivafjord/basin.txt
External symbols
| Name | Symbol | Type |
|---|---|---|
| Fjord layer | layer | compartment |
| All basins | all_basins | index_set |
| Layer index | layer_idx | index_set |
Parameters
| Name | Symbol | Unit | Description |
|---|---|---|---|
| Layer thickness | |||
| Stable layer thickness | dz0 | m | |
| Layer area | Distributes like: layer | ||
| Layer area | A | m² |
NIVAFjord basin
Version: 0.0.3
File: modules/nivafjord/basin.txt
Description
This is the physics component for a single basin of the NIVAFjord model.
The model is loosely based on the model Eutrofimodell for Indre Oslofjord (Norwegian only).
Each basin is divided into a set of (assumed horizontally mixed) layers of potentially varying thickness.
Turbulent vertical mixing is computed assuming constant turbulent energy (per layer), which implies a fixed dependency of the mixing rate on the Brunt-Väisälä frequency proportional to
\[r_0(N/N_0)^\alpha\]where \(N\) is the Brunt-Väisälä frequency, \(N_0\) a reference frequency, \(r_0\) the mixing rate at the reference frequency and \(\alpha \sim 1.4\) an exponential dependency. The reference rate \(r_0\) can be set separately per layer.
Wind-driven mixing and mixing from ship traffic is added on top.
The basin model is also similar to MyLake.
MyLake—A multi-year lake simulation model code suitable for uncertainty and sensitivity analysis simulations, Tuomo M. Saloranta and Tom Andersen 2007, Ecological Modelling 207(1), 45-60, https://doi.org/10.1016/j.ecolmodel.2007.03.018
Authors: Magnus D. Norling
External symbols
| Name | Symbol | Type |
|---|---|---|
| Atmosphere | air | compartment |
| sw_sed | loc | |
| Depth | z | property |
| Density | rho | property |
| Basin | basin | compartment |
| Fjord layer | layer | compartment |
| Water | water | quantity |
| Salinity | salinity | property |
| Ice formation temperature | freeze_temp | property |
| Salt | salt | quantity |
| Heat energy | heat | quantity |
| Wind speed | wind | property |
| Temperature | temp | property |
| Pressure | pressure | property |
| Global radiation | g_rad | property |
| Attenuation | attn | property |
| Thickness | dz | property |
| Sea level | h | property |
| Area | area | property |
| Shortwave radiation | sw | property |
| Fjord vertical | vert | connection |
| Shortwave vertical | sw_vert | connection |
Parameters
| Name | Symbol | Unit | Description |
|---|---|---|---|
| Mixing parameters | Distributes like: basin | ||
| Brunt-Väisälä frequency reference | N0 | s⁻¹ | |
| Minimum B-V frequency | Nmin | s⁻¹ | |
| Mixing non-linear coefficient | alpha | ||
| Surface additional mixing energy | Es0 | m² s⁻³ | |
| Halving depth of additional mixing energy | zshalf | m | |
| Diminishing rate of additional mixing energy | hsfact | m | |
| Layer specific mixing | Distributes like: layer | ||
| Mixing factor reference | K0 | m² s⁻¹ | Mixing factor when the B-V frequency is equal to the reference |
| Initial layer physical | Distributes like: layer | ||
| Initial layer temperature | init_t | °C | |
| Initial layer salinity | init_s |
State variables
Air temperature
Location: air.temp
Unit: °C
This series is externally defined. It may be an input series.
Wind speed
Location: air.wind
Unit: m s⁻¹
This series is externally defined. It may be an input series.
Global radiation
Location: air.g_rad
Unit: W m⁻²
This series is externally defined. It may be an input series.
Ice formation temperature
Location: basin.freeze_temp
Unit: °C
Value:
\[\href{stdlib.html#seawater}{\mathrm{ice\_formation\_temperature}}\left(\mathrm{layer}.\mathrm{water}.\mathrm{salinity}\lbrack\mathrm{vert}.\mathrm{top}\rbrack\right)\]Layer thickness
Location: layer.dz
Unit: m
Value:
\[\mathrm{Aavg} = 0.5\cdot \left(\mathrm{A}+\mathrm{A}\lbrack\mathrm{vert}.\mathrm{below}\rbrack\right) \\ \frac{\mathrm{water}}{\mathrm{Aavg}}\]Initial value:
\[\mathrm{dz0}\]Depth (to bottom of layer)
Location: layer.z
Unit: m
Value:
\[\mathrm{z}\lbrack\mathrm{vert}.\mathrm{above}\rbrack+\mathrm{dz}\lbrack\mathrm{vert}.\mathrm{above}\rbrack\]Basin sea level
Location: basin.h
Unit: m
Value:
\[\mathrm{aggregate}\left(\mathrm{layer}.\mathrm{dz}\right)-\mathrm{aggregate}\left(\mathrm{dz0}\right)\]Basin area
Location: basin.area
Unit: m²
Value:
\[\mathrm{A}\lbrack\mathrm{vert}.\mathrm{top}\rbrack\]Layer water
Location: layer.water
Unit: m³
Initial value:
\[\mathrm{Aavg} = 0.5\cdot \left(\mathrm{A}+\mathrm{A}\lbrack\mathrm{vert}.\mathrm{below}\rbrack\right) \\ \mathrm{Aavg}\cdot \mathrm{dz0}\]Layer salt
Location: layer.water.salt
Unit: kg
Conc. unit: kg m⁻³
Initial value (concentration):
\[\mathrm{salinity}\cdot 0.001\cdot \mathrm{rho\_water}\]Layer thermal energy
Location: layer.water.heat
Unit: J
Initial value (concentration):
\[\mathrm{C\_water}\cdot \left(\mathrm{temp}\rightarrow \mathrm{K}\,\right)\cdot \mathrm{rho\_water}\]Layer temperature
Location: layer.water.temp
Unit: °C
Value:
\[\left(\frac{\mathrm{heat}}{\mathrm{water}\cdot \mathrm{C\_water}\cdot \mathrm{rho\_water}}\rightarrow \mathrm{°C}\,\right)\]Initial value:
\[\mathrm{init\_t}\]Layer salinity
Location: layer.water.salinity
Unit:
Value:
\[1000\cdot \frac{\mathrm{conc}\left(\mathrm{salt}\right)}{\mathrm{rho\_water}}\]Initial value:
\[\mathrm{init\_s}\]Potential density
Location: layer.water.rho
Unit: kg m⁻³
Value:
\[\href{stdlib.html#seawater}{\mathrm{seawater\_pot\_dens}}\left(\mathrm{temp},\, \mathrm{salinity}\right)\]Pressure
Location: layer.water.pressure
Unit: Pa
Value:
\[\mathrm{pressure}\lbrack\mathrm{vert}.\mathrm{above}\rbrack+\mathrm{rho}\cdot \mathrm{grav}\cdot \mathrm{dz}\]d(dens)
Location: layer.water.ddens
Unit: kg m⁻³
Value:
\[\mathrm{rho}\lbrack\mathrm{vert}.\mathrm{below}\rbrack-\mathrm{rho}\]Brunt-Väisälä frequency
Location: layer.water.Nfreq
Unit: s⁻¹
Value:
\[\mathrm{mdz} = 0.5\cdot \left(\mathrm{dz}+\mathrm{dz}\lbrack\mathrm{vert}.\mathrm{below}\rbrack\right) \\ \mathrm{N2} = \mathrm{grav}\cdot \frac{\mathrm{ddens}}{\mathrm{mdz}\cdot \mathrm{rho}} \\ \sqrt{\mathrm{max}\left(\mathrm{Nmin}^{2},\, \mathrm{N2}\right)}\]Wind stress
Location: basin.stress
Unit: N m⁻²
Value:
\[\mathrm{u} = \mathrm{air}.\mathrm{wind} \\ \mathrm{c\_stress} = 0.001\cdot \left(0.8+0.9\cdot \frac{\mathrm{u}^{8}}{\mathrm{u}^{8}+10^{8} \mathrm{m}^{8}\,\mathrm{s}^{-8}\,}\right) \\ \mathrm{air}.\mathrm{rho}\cdot \mathrm{c\_stress}\cdot \mathrm{u}^{2}\]Total wind mixing energy
Location: basin.emix
Unit: J
Value:
\[\mathrm{A}\lbrack\mathrm{vert}.\mathrm{top}\rbrack\cdot \sqrt{\frac{\mathrm{stress}^{3}}{\mathrm{layer}.\mathrm{water}.\mathrm{rho}\lbrack\mathrm{vert}.\mathrm{top}\rbrack}}\cdot \mathrm{time}.\mathrm{step\_length\_in\_seconds}\]Sum V above
Location: layer.water.sumV
Unit: m³
Value:
\[\mathrm{sumV}\lbrack\mathrm{vert}.\mathrm{above}\rbrack+\mathrm{water}\lbrack\mathrm{vert}.\mathrm{above}\rbrack\]Potential energy needed for wind mixing
Location: layer.water.potmix
Unit: J
Value:
\[\mathrm{max}\left(0,\, \mathrm{grav}\cdot \mathrm{ddens}\cdot \mathrm{sumV}\cdot \frac{\mathrm{water}}{\mathrm{sumV}+\mathrm{water}}\cdot \frac{\mathrm{z}+0.5\cdot \mathrm{dz}}{2}\right)\]Wind mixing energy
Location: layer.water.emix
Unit: J
Value:
\[\mathrm{rem} = \mathrm{max}\left(0,\, \mathrm{basin}.\mathrm{emix}-\mathrm{summix}\right) \\ \mathrm{min}\left(\mathrm{rem},\, \mathrm{potmix}\right)\]Sum used wind mixing energy
Location: layer.water.summix
Unit: J
Value:
\[\mathrm{emix}\lbrack\mathrm{vert}.\mathrm{above}\rbrack+\mathrm{summix}\lbrack\mathrm{vert}.\mathrm{above}\rbrack\]Wind mixing
Location: layer.water.v_w
Unit: m s⁻¹
Value:
\[\mathrm{rem} = \mathrm{max}\left(0,\, \mathrm{basin}.\mathrm{emix}-\mathrm{summix}\lbrack\mathrm{vert}.\mathrm{below}\rbrack\right) \\ \mathrm{mixspeed} = \frac{1 \mathrm{m}\,}{\mathrm{time}.\mathrm{step\_length\_in\_seconds}} \\ \begin{cases}0 \mathrm{m}\,\mathrm{s}^{-1}\, & \text{if}\;\mathrm{is\_at}\lbrack\mathrm{vert}.\mathrm{bottom}\rbrack \\ \left(\mathrm{mixspeed}\rightarrow \mathrm{m}\,\mathrm{s}^{-1}\,\right) & \text{if}\;\mathrm{rem}>10^{-30} \mathrm{J}\,\;\text{and}\;\mathrm{potmix}\lbrack\mathrm{vert}.\mathrm{below}\rbrack<10^{-30} \mathrm{J}\, \\ \left(\mathrm{mixspeed}\cdot \href{stdlib.html#basic}{\mathrm{safe\_divide}}\left(\mathrm{emix}\lbrack\mathrm{vert}.\mathrm{below}\rbrack,\, \mathrm{potmix}\lbrack\mathrm{vert}.\mathrm{below}\rbrack\right)\rightarrow \mathrm{m}\,\mathrm{s}^{-1}\,\right) & \text{otherwise}\end{cases}\]Turbulent mixing
Location: layer.water.v_t
Unit: m s⁻¹
Value:
\[\mathrm{dz\_} = 0.5\cdot \left(\mathrm{dz}+\mathrm{dz}\lbrack\mathrm{vert}.\mathrm{below}\rbrack\right) \\ \href{stdlib.html#basic}{\mathrm{safe\_divide}}\left(\mathrm{K0},\, \mathrm{dz\_}\cdot \left(\frac{\mathrm{Nfreq}}{\mathrm{N0}}\right)^{\mathrm{alpha}}\right)\]Additional mixing
Location: layer.water.v_s
Unit: m s⁻¹
Value:
\[\mathrm{dz\_} = 0.5\cdot \left(\mathrm{dz}+\mathrm{dz}\lbrack\mathrm{vert}.\mathrm{below}\rbrack\right) \\ \mathrm{eta} = e^{\frac{-\left(\mathrm{z}-\mathrm{zshalf}\right)}{\mathrm{hsfact}}} \\ \mathrm{Es} = \mathrm{Es0}\cdot \frac{\mathrm{eta}}{1+\mathrm{eta}} \\ \frac{\mathrm{Es}}{\mathrm{dz\_}\cdot \mathrm{Nfreq}^{2}}\]Layer shortwave radiation
Location: layer.water.sw
Unit: W m⁻²
Value:
\[\left(\frac{\mathrm{in\_flux}\left(\mathrm{sw\_vert},\, \mathrm{layer}.\mathrm{water}.\mathrm{heat}\right)}{\mathrm{A}}\rightarrow \mathrm{W}\,\mathrm{m}^{-2}\,\right)\]Fluxes
Layer mixing down
Source: layer.water
Target: vert
Unit: m³ day⁻¹
This is a mixing flux (affects dissolved quantities only)
Value:
\[\left(\left(\mathrm{v\_t}+\mathrm{v\_s}+\mathrm{v\_w}\right)\cdot \mathrm{A}\lbrack\mathrm{vert}.\mathrm{below}\rbrack\rightarrow \mathrm{m}^{3}\,\mathrm{day}^{-1}\,\right)\]Shortwave shine-through
Source: layer.water.heat
Target: sw_vert
Unit: J day⁻¹
Value:
\[\left(\mathrm{in\_flux}\left(\mathrm{sw\_vert},\, \mathrm{layer}.\mathrm{water}.\mathrm{heat}\right)\rightarrow \mathrm{J}\,\mathrm{day}^{-1}\,\right)\cdot \left(1-\mathrm{attn}\right)\cdot \frac{\mathrm{A}\lbrack\mathrm{vert}.\mathrm{below}\rbrack}{\mathrm{A}}\]Shortwave to sediments
Source: layer.water.heat
Target: sw_sed
Unit: J day⁻¹
Value:
\[\left(\mathrm{in\_flux}\left(\mathrm{sw\_vert},\, \mathrm{layer}.\mathrm{water}.\mathrm{heat}\right)\rightarrow \mathrm{J}\,\mathrm{day}^{-1}\,\right)\cdot \left(1-\mathrm{attn}\right)\cdot \frac{\mathrm{A}-\mathrm{A}\lbrack\mathrm{vert}.\mathrm{below}\rbrack}{\mathrm{A}}\]