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 2024-11-12 13:40:23.
NIVAFjord dimensions
Version: 0.0.0
File: modules/nivafjord/basin.txt
External symbols
| Name | Symbol | Type |
|---|---|---|
| Fjord layer | layer | compartment |
| All layers | all_layer | compartment |
Parameters
| Name | Symbol | Unit | Description |
|---|---|---|---|
| Layer thickness | Distributes like: all_layer | ||
| 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 |
| Salinity | salinity | property |
| Water | water | quantity |
| 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 |
| ice_ind | loc | |
| Fjord vertical | vert | connection |
| Shortwave vertical | sw_vert | connection |
Constants
| Name | Symbol | Unit | Value |
|---|---|---|---|
| Sediment albedo | sed_alb | 0.3 |
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 |
| Mixing factor reference under ice | K0ice | m² s⁻¹ | |
| 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:
\[\;\text{not}\;\mathrm{ice\_ind}\cdot \mathrm{A}\lbrack\mathrm{vert}.\mathrm{top}\rbrack\cdot \sqrt{\frac{\mathrm{stress}^{3}}{\mathrm{layer}.\mathrm{water}.\mathrm{rho}\lbrack\mathrm{vert}.\mathrm{top}\rbrack}}\cdot \mathrm{time}.\mathrm{step\_length\_in\_seconds}\]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:
\[\mathrm{K} = \begin{cases}\mathrm{K0ice} & \text{if}\;\mathrm{ice\_ind} \\ \mathrm{K0} & \text{otherwise}\end{cases} \\ \mathrm{dz\_} = 0.5\cdot \left(\mathrm{dz}+\mathrm{dz}\lbrack\mathrm{vert}.\mathrm{below}\rbrack\right) \\ \href{stdlib.html#basic}{\mathrm{safe\_divide}}\left(\mathrm{K},\, \mathrm{dz\_}\cdot \left(\frac{\mathrm{Nfreq}}{\mathrm{N0}}\right)^{\mathrm{alpha}}\right)\]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:
\[\left(\mathrm{in\_flux}\left(\mathrm{sw\_vert},\, \mathrm{layer}.\mathrm{water}.\mathrm{heat}\right)\rightarrow \mathrm{J}\,\mathrm{day}^{-1}\,\right)\cdot \left(1-\mathrm{attn}\right)\cdot \left(1-\mathrm{sed\_alb}\right)\cdot \frac{\mathrm{A}-\mathrm{A}\lbrack\mathrm{vert}.\mathrm{below}\rbrack}{\mathrm{A}}\]NIVAFjord chemistry rates
Version: 0.0.1
File: modules/nivafjord/fjordchem.txt
Parameters
| Name | Symbol | Unit | Description |
|---|---|---|---|
| Oxygen | |||
| Bubble formation coefficient | bubble | day⁻¹ | |
| Oxicity threshold | ox_th | mg l⁻¹ | |
| Microbes | |||
| Decomposition Q10 | decompQ10 | Adjustment of rate with 10°C change in temperature | |
| Maximal decomposition rate at 20°C | maxdecomp_20 | day⁻¹ | |
| Maximal denitrification rate at 20°C | maxdenitr_20 | day⁻¹ | |
| Molar O₂/C ratio in respiration | O2toC | ||
| N mineralization and nitrification rate modifier | n_min | ||
| P mineralization modifier | p_min | ||
| NO3 threshold for denitrification | n_denit_th | mg l⁻¹ | |
| POM dissolution rate | diss_r | day⁻¹ | |
| P desorption / adsorption | |||
| PO4 sorption coefficient | k_sorp | l mg⁻¹ | |
| PO4 sorption rate | r_sorp | day⁻¹ |
NIVAFjord chemistry
Version: 0.0.5
File: modules/nivafjord/fjordchem.txt
Description
NIVAFjord module for O₂, dissolved nutrients and particles as well as microbial processes.
Authors: Magnus Dahler Norling, François Clayer
External symbols
| Name | Symbol | Type |
|---|---|---|
| Atmosphere | air | compartment |
| CO₂ | co2 | quantity |
| Cosine of the solar zenith angle | cos_z | property |
| Depth | z | property |
| O₂ saturation concentration | o2satconc | property |
| Fjord layer | layer | compartment |
| CH₄ | ch4 | quantity |
| Fjord sediment | sediment | compartment |
| Organic nitrogen | on | quantity |
| Water | water | quantity |
| O₂ | o2 | quantity |
| Temperature | temp | property |
| Organic carbon | oc | quantity |
| Nitrate | din | quantity |
| Total nitrogen | tn | property |
| Phosphate | phos | quantity |
| Organic phosphorous | op | quantity |
| Sediments | sed | quantity |
| Fjord phytoplankton | phyt | quantity |
| Total phosphorous | tp | property |
| Salinity | salin | property |
| Thickness | dz | property |
| Attenuation | attn | property |
| Area | area | property |
| Shortwave radiation | sw | property |
| Fjord vertical | vert | connection |
| Compute DIC (CO₂, CH₄) | compute_dic | par_bool |
Parameters
| Name | Symbol | Unit | Description |
|---|---|---|---|
| Initial chem | Distributes like: layer | ||
| Initial O₂ saturation | init_O2 | ||
| Initial DOC concentration | init_DOC | mg l⁻¹ | |
| Initial suspended sediment concentration | init_ss | mg l⁻¹ | |
| Initial particle organic carbon content | init_foc | g kg⁻¹ | |
| Light | |||
| Diffuse attenuation coefficent (clear water) | attn0 | m⁻¹ | |
| Shading factor | shade_f | m⁻¹ l mg⁻¹ | Shading provided by suspended particles and DOM |
| Suspended particles | |||
| Settling velocity | sett_vel | m day⁻¹ |
State variables
Layer O₂
Location: layer.water.o2
Unit: kg
Conc. unit: mg l⁻¹
Initial value (concentration):
\[\left(\href{stdlib.html#sea-oxygen}{\mathrm{o2\_saturation\_concentration}}\left(\mathrm{temp},\, \mathrm{salin}\right)\cdot \mathrm{init\_O2}\cdot \mathrm{o2\_mol\_mass}\rightarrow \mathrm{kg}\,\right)\]Layer DOC
Location: layer.water.oc
Unit: kg
Conc. unit: mg l⁻¹
Initial value (concentration):
\[\mathrm{init\_DOC}\]Layer CO₂
Location: layer.water.co2
Unit: kg
Conc. unit: mg l⁻¹
Layer CH₄
Location: layer.water.ch4
Unit: kg
Conc. unit: mg l⁻¹
Layer DIN
Location: layer.water.din
Unit: kg
Conc. unit: mg l⁻¹
Layer DON
Location: layer.water.on
Unit: kg
Conc. unit: mg l⁻¹
Layer DIP
Location: layer.water.phos
Unit: kg
Conc. unit: mg l⁻¹
Layer DOP
Location: layer.water.op
Unit: kg
Conc. unit: mg l⁻¹
Layer suspended sediments
Location: layer.water.sed
Unit: kg
Conc. unit: mg l⁻¹
Initial value (concentration):
\[\mathrm{init\_ss}\]Layer POC
Location: layer.water.sed.oc
Unit: kg
Conc. unit: g kg⁻¹
Initial value (concentration):
\[\mathrm{init\_foc}\]Layer PIP
Location: layer.water.sed.phos
Unit: kg
Conc. unit: g kg⁻¹
Layer POP
Location: layer.water.sed.op
Unit: kg
Conc. unit: g kg⁻¹
Layer PON
Location: layer.water.sed.on
Unit: kg
Conc. unit: g kg⁻¹
Layer TN
Location: layer.water.tn
Unit: mg l⁻¹
Value:
\[\mathrm{conc}\left(\mathrm{din}\right)+\mathrm{conc}\left(\mathrm{on}\right)+\left(\mathrm{conc}\left(\mathrm{sed}\right)\cdot \mathrm{conc}\left(\mathrm{sed}.\mathrm{on}\right)\rightarrow \mathrm{mg}\,\mathrm{l}^{-1}\,\right)\]Layer TP
Location: layer.water.tp
Unit: mg l⁻¹
Value:
\[\mathrm{conc}\left(\mathrm{phos}\right)+\mathrm{conc}\left(\mathrm{op}\right)+\left(\mathrm{conc}\left(\mathrm{sed}\right)\cdot \left(\mathrm{conc}\left(\mathrm{sed}.\mathrm{op}\right)+\mathrm{conc}\left(\mathrm{sed}.\mathrm{phos}\right)\right)\rightarrow \mathrm{mg}\,\mathrm{l}^{-1}\,\right)\]O₂ saturation concentration
Location: layer.water.o2satconc
Unit: mg l⁻¹
Value:
\[\left(\href{stdlib.html#sea-oxygen}{\mathrm{o2\_saturation\_concentration}}\left(\mathrm{temp},\, \mathrm{salin}\right)\cdot \mathrm{o2\_mol\_mass}\rightarrow \mathrm{mg}\,\mathrm{l}^{-1}\,\right)\]O₂ saturation
Location: layer.water.o2sat
Unit:
Value:
\[\frac{\mathrm{conc}\left(\mathrm{layer}.\mathrm{water}.\mathrm{o2}\right)}{\mathrm{layer}.\mathrm{water}.\mathrm{o2satconc}}\]Layer attenuation
Location: layer.water.attn
Unit:
Value:
\[\mathrm{att\_c} = \mathrm{attn0}+\left(\mathrm{conc}\left(\mathrm{sed}\right)+\mathrm{aggregate}\left(\mathrm{conc}\left(\mathrm{phyt}\right)\right)+\mathrm{conc}\left(\mathrm{oc}\right)\right)\cdot \mathrm{shade\_f} \\ \mathrm{cz} = \mathrm{max}\left(0.01,\, \href{stdlib.html#radiation}{\mathrm{refract}}\left(\mathrm{air}.\mathrm{cos\_z},\, \mathrm{refraction\_index\_water}\right)\right) \\ \mathrm{th} = \frac{\mathrm{dz}}{\mathrm{cz}} \\ 1-e^{-\mathrm{att\_c}\cdot \mathrm{th}}\]Oxicity factor
Location: layer.water.ox_fac
Unit:
Value:
\[\mathrm{wd} = 1 \\ \href{stdlib.html#response}{\mathrm{s\_response}}\left(\mathrm{conc}\left(\mathrm{o2}\right),\, \left(1-\mathrm{wd}\right)\cdot \mathrm{ox\_th},\, \left(1+\mathrm{wd}\right)\cdot \mathrm{ox\_th},\, 0,\, 1\right)\]Temperature factor
Location: layer.water.temp_fac
Unit:
Value:
\[\href{stdlib.html#response}{\mathrm{q10\_adjust}}\left(1,\, 20 \mathrm{°C}\,,\, \mathrm{temp},\, \mathrm{decompQ10}\right)\]OM mineralization rate
Location: layer.water.min_rat
Unit: day⁻¹
Value:
\[\mathrm{ox\_fac}\cdot \mathrm{temp\_fac}\cdot \mathrm{maxdecomp\_20}\]Denitrification rate
Location: layer.water.denit_rat
Unit: day⁻¹
Value:
\[\mathrm{wd} = 0.5 \\ \mathrm{n\_fac} = \href{stdlib.html#response}{\mathrm{s\_response}}\left(\frac{\mathrm{conc}\left(\mathrm{din}\right)}{\mathrm{n\_denit\_th}},\, 1-\mathrm{wd},\, 1+\mathrm{wd},\, 0,\, 1\right) \\ \left(1-\mathrm{ox\_fac}\right)\cdot \mathrm{temp\_fac}\cdot \mathrm{maxdenitr\_20}\cdot \mathrm{n\_fac}\]Fluxes
O₂ bubble formation
Source: layer.water.o2
Target: out
Unit: kg day⁻¹
Value:
\[\mathrm{pressure\_corr} = 1+0.476 \mathrm{m}^{-1}\,\cdot \mathrm{z}\lbrack\mathrm{vert}.\mathrm{above}\rbrack \\ \mathrm{satconc} = \mathrm{o2satconc}\cdot \mathrm{pressure\_corr} \\ \left(\mathrm{max}\left(0,\, \mathrm{bubble}\cdot \left(\mathrm{conc}\left(\mathrm{o2}\right)-\mathrm{satconc}\right)\cdot \mathrm{water}\right)\rightarrow \mathrm{kg}\,\mathrm{day}^{-1}\,\right)\]Layer particle settling
Source: layer.water.sed
Target: vert
Unit: kg day⁻¹
Value:
\[\left(\mathrm{sett\_vel}\cdot \mathrm{conc}\left(\mathrm{sed}\right)\cdot \mathrm{A}\lbrack\mathrm{vert}.\mathrm{below}\rbrack\rightarrow \mathrm{kg}\,\mathrm{day}^{-1}\,\right)\]Layer particle settling to bottom
Source: layer.water.sed
Target: sediment.sed
Unit: kg day⁻¹
Value:
\[\left(\mathrm{sett\_vel}\cdot \mathrm{conc}\left(\mathrm{sed}\right)\cdot \mathrm{sediment}.\mathrm{area}\rightarrow \mathrm{kg}\,\mathrm{day}^{-1}\,\right)\]Layer POC dissolution
Source: layer.water.sed.oc
Target: layer.water.oc
Unit: kg day⁻¹
Value:
\[\mathrm{diss\_r}\cdot \mathrm{sed}.\mathrm{oc}\]Layer PON dissolution
Source: layer.water.sed.on
Target: layer.water.on
Unit: kg day⁻¹
Value:
\[\mathrm{diss\_r}\cdot \mathrm{sed}.\mathrm{on}\]DOC mineralization
Source: layer.water.oc
Target: out
Unit: kg day⁻¹
Value:
\[\mathrm{oc}\cdot \mathrm{min\_rat}\]POC mineralization
Source: layer.water.sed.oc
Target: out
Unit: kg day⁻¹
Value:
\[\mathrm{sed}.\mathrm{oc}\cdot \mathrm{min\_rat}\]DON mineralization and nitrification
Source: layer.water.on
Target: layer.water.din
Unit: kg day⁻¹
Value:
\[\mathrm{on}\cdot \mathrm{min\_rat}\cdot \mathrm{n\_min}\]PON mineralization and nitrification
Source: layer.water.sed.on
Target: layer.water.din
Unit: kg day⁻¹
Value:
\[\mathrm{sed}.\mathrm{on}\cdot \mathrm{min\_rat}\cdot \mathrm{n\_min}\]DOP mineralization
Source: layer.water.op
Target: layer.water.phos
Unit: kg day⁻¹
Value:
\[\mathrm{op}\cdot \mathrm{temp\_fac}\cdot \mathrm{maxdecomp\_20}\cdot \mathrm{p\_min}\]POP mineralization
Source: layer.water.sed.op
Target: layer.water.phos
Unit: kg day⁻¹
Value:
\[\mathrm{sed}.\mathrm{op}\cdot \mathrm{temp\_fac}\cdot \mathrm{maxdecomp\_20}\cdot \mathrm{p\_min}\]O₂ microbial consumption
Source: layer.water.o2
Target: out
Unit: kg day⁻¹
Value:
\[\left(\mathrm{oc}+\mathrm{sed}.\mathrm{oc}\right)\cdot \mathrm{min\_rat}\cdot \frac{\mathrm{o2\_mol\_mass}}{\mathrm{c\_mol\_mass}}\cdot \mathrm{O2toC}+\left(\mathrm{on}+\mathrm{sed}.\mathrm{on}\right)\cdot \mathrm{min\_rat}\cdot \mathrm{n\_min}\cdot \frac{\mathrm{o2\_mol\_mass}}{\mathrm{n\_mol\_mass}}\cdot 1.5\]Microbial CO2 production
Source: out
Target: layer.water.co2
Unit: kg day⁻¹
Value:
\[\left(\mathrm{oc}+\mathrm{sed}.\mathrm{oc}\right)\cdot \left(\mathrm{min\_rat}+\mathrm{denit\_rat}\right)\]DOC mineralization by denitrification
Source: layer.water.oc
Target: out
Unit: kg day⁻¹
Value:
\[\mathrm{water}.\mathrm{oc}\cdot \mathrm{denit\_rat}\]POC mineralization by denitrification
Source: layer.water.sed.oc
Target: out
Unit: kg day⁻¹
Value:
\[\mathrm{water}.\mathrm{sed}.\mathrm{oc}\cdot \mathrm{denit\_rat}\]NO3 denitrification consumption
Source: layer.water.din
Target: out
Unit: kg day⁻¹
Value:
\[\mathrm{bo2} = \left(\mathrm{water}.\mathrm{oc}+\mathrm{water}.\mathrm{sed}.\mathrm{oc}\right)\cdot \mathrm{denit\_rat}\cdot \mathrm{O2toC}\cdot \frac{\mathrm{o2\_mol\_mass}}{\mathrm{c\_mol\_mass}} \\ \mathrm{bo2}\cdot 1.5\cdot \frac{\mathrm{n\_mol\_mass}}{\mathrm{o2\_mol\_mass}}\]PO4 adsorption / desorption to particles
Source: layer.water.phos
Target: layer.water.sed.phos
Unit: kg day⁻¹
Value:
\[\mathrm{epc0} = \left(\frac{\mathrm{conc}\left(\mathrm{sed}.\mathrm{phos}\right)}{\mathrm{k\_sorp}}\rightarrow \mathrm{mg}\,\mathrm{l}^{-1}\,\right) \\ \mathrm{epc0\_} = \mathrm{min}\left(\mathrm{epc0},\, 0 \mathrm{mg}\,\mathrm{l}^{-1}\,\right) \\ \mathrm{r\_sorp}\cdot \left(\left(\mathrm{ox\_fac}\cdot \left(\mathrm{conc}\left(\mathrm{water}.\mathrm{phos}\right)-\mathrm{epc0\_}\right)\cdot \mathrm{water}\rightarrow \mathrm{kg}\,\right)-\left(1-\mathrm{ox\_fac}\right)\cdot \mathrm{sed}.\mathrm{phos}\right)\]NIVAFjord sediments
Version: 0.0.4
File: modules/nivafjord/sediment.txt
External symbols
| Name | Symbol | Type |
|---|---|---|
| CO₂ | co2 | quantity |
| Depth | z | property |
| Fjord layer | layer | compartment |
| CH₄ | ch4 | quantity |
| Fjord sediment | sediment | compartment |
| Organic nitrogen | on | quantity |
| Water | water | quantity |
| O₂ | o2 | quantity |
| Salinity | salin | property |
| Sediments | sed | quantity |
| Temperature | temp | property |
| Organic carbon | oc | quantity |
| Nitrate | din | quantity |
| Phosphate | phos | quantity |
| Organic phosphorous | op | quantity |
| Heat energy | heat | quantity |
| Area | area | property |
| Thickness | dz | property |
| Fjord vertical | vert | connection |
| Compute DIC (CO₂, CH₄) | compute_dic | par_bool |
Constants
| Name | Symbol | Unit | Value |
|---|---|---|---|
| Sediment density | sed_rho | kg m⁻³ | 2600 |
| Sediment specific heat capacity | sed_C | J kg⁻¹ K⁻¹ | 4000 |
| Sediment heat conductivity coefficient | sed_k | W m⁻¹ K⁻¹ | 2.2 |
| Sediment C/N | sed_cn | 6.25 | |
| Sediment C/P | sed_cp | 106 |
Parameters
| Name | Symbol | Unit | Description |
|---|---|---|---|
| Sediments | |||
| Active sediment thickness | th | m | |
| Sediment porosity | porosity | ||
| Resuspension fraction | resus | Fraction of settling material that is resuspended | |
| Biochemistry | |||
| Sediment relative microbial rate | micr_rel | Rate of sediment microbial processes relative to water column rate | |
| Sediment CH4 production scaler | ch4_production_scaler | sediment CH4 production relative to sediment CO2 production | |
| Bubble CH4 formation coefficient | bubble_ch4 | day⁻¹ | |
| Initial chem | Distributes like: sediment | ||
| Initial sediment C fraction | init_c | g kg⁻¹ | |
| Initial sediment IP fraction | init_p | g kg⁻¹ | |
| Sediment pore water DOC concentration | sed_doc | mg l⁻¹ | |
| Sediment temperature | |||
| Thickness of thermally active sediment layer | dzh | m | |
| Deep sediment temperature | T_bot | °C |
State variables
Active sediment thickness
Location: sediment.dz
Unit: m
Value:
\[\mathrm{th}\]Sediment thermal energy
Location: sediment.heat
Unit: J
Initial value:
\[\left(\mathrm{temp}\rightarrow \mathrm{K}\,\right)\cdot \mathrm{sed\_C}\cdot \mathrm{area}\cdot \mathrm{dzh}\cdot \mathrm{sed\_rho}\]Sediment surface temperature
Location: sediment.temp
Unit: °C
Value:
\[\mathrm{V} = \mathrm{area}\cdot \mathrm{dzh} \\ \mathrm{T\_avg} = \left(\frac{\mathrm{heat}}{\mathrm{sed\_C}\cdot \mathrm{sed\_rho}\cdot \mathrm{area}\cdot \mathrm{dzh}}\rightarrow \mathrm{°C}\,\right) \\ 2\cdot \mathrm{T\_avg}-\mathrm{T\_bot}\]Initial value:
\[\mathrm{T\_bot}\]Sediment area
Location: sediment.area
Unit: m²
Value:
\[\mathrm{A}-\mathrm{A}\lbrack\mathrm{vert}.\mathrm{below}\rbrack\]Sediment mass
Location: sediment.sed
Unit: kg
Initial value:
\[\mathrm{area}\cdot \mathrm{th}\cdot \mathrm{sed\_rho}\cdot \left(1-\mathrm{porosity}\right)\]Sediment organic carbon
Location: sediment.sed.oc
Unit: kg
Conc. unit: g kg⁻¹
Initial value (concentration):
\[\mathrm{init\_c}\]Sediment CH4
Location: sediment.sed.ch4
Unit: kg
Conc. unit: g kg⁻¹
Sediment organic N
Location: sediment.sed.on
Unit: kg
Conc. unit: g kg⁻¹
Initial value (concentration):
\[\frac{\mathrm{init\_c}}{\href{stdlib.html#chemistry}{\mathrm{cn\_molar\_to\_mass\_ratio}}\left(\mathrm{sed\_cn}\right)}\]Sediment IP
Location: sediment.sed.phos
Unit: kg
Conc. unit: g kg⁻¹
Initial value (concentration):
\[\mathrm{init\_p}\]Sediment OP
Location: sediment.sed.op
Unit: kg
Conc. unit: g kg⁻¹
Initial value (concentration):
\[\frac{\mathrm{init\_c}}{\href{stdlib.html#chemistry}{\mathrm{cp\_molar\_to\_mass\_ratio}}\left(\mathrm{sed\_cp}\right)}\]Sediment pore water
Location: sediment.water
Unit: m³
Value:
\[\mathrm{area}\cdot \mathrm{th}\cdot \mathrm{porosity}\]Sediment pore water DOC
Location: sediment.water.oc
Unit: kg
Conc. unit: mg l⁻¹
Value (concentration):
\[\mathrm{sed\_doc}\]CH4 saturation concentration
Location: sediment.sed.ch4satconc
Unit: g kg⁻¹
Value:
\[\mathrm{ch4\_mol\_mass}\cdot \left(0.00247 \mathrm{mol}\,\mathrm{kg}^{-1}\,-4.033\cdot 10^{5} \mathrm{mol}\,\mathrm{kg}^{-1}\,\mathrm{°C}^{-1}\,\cdot \mathrm{sediment}.\mathrm{temp}\right)\cdot \left(1-\left(0.2844-0.001775 \mathrm{°C}^{-1}\,\cdot \mathrm{sediment}.\mathrm{temp}\right)\cdot \frac{\mathrm{layer}.\mathrm{water}.\mathrm{salin}}{58.44}\right)\cdot \left(1+44.6 \mathrm{m}^{-1}\,\cdot \frac{\mathrm{layer}.\mathrm{z}\lbrack\mathrm{vert}.\mathrm{above}\rbrack}{490}\right)\]Fluxes
Water-sediment heat conduction
Source: layer.water.heat
Target: sediment.heat
Unit: J day⁻¹
Value:
\[\mathrm{dz\_} = 0.5 \mathrm{m}\, \\ \left(\mathrm{sediment}.\mathrm{area}\cdot \left(\left(\mathrm{layer}.\mathrm{water}.\mathrm{temp}\rightarrow \mathrm{K}\,\right)-\left(\mathrm{sediment}.\mathrm{temp}\rightarrow \mathrm{K}\,\right)\right)\cdot \frac{\mathrm{sed\_k}}{\mathrm{dz\_}}\rightarrow \mathrm{J}\,\mathrm{day}^{-1}\,\right)\]Sediment resuspension
Source: sediment.sed
Target: layer.water.sed
Unit: kg day⁻¹
Value:
\[\left(\mathrm{in\_flux}\left(\mathrm{sed}\right)\cdot \mathrm{resus}\rightarrow \mathrm{kg}\,\mathrm{day}^{-1}\,\right)\]Sediment burial
Source: sediment.sed
Target: out
Unit: kg day⁻¹
Value:
\[\left(\mathrm{in\_flux}\left(\mathrm{sed}\right)\cdot \left(1-\mathrm{resus}\right)\rightarrow \mathrm{kg}\,\mathrm{day}^{-1}\,\right)\]POC mineralization
Source: sediment.sed.oc
Target: out
Unit: kg day⁻¹
Value:
\[\mathrm{sed}.\mathrm{oc}\cdot \mathrm{layer}.\mathrm{water}.\mathrm{min\_rat}\cdot \mathrm{micr\_rel}\]PON mineralization and nitrification
Source: sediment.sed.on
Target: layer.water.din
Unit: kg day⁻¹
Value:
\[\mathrm{sed}.\mathrm{on}\cdot \mathrm{layer}.\mathrm{water}.\mathrm{min\_rat}\cdot \mathrm{micr\_rel}\cdot \mathrm{n\_min}\]POP mineralization
Source: sediment.sed.op
Target: sediment.sed.phos
Unit: kg day⁻¹
Value:
\[\mathrm{sed}.\mathrm{op}\cdot \mathrm{layer}.\mathrm{water}.\mathrm{temp\_fac}\cdot \mathrm{maxdecomp\_20}\cdot \mathrm{p\_min}\]O₂ sediment microbial consumption
Source: layer.water.o2
Target: out
Unit: kg day⁻¹
Value:
\[\mathrm{mr} = \mathrm{layer}.\mathrm{water}.\mathrm{min\_rat}\cdot \mathrm{micr\_rel} \\ \mathrm{sediment}.\mathrm{sed}.\mathrm{oc}\cdot \mathrm{mr}\cdot \frac{\mathrm{o2\_mol\_mass}}{\mathrm{c\_mol\_mass}}\cdot \mathrm{O2toC}+\mathrm{sediment}.\mathrm{sed}.\mathrm{on}\cdot \mathrm{mr}\cdot \mathrm{n\_min}\cdot \frac{\mathrm{o2\_mol\_mass}}{\mathrm{n\_mol\_mass}}\cdot 1.5\]CO₂ sediment microbial production
Source: out
Target: layer.water.co2
Unit: kg day⁻¹
Value:
\[\mathrm{mr} = \mathrm{layer}.\mathrm{water}.\mathrm{min\_rat}\cdot \mathrm{micr\_rel} \\ \mathrm{dr} = \mathrm{layer}.\mathrm{water}.\mathrm{denit\_rat}\cdot \mathrm{micr\_rel} \\ \mathrm{sediment}.\mathrm{sed}.\mathrm{oc}\cdot \left(\mathrm{mr}+\mathrm{dr}\right)\]CH4 sediment microbial production
Source: out
Target: sediment.sed.ch4
Unit: kg day⁻¹
Value:
\[\mathrm{mr} = \mathrm{layer}.\mathrm{water}.\mathrm{min\_rat}\cdot \mathrm{micr\_rel} \\ \mathrm{sediment}.\mathrm{sed}.\mathrm{oc}\cdot \mathrm{mr}\cdot \mathrm{ch4\_production\_scaler}\]CH4 sediment bubbling
Source: sediment.sed.ch4
Target: out
Unit: kg day⁻¹
Value:
\[\left(\mathrm{max}\left(0,\, \mathrm{bubble\_ch4}\cdot \left(\mathrm{conc}\left(\mathrm{ch4}\right)-\mathrm{ch4satconc}\right)\cdot \mathrm{sediment}.\mathrm{sed}\right)\rightarrow \mathrm{kg}\,\mathrm{day}^{-1}\,\right)\]CH4 sediment diffusion release
Source: sediment.sed.ch4
Target: layer.water.ch4
Unit: kg day⁻¹
Value:
\[\mathrm{diff\_coeff} = \left(4.18\cdot 10^{11} \mathrm{m}^{2}\,\mathrm{s}^{-1}\,\mathrm{°C}^{-1}\,\cdot \mathrm{sediment}.\mathrm{temp}+8.06\cdot 10^{10} \mathrm{m}^{2}\,\mathrm{s}^{-1}\,\rightarrow \mathrm{m}^{2}\,\mathrm{day}^{-1}\,\right) \\ \mathrm{diff\_coeff}\cdot \left(\mathrm{conc}\left(\mathrm{sediment}.\mathrm{sed}.\mathrm{ch4}\right)\cdot 1000 \mathrm{g}\,\mathrm{l}^{-1}\,\cdot \mathrm{porosity}-\mathrm{conc}\left(\mathrm{layer}.\mathrm{water}.\mathrm{ch4}\right)\right)\cdot \frac{0.001 \mathrm{kg}\,\mathrm{g}^{-1}\,}{0.25 \mathrm{m}\,}\cdot \mathrm{sediment}.\mathrm{area}\]POC mineralization by denitrification
Source: sediment.sed.oc
Target: out
Unit: kg day⁻¹
Value:
\[\mathrm{sediment}.\mathrm{sed}.\mathrm{oc}\cdot \mathrm{layer}.\mathrm{water}.\mathrm{denit\_rat}\]NO3 sediment denitrification consumption
Source: layer.water.din
Target: out
Unit: kg day⁻¹
Value:
\[\mathrm{bo2} = \mathrm{sediment}.\mathrm{sed}.\mathrm{oc}\cdot \mathrm{layer}.\mathrm{water}.\mathrm{denit\_rat}\cdot \mathrm{O2toC}\cdot \frac{\mathrm{o2\_mol\_mass}}{\mathrm{c\_mol\_mass}} \\ \mathrm{bo2}\cdot 1.5\cdot \frac{\mathrm{n\_mol\_mass}}{\mathrm{o2\_mol\_mass}}\]PO4 adsorption / desorption to sediment layer
Source: layer.water.phos
Target: sediment.sed.phos
Unit: kg day⁻¹
Value:
\[\mathrm{epc0} = \left(\frac{\mathrm{conc}\left(\mathrm{sediment}.\mathrm{sed}.\mathrm{phos}\right)}{\mathrm{k\_sorp}}\rightarrow \mathrm{mg}\,\mathrm{l}^{-1}\,\right) \\ \mathrm{epc0\_} = \mathrm{min}\left(\mathrm{epc0},\, 0 \mathrm{mg}\,\mathrm{l}^{-1}\,\right) \\ \mathrm{r\_sorp}\cdot \left(\left(\mathrm{ox\_fac}\cdot \left(\mathrm{conc}\left(\mathrm{water}.\mathrm{phos}\right)-\mathrm{epc0\_}\right)\cdot \mathrm{water}\rightarrow \mathrm{kg}\,\right)-\left(1-\mathrm{ox\_fac}\right)\cdot \mathrm{sediment}.\mathrm{sed}.\mathrm{phos}\right)\]