EasyLake
This is auto-generated documentation based on the model code in models/easylake_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.
EasyLake
Version: 0.1.0
File: modules/easylake.txt
Description
EasyLake is a simple lake model for use along with catchment models. It simulates residence time in the lake in an upper and lower compartment, and it has separate modules for nutrient retention and contaminants.
The physical part of the model simulates water balance and temperature.
The lake can also be equipped with an ice module (defined in the AirSea module).
The internal heat distribution is inspired by (but not as complex as) the FLake model.
We assume that the hypsograph of the lake follows a shape so that
\[A(z) = A_0 \left(\frac{z}{z_{max}}\right)^{\theta+1}\]where \(A(z)\) is the area of the horizontal cross-section of the lake at level \(z\) measuring up from the maximal depth \(z_{max}\), \(A_0\) is the surface area at the zero level of the outlet, and \(\theta\) is a user-defined parameter.
We also assume that the discharge is linearly proportional to the water level at the outlet.
The lake is partitioned into an epilimnion and a hypolimnion. The epilimnion is assumed to have a temperature profile that does not depend on the depth. In the hypolimnion, the temperature profile follows
\[T(z) = (T_e - T_b)\left(\frac{z}{z_{max}}\right)^2 + T_b,\; z < z_e\]Where \(T_e\) is current epilimnion temperature and \(T_b\) is bottom temperature (user-defined constant parameter), and \(z_e\) is epilimnion thickness. The total heat of the lake is then proportional to
\[\int_0^{z_{max}} A(z)T(z)\mathrm{d}z\]which has an exact solution, which one can back-solve for \(T_e\) if the total heat of the lake is known.
The total heat is computed as an ordinary differential equation, and depends mostly on surface heat exchange (computed by the AirSea module).
The epilimnion is set to have a dynamic thickness. This is not simulated, but is instead determined by user-defined empirical parameters. The epilimnion and hypolimnion mix when the difference between epilimnion temperature and mean hypolimnion temperature is less than 0.4°C (typically in spring and autumn).
The thickness is set to have a given winter value, then is set to an initial thickness after spring mixing, after which it increases linearly.
Authors: François Clayer, Magnus D. Norling
External symbols
| Name | Symbol | Type |
|---|---|---|
| Epilimnion | epi | compartment |
| Hypolimnion | hyp | compartment |
| Water | water | quantity |
| Heat energy | heat | quantity |
| Temperature | temp | property |
| Thickness | th | property |
| Ice formation temperature | freeze_temp | property |
| Surface area | area | property |
| epi_target | loc |
Module functions
shape_cross_section_A(A_0 : m², z_0 : m, z : m, theta) =
\[\mathrm{A\_0}\cdot \left(\frac{\mathrm{z}}{\mathrm{z\_0}}\right)^{\mathrm{theta}+1}\]shape_tip_V(A_0 : m², z_0 : m, z : m, theta) =
\[\mathrm{A\_0}\cdot \mathrm{z}\cdot \frac{\left(\frac{\mathrm{z}}{\mathrm{z\_0}}\right)^{\mathrm{theta}+1}}{\mathrm{theta}+2}\]shape_section_V(A_0 : m², z_0 : m, z1 : m, z2 : m, theta) =
\[\mathrm{shape\_tip\_V}\left(\mathrm{A\_0},\, \mathrm{z\_0},\, \mathrm{z1},\, \mathrm{theta}\right)-\mathrm{shape\_tip\_V}\left(\mathrm{A\_0},\, \mathrm{z\_0},\, \mathrm{z2},\, \mathrm{theta}\right)\]shape_tip_z(A_0 : m², z_0 : m, V : m³, theta) =
\[\mathrm{zz\_0} = \left(\mathrm{z\_0}\Rightarrow 1\right) \\ \mathrm{f} = \left(\mathrm{V}\cdot \left(\mathrm{theta}+2\right)\cdot \frac{\mathrm{zz\_0}^{\mathrm{theta}+1}}{\mathrm{A\_0}}\Rightarrow 1\right) \\ \left(\mathrm{f}^{\frac{1}{\mathrm{theta}+2}}\Rightarrow \mathrm{m}\,\right)\]hypo_temperature_integral(A_0 : m², T_e : °C, T_b : °C, z_e : m, z_0 : m, theta) =
\[\left(2\cdot \mathrm{T\_b}+\left(\mathrm{theta}+2\right)\cdot \mathrm{T\_e}\right)\cdot \mathrm{A\_0}\cdot \frac{\mathrm{z\_e}^{3}\cdot \left(\frac{\mathrm{z\_e}}{\mathrm{z\_0}}\right)^{\mathrm{theta}+1}}{\left(\mathrm{theta}^{2}+6\cdot \mathrm{theta}+8\right)\cdot \mathrm{z\_e}^{2}}\]Parameters
| Name | Symbol | Unit | Description |
|---|---|---|---|
| Lake physical | Distributes like: epi | ||
| Lake surface area | A_surf | m² | |
| Water level at which outflow is 0 | z_outflow | m | |
| Winter epilimnion thickness | th_epi_w | m | |
| Spring epilimnion thickness | th_epi_s | m | |
| Lake bathymetry factor | theta | The cross-section area of the lake at level z is A_0*(z/z_0)^theta | |
| Epilimnion thickening rate | dz_epi | m day⁻¹ | How fast the thickness of the epilimnion changes during summer |
| Rating function linear component | rate_l | m² s⁻¹ | |
| Initial epilimnion temperature | t_epi | °C | |
| Bottom temperature | t_bot | °C |
State variables
Ice formation temperature
Location: epi.freeze_temp
Unit: °C
Value:
\[0 \mathrm{°C}\,\]Epilimnion volume
Location: epi.water
Unit: m³
Initial value:
\[\mathrm{shape\_section\_V}\left(\mathrm{A\_surf},\, \mathrm{z\_outflow},\, \mathrm{z\_outflow},\, \mathrm{z\_outflow}-\mathrm{th},\, \mathrm{theta}\right)\]Hypolimnion volume
Location: hyp.water
Unit: m³
Initial value:
\[\mathrm{shape\_tip\_V}\left(\mathrm{A\_surf},\, \mathrm{z\_outflow},\, \mathrm{z\_outflow}-\mathrm{epi}.\mathrm{th},\, \mathrm{theta}\right)\]Epilimnion thickness (relative to zero outflow)
Location: epi.th
Unit: m
Value:
\[\mathrm{doy} = \mathrm{time}.\mathrm{day\_of\_year} \\ \mathrm{spring\_mixing} = \mathrm{last}\left(\mathrm{ind}\right)\;\text{and}\;\left(\mathrm{last}\left(\mathrm{water}.\mathrm{temp}\right)>\mathrm{last}\left(\mathrm{hyp}.\mathrm{water}.\mathrm{temp}\right)\;\text{or}\;\mathrm{doy}<150 \mathrm{day}\,\right) \\ \mathrm{is\_winter} = \mathrm{last}\left(\mathrm{water}.\mathrm{temp}\right)<\mathrm{t\_bot}\;\text{and}\;\left(\mathrm{doy}<90 \mathrm{day}\,\;\text{or}\;\mathrm{doy}>275 \mathrm{day}\,\right) \\ \begin{cases}\mathrm{th\_epi\_s} & \text{if}\;\mathrm{spring\_mixing} \\ \mathrm{th\_epi\_w} & \text{if}\;\mathrm{is\_winter} \\ \mathrm{last}\left(\mathrm{th}\right)+\left(\mathrm{dz\_epi}\cdot \mathrm{time}.\mathrm{step\_length\_in\_seconds}\rightarrow \mathrm{m}\,\right) & \text{otherwise}\end{cases}\]Initial value:
\[\mathrm{th\_epi\_w}\]Lake water level
Location: epi.level
Unit: m
Value:
\[\mathrm{shape\_tip\_z}\left(\mathrm{A\_surf},\, \mathrm{z\_outflow},\, \mathrm{epi}.\mathrm{water}+\mathrm{hyp}.\mathrm{water},\, \mathrm{theta}\right)-\mathrm{z\_outflow}\]Epilimnion surface area
Location: epi.area
Unit: m²
Value:
\[\mathrm{shape\_cross\_section\_A}\left(\mathrm{A\_surf},\, \mathrm{z\_outflow},\, \mathrm{level}+\mathrm{z\_outflow},\, \mathrm{theta}\right)\]Hypolimnion surface area
Location: hyp.area
Unit: m²
Value:
\[\mathrm{shape\_cross\_section\_A}\left(\mathrm{A\_surf},\, \mathrm{z\_outflow},\, \mathrm{z\_outflow}-\mathrm{epi}.\mathrm{th},\, \mathrm{theta}\right)\]Heat energy
Location: epi.water.heat
Unit: J
Initial value:
\[\href{stdlib.html#water-utils}{\mathrm{water\_temp\_to\_heat}}\left(\mathrm{water},\, \mathrm{t\_epi}\right)\]Heat energy
Location: hyp.water.heat
Unit: J
Initial value:
\[\mathrm{t\_hyp} = \frac{\mathrm{hypo\_temperature\_integral}\left(\mathrm{A\_surf},\, \mathrm{t\_epi},\, \mathrm{t\_bot},\, \mathrm{z\_outflow}-\mathrm{epi}.\mathrm{th},\, \mathrm{z\_outflow},\, \mathrm{theta}\right)}{\mathrm{water}} \\ \href{stdlib.html#water-utils}{\mathrm{water\_temp\_to\_heat}}\left(\mathrm{water},\, \mathrm{t\_hyp}\right)\]Epilimnion temperature
Location: epi.water.temp
Unit: °C
Value:
\[\href{stdlib.html#water-utils}{\mathrm{water\_heat\_to\_temp}}\left(\mathrm{water},\, \mathrm{water}.\mathrm{heat}\right)\]Initial value:
\[\mathrm{t\_epi}\]Hypolimnion temperature (mean)
Location: hyp.water.temp
Unit: °C
Value:
\[\href{stdlib.html#water-utils}{\mathrm{water\_heat\_to\_temp}}\left(\mathrm{water},\, \mathrm{water}.\mathrm{heat}\right)\]Mixing indicator
Location: epi.ind
Unit:
Value:
\[\left|\mathrm{water}.\mathrm{temp}-\mathrm{hyp}.\mathrm{water}.\mathrm{temp}\right|<0.4 \mathrm{°C}\,\]Fluxes
Metalimnion movement
Source: epi.water
Target: hyp.water
Unit: m³ day⁻¹
Value:
\[\mathrm{hyp\_vol\_last} = \mathrm{shape\_tip\_V}\left(\mathrm{A\_surf},\, \mathrm{z\_outflow},\, \mathrm{z\_outflow}-\mathrm{last}\left(\mathrm{th}\right),\, \mathrm{theta}\right) \\ \mathrm{hyp\_vol\_now} = \mathrm{shape\_tip\_V}\left(\mathrm{A\_surf},\, \mathrm{z\_outflow},\, \mathrm{z\_outflow}-\mathrm{th},\, \mathrm{theta}\right) \\ \left(\frac{\mathrm{hyp\_vol\_now}-\mathrm{hyp\_vol\_last}}{\mathrm{time}.\mathrm{step\_length\_in\_seconds}}\rightarrow \mathrm{m}^{3}\,\mathrm{day}^{-1}\,\right)\]Lake outflow flux
Source: epi.water
Target: epi_target
Unit: m³ s⁻¹
Value:
\[\mathrm{max}\left(0,\, \mathrm{rate\_l}\cdot \mathrm{level}\right)\]Layer heat transfer
Source: epi.water.heat
Target: hyp.water.heat
Unit: J day⁻¹
Value:
\[\mathrm{V} = \mathrm{water}+\mathrm{hyp}.\mathrm{water} \\ \mathrm{lake\_t} = \href{stdlib.html#water-utils}{\mathrm{water\_heat\_to\_temp}}\left(\mathrm{V},\, \mathrm{heat}+\mathrm{hyp}.\mathrm{water}.\mathrm{heat}\right) \\ \mathrm{hypo\_temp} = \mathrm{hypo\_temperature\_integral}\left(\mathrm{A\_surf},\, \mathrm{temp},\, \mathrm{t\_bot},\, \mathrm{z\_outflow}-\mathrm{epi}.\mathrm{th},\, \mathrm{z\_outflow},\, \mathrm{theta}\right) \\ \mathrm{T\_e\_should\_be} = \frac{\mathrm{lake\_t}\cdot \mathrm{V}-\mathrm{hypo\_temp}}{\mathrm{water}} \\ \mathrm{epi\_heat\_should\_be} = \href{stdlib.html#water-utils}{\mathrm{water\_temp\_to\_heat}}\left(\mathrm{water},\, \mathrm{T\_e\_should\_be}\right) \\ 5 \mathrm{day}^{-1}\,\cdot \left(\mathrm{heat}-\mathrm{epi\_heat\_should\_be}\right)\]Mixing
Source: epi.water
Target: hyp.water
Unit: m³ day⁻¹
This is a mixing flux (affects dissolved quantities only)
Value:
\[\mathrm{A\_surf}\cdot \mathrm{epi}.\mathrm{th}\cdot \mathrm{epi}.\mathrm{ind}\cdot 0.1 \mathrm{day}^{-1}\,\]AirSea Lake
Version: 0.1.1
File: modules/airsea.txt
Description
Air-sea/lake heat fluxes are based off of Kondo 1975
The implementation used here is influenced by the implementation in GOTM.
The ice module is influenced by the ice module in MyLake, and uses Stefan’s law for ice accumulation.
Air-Sea bulk transfer coefficients in diabatic conditions, Junsei Kondo, 1975, Boundary-Layer Meteorology 9(1), 91-112 https://doi.org/10.1007/BF00232256
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 |
| Cosine of the solar zenith angle | cos_z | property |
| Epilimnion | surf | compartment |
| Actual specific humidity | a_hum | property |
| Density | rho | property |
| Ice | ice | quantity |
| Heat energy | heat | quantity |
| Temperature | temp | property |
| Wind speed | wind | property |
| Precipitation | precip | property |
| Global radiation | g_rad | property |
| Pressure | pressure | property |
| Downwelling longwave radiation | lwd | property |
| Shortwave radiation | sw | property |
| Attenuation coefficient | attn | property |
| Ice formation temperature | freeze_temp | property |
| Ice indicator | indicator | property |
| Evaporation | evap | property |
| A_surf | loc | |
| top_water | loc | |
| top_water_heat_sw | loc |
Constants
| Name | Symbol | Unit | Value |
|---|---|---|---|
| Ice density | rho_ice | kg m⁻³ | 917 |
| Latent heat of freezing | l_freeze | J kg⁻¹ | 333500 |
| Ice heat conduction coefficient | lambda_ice | W m⁻¹ K⁻¹ | 2.1 |
| Water albedo | water_alb | 0.045 |
Parameters
| Name | Symbol | Unit | Description |
|---|---|---|---|
| Ice | Distributes like: epi | ||
| Initial ice thickness | init_ice | m | |
| Ice albedo | ice_alb | ||
| Ice attenuation coefficient | ice_att_c | m⁻¹ | |
| Frazil threshold | th_frazil | m |
State variables
Wind speed
Location: air.wind
Unit: m s⁻¹
This series is externally defined. It may be an input series.
Stability
Location: surf.stab
Unit:
Value:
\[\href{stdlib.html#air-sea}{\mathrm{surface\_stability}}\left(\mathrm{air}.\mathrm{wind},\, \mathrm{top\_water}.\mathrm{temp},\, \mathrm{air}.\mathrm{temp}\right)\]Transfer coefficient for latent heat flux
Location: surf.ced
Unit:
Value:
\[\href{stdlib.html#air-sea}{\mathrm{tc\_latent\_heat}}\left(\mathrm{air}.\mathrm{wind},\, \mathrm{stab}\right)\]Transfer coefficent for sensible heat flux
Location: surf.chd
Unit:
Value:
\[\href{stdlib.html#air-sea}{\mathrm{tc\_sensible\_heat}}\left(\mathrm{air}.\mathrm{wind},\, \mathrm{stab}\right)\]Saturation specific humidity
Location: surf.s_hum
Unit:
Value:
\[\mathrm{svap} = \href{stdlib.html#meteorology}{\mathrm{saturation\_vapor\_pressure}}\left(\mathrm{top\_water}.\mathrm{temp}\right) \\ \href{stdlib.html#meteorology}{\mathrm{specific\_humidity\_from\_pressure}}\left(\mathrm{air}.\mathrm{pressure},\, \mathrm{svap}\right)\]Emitted longwave radiation
Location: surf.lwu
Unit: W m⁻²
Value:
\[\mathrm{emissivity} = 0.98 \\ \mathrm{emissivity}\cdot \href{stdlib.html#thermodynamics}{\mathrm{black\_body\_radiation}}\left(\left(\mathrm{top\_water}.\mathrm{temp}\rightarrow \mathrm{K}\,\right)\right)\]Albedo
Location: surf.albedo
Unit:
Value:
\[\begin{cases}\mathrm{ice\_alb} & \text{if}\;\mathrm{ice}.\mathrm{indicator} \\ \mathrm{water\_alb} & \text{otherwise}\end{cases}\]Shortwave radiation
Location: surf.sw
Unit: W m⁻²
Value:
\[\left(1-\mathrm{albedo}\right)\cdot \left(1-\mathrm{ice}.\mathrm{attn}\right)\cdot \mathrm{air}.\mathrm{g\_rad}\]Evaporation
Location: surf.evap
Unit: mm day⁻¹
Value:
\[\mathrm{rho\_ref} = 1025 \mathrm{kg}\,\mathrm{m}^{-3}\, \\ \left(\;\text{not}\;\mathrm{surf}.\mathrm{ice}.\mathrm{indicator}\cdot \frac{\mathrm{air}.\mathrm{rho}}{\mathrm{rho\_ref}}\cdot \mathrm{chd}\cdot \mathrm{air}.\mathrm{wind}\cdot \left(\mathrm{s\_hum}-\mathrm{air}.\mathrm{a\_hum}\right)\rightarrow \mathrm{mm}\,\mathrm{day}^{-1}\,\right)\]Ice thickness
Location: surf.ice
Unit: m
Initial value:
\[\mathrm{init\_ice}\]Freeze energy
Location: surf.ice.energy
Unit: W m⁻²
Value:
\[\mathrm{z\_surf} = 1 \mathrm{m}\, \\ \mathrm{K\_ice} = 200 \mathrm{W}\,\mathrm{m}^{-3}\,\mathrm{°C}^{-1}\, \\ \mathrm{e} = \left(\mathrm{freeze\_temp}-\mathrm{top\_water}.\mathrm{temp}\right)\cdot \mathrm{z\_surf}\cdot \mathrm{K\_ice} \\ \begin{cases}0 & \text{if}\;\mathrm{ice}<10^{-6} \mathrm{m}\,\;\text{and}\;\mathrm{e}<0 \\ \mathrm{e} & \text{otherwise}\end{cases}\]Ice indicator
Location: surf.ice.indicator
Unit:
Value:
\[\mathrm{ice}>\mathrm{th\_frazil}\]Attenuation coefficient
Location: surf.ice.attn
Unit:
Value:
\[\mathrm{cz} = \mathrm{max}\left(0.01,\, \href{stdlib.html#radiation}{\mathrm{refract}}\left(\mathrm{air}.\mathrm{cos\_z},\, \mathrm{refraction\_index\_ice}\right)\right) \\ \mathrm{th} = \frac{\mathrm{ice}}{\mathrm{cz}} \\ \begin{cases}0 & \text{if}\;\;\text{not}\;\mathrm{indicator} \\ 1-e^{-\mathrm{ice\_att\_c}\cdot \mathrm{th}} & \text{otherwise}\end{cases}\]Ice surface temperature
Location: surf.ice.temp
Unit: °C
Value:
\[\mathrm{alpha} = \frac{1}{10 \mathrm{m}^{-1}\,\cdot \mathrm{ice}} \\ \begin{cases}\frac{\mathrm{alpha}\cdot \mathrm{freeze\_temp}+\mathrm{air}.\mathrm{temp}}{1+\mathrm{alpha}} & \text{if}\;\mathrm{indicator} \\ 0 & \text{otherwise}\end{cases}\]Fluxes
Net shortwave
Source: out
Target: top_water_heat_sw
Unit: J day⁻¹
Value:
\[\left(\mathrm{A\_surf}\cdot \mathrm{surf}.\mathrm{sw}\rightarrow \mathrm{J}\,\mathrm{day}^{-1}\,\right)\]Net longwave
Source: out
Target: top_water.heat
Unit: J day⁻¹
Value:
\[\mathrm{net\_rad} = \left(1-\mathrm{surf}.\mathrm{albedo}\right)\cdot \mathrm{air}.\mathrm{lwd}-\mathrm{surf}.\mathrm{lwu} \\ \left(\;\text{not}\;\mathrm{surf}.\mathrm{ice}.\mathrm{indicator}\cdot \mathrm{A\_surf}\cdot \mathrm{net\_rad}\rightarrow \mathrm{J}\,\mathrm{day}^{-1}\,\right)\]Freeze heating
Source: out
Target: top_water.heat
Unit: J day⁻¹
Value:
\[\left(\mathrm{A\_surf}\cdot \mathrm{surf}.\mathrm{ice}.\mathrm{energy}\rightarrow \mathrm{J}\,\mathrm{day}^{-1}\,\right)\]Latent heat flux
Source: out
Target: top_water.heat
Unit: J day⁻¹
Value:
\[\mathrm{l\_vap} = \href{stdlib.html#meteorology}{\mathrm{latent\_heat\_of\_vaporization}}\left(\mathrm{top\_water}.\mathrm{temp}\right) \\ \left(\;\text{not}\;\mathrm{surf}.\mathrm{ice}.\mathrm{indicator}\cdot \mathrm{A\_surf}\cdot \mathrm{surf}.\mathrm{ced}\cdot \mathrm{l\_vap}\cdot \mathrm{air}.\mathrm{rho}\cdot \mathrm{air}.\mathrm{wind}\cdot \left(\mathrm{air}.\mathrm{a\_hum}-\mathrm{surf}.\mathrm{s\_hum}\right)\rightarrow \mathrm{J}\,\mathrm{day}^{-1}\,\right)\]Sensible heat flux
Source: out
Target: top_water.heat
Unit: J day⁻¹
Value:
\[\left(\;\text{not}\;\mathrm{surf}.\mathrm{ice}.\mathrm{indicator}\cdot \mathrm{A\_surf}\cdot \mathrm{surf}.\mathrm{chd}\cdot \mathrm{C\_air}\cdot \mathrm{air}.\mathrm{rho}\cdot \mathrm{air}.\mathrm{wind}\cdot \left(\left(\mathrm{air}.\mathrm{temp}\rightarrow \mathrm{K}\,\right)-\left(\mathrm{top\_water}.\mathrm{temp}\rightarrow \mathrm{K}\,\right)\right)\rightarrow \mathrm{J}\,\mathrm{day}^{-1}\,\right)\]Evaporation
Source: top_water
Target: out
Unit: m³ day⁻¹
Value:
\[\left(\mathrm{surf}.\mathrm{evap}\cdot \mathrm{A\_surf}\rightarrow \mathrm{m}^{3}\,\mathrm{day}^{-1}\,\right)\]Precipitation to surface
Source: out
Target: top_water
Unit: m³ day⁻¹
Value:
\[\left(\mathrm{air}.\mathrm{precip}\cdot \mathrm{A\_surf}\rightarrow \mathrm{m}^{3}\,\mathrm{day}^{-1}\,\right)\]Precipitation heat
Source: out
Target: top_water.heat
Unit: J day⁻¹
Value:
\[\mathrm{precip\_t} = \mathrm{max}\left(0 \mathrm{°C}\,,\, \mathrm{air}.\mathrm{temp}\right) \\ \mathrm{V} = \left(\mathrm{A\_surf}\cdot \mathrm{air}.\mathrm{precip}\rightarrow \mathrm{m}^{3}\,\mathrm{day}^{-1}\,\right) \\ \left(\href{stdlib.html#water-utils}{\mathrm{water\_temp\_to\_heat}}\left(\left(\mathrm{V}\Rightarrow \mathrm{m}^{3}\,\right),\, \mathrm{precip\_t}\right)\Rightarrow \mathrm{J}\,\mathrm{day}^{-1}\,\right)\]Ice change
Source: out
Target: surf.ice
Unit: m day⁻¹
Value:
\[\left(\frac{\mathrm{energy}+\begin{cases}\mathrm{lambda\_ice}\cdot \frac{\left(\mathrm{freeze\_temp}\rightarrow \mathrm{K}\,\right)-\left(\mathrm{temp}\rightarrow \mathrm{K}\,\right)}{\mathrm{ice}} & \text{if}\;\mathrm{temp}\leq \mathrm{freeze\_temp}\;\text{and}\;\mathrm{indicator} \\ -\left(1-\mathrm{albedo}\right)\cdot \mathrm{air}.\mathrm{g\_rad}\cdot \mathrm{attn} & \text{if}\;\mathrm{indicator} \\ 0 & \text{otherwise}\end{cases}}{\mathrm{rho\_ice}\cdot \mathrm{l\_freeze}}\rightarrow \mathrm{m}\,\mathrm{day}^{-1}\,\right)+\left(\begin{cases}\mathrm{air}.\mathrm{precip} & \text{if}\;\mathrm{indicator}\;\text{and}\;\mathrm{air}.\mathrm{temp}\leq \mathrm{freeze\_temp} \\ 0 & \text{otherwise}\end{cases}\rightarrow \mathrm{m}\,\mathrm{day}^{-1}\,\right)\]EasyChem
Version: 0.0.5
File: modules/easychem.txt
Description
This is a simple lake biogeochemical model for CNP and O₂ made to fit with EasyLake.
More description to be written.
Many of the equations are inspired by Selma, but with simplifications.
Authors: François Clayer, Magnus D. Norling
External symbols
| Name | Symbol | Type |
|---|---|---|
| Atmosphere | air | compartment |
| Total organic carbon | toc | property |
| Epilimnion | epi | compartment |
| Hypolimnion | hyp | compartment |
| Organic nitrogen | on | quantity |
| Water | water | quantity |
| Wind speed | wind | property |
| Temperature | temp | property |
| Organic carbon | oc | quantity |
| Phytoplankton | phyt | quantity |
| O₂ | o2 | quantity |
| Ice | ice | quantity |
| Inorganic nitrogen | din | quantity |
| Total nitrogen | tn | property |
| Inorganic phosphorous | phos | quantity |
| Organic phosphorous | op | quantity |
| Particles | sed | quantity |
| Precipitation | precip | property |
| Total dissolved phosphorous | tdp | property |
| Shortwave radiation | sw | property |
| Ice indicator | indicator | property |
| Total phosphorous | tp | property |
| Surface area | area | property |
Constants
| Name | Symbol | Unit | Value |
|---|---|---|---|
| Fraction of PAR in SW radiation | f_par | 0.45 | |
| Phytoplankton increased death rate from anoxicity | phyt_death_anox | 10 | |
| Anoxicity threshold | anox_threshold | mg l⁻¹ | 2 |
Parameters
| Name | Symbol | Unit | Description |
|---|---|---|---|
| Lake specific chemistry | Distributes like: epi | ||
| Initial O₂ saturation | init_O2 | ||
| Initial lake DOC concentration | init_c | mg l⁻¹ | |
| Initial lake DIN concentration | init_in | mg l⁻¹ | |
| Initial lake DIP concentration | init_ip | mg l⁻¹ | |
| Initial phytoplankton concentration | init_phyt | mg l⁻¹ | |
| Direct lake DIN deposition | din_dep | kg ha⁻¹ year⁻¹ | |
| Oxygen | Distributes like: epi | ||
| Piston velocity scaler for O₂ | pvel_scaler | ||
| Background sediment O₂ demand | sod | g m⁻² day⁻¹ | |
| Microbes | |||
| Respiration rate | K_OM | year⁻¹ | |
| Respiration Q10 | respQ10 | Adjustment of rate with 10°C change in temperature | |
| Half-saturation concentration O₂ | Km_o2 | mmol m⁻³ | |
| P mineralization rel rate | relrate_p | ||
| N mineralization rel rate | relrate_n | ||
| Denitrification rate | denit | m⁻² year⁻¹ | |
| Denitrification Q10 | denitQ10 | Adjustment of rate with 10°C change in temperature | |
| Phytoplankton | |||
| Chl-a of phyto at equilibrium | phyt_eq_20 | mg l⁻¹ | Assuming 20°C and no nutrient or light limitations. |
| Q10 of Phyto equilibrium | phyt_q10 | ||
| Phytoplankton turnover rate | phyt_turnover | day⁻¹ | |
| Excretion rate | excr | day⁻¹ | |
| Optimal PAR intensity | iopt | W m⁻² | |
| Half-saturation for nutrient uptake | halfsat | mmol m⁻³ | |
| Molar C/N ratio in Phytoplankton | phyt_cn | ||
| Molar C/P ratio in Phytoplankton | phyt_cp | ||
| Chl-a fraction | chl_a_f | % | How large a fraction of the phytoplankton mass is chlorophyll a |
| Lake specific phytoplankton | Distributes like: epi | ||
| Phytoplankton amenability | phyt_a | Adjustment factor to account for shallow lakes being better for plankton, after taking nutrients and light into consideration | |
| Lake specific denitrification | denit_a |
State variables
Epilimnion O₂
Location: epi.water.o2
Unit: kg
Conc. unit: mg l⁻¹
Initial value (concentration):
\[\left(\href{stdlib.html#sea-oxygen}{\mathrm{o2\_saturation}}\left(\mathrm{temp},\, 0\right)\cdot \mathrm{init\_O2}\cdot \mathrm{o2\_mol\_mass}\rightarrow \mathrm{kg}\,\right)\]Hypolimnion O₂
Location: hyp.water.o2
Unit: kg
Conc. unit: mg l⁻¹
Initial value (concentration):
\[\left(\href{stdlib.html#sea-oxygen}{\mathrm{o2\_saturation}}\left(\mathrm{temp},\, 0\right)\cdot \mathrm{init\_O2}\cdot \mathrm{o2\_mol\_mass}\rightarrow \mathrm{kg}\,\right)\]Epilimnion DOC
Location: epi.water.oc
Unit: kg
Conc. unit: mg l⁻¹
Initial value (concentration):
\[\mathrm{init\_c}\]Hypolimnion DOC
Location: hyp.water.oc
Unit: kg
Conc. unit: mg l⁻¹
Initial value (concentration):
\[\mathrm{init\_c}\]Epilimnion POC
Location: epi.water.sed.oc
Unit: kg
Hypolimnion POC
Location: hyp.water.sed.oc
Unit: kg
Epilimnion DIN
Location: epi.water.din
Unit: kg
Conc. unit: mg l⁻¹
Initial value (concentration):
\[\mathrm{init\_in}\]Hypolimnion DIN
Location: hyp.water.din
Unit: kg
Conc. unit: mg l⁻¹
Initial value (concentration):
\[\mathrm{init\_in}\]Epilimnion DON
Location: epi.water.on
Unit: kg
Conc. unit: mg l⁻¹
Initial value (concentration):
\[\frac{\mathrm{init\_c}}{\href{stdlib.html#chemistry}{\mathrm{cn\_molar\_to\_mass\_ratio}}\left(\mathrm{om\_cn}\right)}\]Hypolimnion DON
Location: hyp.water.on
Unit: kg
Conc. unit: mg l⁻¹
Initial value (concentration):
\[\frac{\mathrm{init\_c}}{\href{stdlib.html#chemistry}{\mathrm{cn\_molar\_to\_mass\_ratio}}\left(\mathrm{om\_cn}\right)}\]Epilimnion PON
Location: epi.water.sed.on
Unit: kg
Hypolimnion PON
Location: hyp.water.sed.on
Unit: kg
Epilimnion DIP
Location: epi.water.phos
Unit: kg
Conc. unit: mg l⁻¹
Initial value (concentration):
\[\mathrm{init\_ip}\]Hypolimnion DIP
Location: hyp.water.phos
Unit: kg
Conc. unit: mg l⁻¹
Initial value (concentration):
\[\mathrm{init\_ip}\]Epilimnion DOP
Location: epi.water.op
Unit: kg
Conc. unit: mg l⁻¹
Initial value (concentration):
\[\frac{\mathrm{init\_c}}{\href{stdlib.html#chemistry}{\mathrm{cp\_molar\_to\_mass\_ratio}}\left(\mathrm{om\_cp}\right)}\]Hypolimnion DOP
Location: hyp.water.op
Unit: kg
Conc. unit: mg l⁻¹
Initial value (concentration):
\[\frac{\mathrm{init\_c}}{\href{stdlib.html#chemistry}{\mathrm{cp\_molar\_to\_mass\_ratio}}\left(\mathrm{om\_cp}\right)}\]Epilimnion PIP
Location: epi.water.sed.phos
Unit: kg
Hypolimnion PIP
Location: hyp.water.sed.phos
Unit: kg
Epilimnion POP
Location: epi.water.sed.op
Unit: kg
Hypolimnion POP
Location: hyp.water.sed.op
Unit: kg
Epilimnion Phytoplankton
Location: epi.water.phyt
Unit: kg
Conc. unit: mg l⁻¹
Initial value (concentration):
\[\mathrm{init\_phyt}\]Hypolimnion Phytoplankton
Location: hyp.water.phyt
Unit: kg
Conc. unit: mg l⁻¹
Initial value (concentration):
\[\mathrm{init\_phyt}\]O₂ piston velocity
Location: epi.water.p_vel
Unit: cm hr⁻¹
Value:
\[\mathrm{pvel\_scaler}\cdot \href{stdlib.html#sea-oxygen}{\mathrm{o2\_piston\_velocity}}\left(\mathrm{air}.\mathrm{wind},\, \mathrm{temp}\right)\]O₂ saturation concentration
Location: epi.water.o2sat
Unit: mg l⁻¹
Value:
\[\left(\href{stdlib.html#sea-oxygen}{\mathrm{o2\_saturation}}\left(\mathrm{temp},\, 0\right)\cdot \mathrm{o2\_mol\_mass}\rightarrow \mathrm{mg}\,\mathrm{l}^{-1}\,\right)\]Sediment O₂ consumption rate
Location: epi.o2rate
Unit: kg m⁻² day⁻¹
Value:
\[\mathrm{q10} = 2 \\ \mathrm{rate20} = \left(\mathrm{sod}\cdot \mathrm{min}\left(1,\, 1-\frac{0.05 \mathrm{mg}\,\mathrm{l}^{-1}\,-\mathrm{conc}\left(\mathrm{water}.\mathrm{o2}\right)}{0.05 \mathrm{mg}\,\mathrm{l}^{-1}\,}\right)\rightarrow \mathrm{kg}\,\mathrm{m}^{-2}\,\mathrm{day}^{-1}\,\right) \\ \href{stdlib.html#response}{\mathrm{q10\_adjust}}\left(\mathrm{rate20},\, 20 \mathrm{°C}\,,\, \mathrm{hyp}.\mathrm{water}.\mathrm{temp},\, \mathrm{q10}\right)\]Bacterial mineralization (epi)
Location: epi.water.resp
Unit: day⁻¹
This series is externally defined. It may be an input series.
Bacterial mineralization (hypo)
Location: hyp.water.resp
Unit: day⁻¹
This series is externally defined. It may be an input series.
Chlorophyll-a
Location: epi.water.chl_a
Unit: mg l⁻¹
Value:
\[\left(\mathrm{conc}\left(\mathrm{phyt}\right)\cdot \mathrm{chl\_a\_f}\rightarrow \mathrm{mg}\,\mathrm{l}^{-1}\,\right)\]Light limitation
Location: epi.water.phyt.light_lim
Unit:
Value:
\[\mathrm{par\_sw} = \mathrm{sw}\cdot \left(1-\mathrm{f\_par}\right) \\ \mathrm{f} = \frac{\mathrm{par\_sw}}{\mathrm{max}\left(0.5\cdot \mathrm{par\_sw},\, \mathrm{iopt}\right)} \\ \mathrm{f}\cdot e^{1-\mathrm{f}}\]Nitrogen limitation
Location: epi.water.phyt.N_lim
Unit:
Value:
\[\mathrm{cmol} = \left(\frac{\mathrm{conc}\left(\mathrm{water}.\mathrm{din}\right)}{\mathrm{n\_mol\_mass}}\rightarrow \mathrm{mmol}\,\mathrm{m}^{-3}\,\right) \\ \frac{\mathrm{cmol}^{2}}{\left(\frac{\mathrm{halfsat}}{\mathrm{phyt\_cn}}\right)^{2}+\mathrm{cmol}^{2}}\]Phosphorus limitation
Location: epi.water.phyt.P_lim
Unit:
Value:
\[\mathrm{cmol} = \left(\frac{\mathrm{conc}\left(\mathrm{water}.\mathrm{phos}\right)}{\mathrm{p\_mol\_mass}}\rightarrow \mathrm{mmol}\,\mathrm{m}^{-3}\,\right) \\ \frac{\mathrm{cmol}^{2}}{\left(\frac{\mathrm{halfsat}}{\mathrm{phyt\_cp}}\right)^{2}+\mathrm{cmol}^{2}}\]Phytoplankton equilibrium concentration
Location: epi.water.phyt.equi
Unit: mg l⁻¹
Value:
\[\mathrm{phyt\_eq} = \frac{\href{stdlib.html#response}{\mathrm{q10\_adjust}}\left(\mathrm{phyt\_eq\_20},\, 20 \mathrm{°C}\,,\, \mathrm{temp},\, \mathrm{phyt\_q10}\right)}{\left(\mathrm{chl\_a\_f}\rightarrow 1\right)} \\ \mathrm{phyt\_eq}\cdot \mathrm{phyt\_a}\cdot \mathrm{min}\left(\mathrm{light\_lim},\, \mathrm{min}\left(\mathrm{N\_lim},\, \mathrm{P\_lim}\right)\right)\]Photosynthetic C fixation
Location: epi.water.phyt.fix
Unit: kg day⁻¹
Value:
\[\left(\mathrm{phyt\_turnover}\cdot \mathrm{epi}.\mathrm{water}.\mathrm{phyt}.\mathrm{equi}\cdot \mathrm{water}\rightarrow \mathrm{kg}\,\mathrm{day}^{-1}\,\right)\]Phytoplankton death rate (epi)
Location: epi.water.phyt.death
Unit: kg day⁻¹
This series is externally defined. It may be an input series.
Phytoplankton death rate (hyp)
Location: hyp.water.phyt.death
Unit: kg day⁻¹
This series is externally defined. It may be an input series.
Epilimnion TDP
Location: epi.water.tdp
Unit: mg l⁻¹
Value:
\[\mathrm{conc}\left(\mathrm{phos}\right)+\mathrm{conc}\left(\mathrm{op}\right)\]Epilimnion TP
Location: epi.water.tp
Unit: mg l⁻¹
Value:
\[\mathrm{tdp}+\mathrm{conc}\left(\mathrm{sed}\right)\cdot \left(\mathrm{conc}\left(\mathrm{sed}.\mathrm{phos}\right)+\mathrm{conc}\left(\mathrm{sed}.\mathrm{op}\right)\right)\]Epilimnion TN
Location: epi.water.tn
Unit: mg l⁻¹
Value:
\[\mathrm{conc}\left(\mathrm{on}\right)+\mathrm{conc}\left(\mathrm{din}\right)+\mathrm{conc}\left(\mathrm{sed}\right)\cdot \mathrm{conc}\left(\mathrm{sed}.\mathrm{on}\right)\]Epilimnion TOC
Location: epi.water.toc
Unit: mg l⁻¹
Value:
\[\mathrm{conc}\left(\mathrm{oc}\right)+\mathrm{conc}\left(\mathrm{sed}.\mathrm{oc}\right)\cdot \mathrm{conc}\left(\mathrm{sed}\right)+\mathrm{conc}\left(\mathrm{phyt}\right)\]Epilimnion STS
Location: epi.water.sts
Unit: mg l⁻¹
Value:
\[\mathrm{conc}\left(\mathrm{epi}.\mathrm{water}.\mathrm{sed}\right)+\mathrm{conc}\left(\mathrm{phyt}\right)\]Fluxes
Precipitation O₂
Source: out
Target: epi.water.o2
Unit: kg day⁻¹
Value:
\[\mathrm{cnc} = \left(0.9\cdot \href{stdlib.html#sea-oxygen}{\mathrm{o2\_saturation}}\left(\mathrm{air}.\mathrm{temp},\, 0\right)\cdot \mathrm{o2\_mol\_mass}\rightarrow \mathrm{mg}\,\mathrm{l}^{-1}\,\right) \\ \left(\mathrm{air}.\mathrm{precip}\cdot \mathrm{area}\cdot \mathrm{cnc}\rightarrow \mathrm{kg}\,\mathrm{day}^{-1}\,\right)\]O₂ gas exchange at surface
Source: out
Target: epi.water.o2
Unit: kg day⁻¹
Value:
\[\left(\;\text{not}\;\mathrm{ice}.\mathrm{indicator}\cdot \mathrm{p\_vel}\cdot \left(\mathrm{o2sat}-\mathrm{conc}\left(\mathrm{o2}\right)\right)\cdot \mathrm{area}\rightarrow \mathrm{kg}\,\mathrm{day}^{-1}\,\right)\]O₂ sediment consumption (epi)
Source: epi.water.o2
Target: out
Unit: kg day⁻¹
Value:
\[\left(\mathrm{epi}.\mathrm{o2rate}\cdot \left(\mathrm{area}-\mathrm{hyp}.\mathrm{area}\right)\rightarrow \mathrm{kg}\,\mathrm{day}^{-1}\,\right)\]Lake N deposition
Source: out
Target: epi.water.din
Unit: kg day⁻¹
Value:
\[\left(\mathrm{area}\cdot \frac{\mathrm{din\_dep}}{365.25 \mathrm{day}\,\mathrm{year}^{-1}\,}\rightarrow \mathrm{kg}\,\mathrm{day}^{-1}\,\right)\]DOC bacterial mineralization (hypo)
Source: hyp.water.oc
Target: out
Unit: kg day⁻¹
Value:
\[\mathrm{resp}\cdot \mathrm{oc}\]DOC bacterial mineralization (epi)
Source: epi.water.oc
Target: out
Unit: kg day⁻¹
Value:
\[\mathrm{resp}\cdot \mathrm{oc}\]O₂ bacterial consumption (hypo)
Source: hyp.water.o2
Target: out
Unit: kg day⁻¹
Value:
\[\mathrm{resp}\cdot \mathrm{oc}\cdot \frac{\mathrm{o2\_mol\_mass}}{\mathrm{c\_mol\_mass}}\]O₂ bacterial consumption (epi)
Source: epi.water.o2
Target: out
Unit: kg day⁻¹
Value:
\[\mathrm{resp}\cdot \mathrm{oc}\cdot \frac{\mathrm{o2\_mol\_mass}}{\mathrm{c\_mol\_mass}}\]DOP mineralization (epi)
Source: epi.water.op
Target: epi.water.phos
Unit: kg day⁻¹
Value:
\[\mathrm{resp}\cdot \mathrm{op}\cdot \mathrm{relrate\_p}\]DOP mineralization (hyp)
Source: hyp.water.op
Target: epi.water.phos
Unit: kg day⁻¹
Value:
\[\mathrm{resp}\cdot \mathrm{op}\cdot \mathrm{relrate\_p}\]POP mineralization (epi)
Source: epi.water.sed.op
Target: epi.water.phos
Unit: kg day⁻¹
Value:
\[\mathrm{resp}\cdot \mathrm{sed}.\mathrm{op}\cdot \mathrm{relrate\_p}\]POP mineralization (hyp)
Source: hyp.water.sed.op
Target: hyp.water.phos
Unit: kg day⁻¹
Value:
\[\mathrm{resp}\cdot \mathrm{sed}.\mathrm{op}\cdot \mathrm{relrate\_p}\]DON mineralization (hyp)
Source: hyp.water.on
Target: hyp.water.din
Unit: kg day⁻¹
Value:
\[\mathrm{resp}\cdot \mathrm{on}\cdot \mathrm{relrate\_n}\]DON mineralization (epi)
Source: epi.water.on
Target: epi.water.din
Unit: kg day⁻¹
Value:
\[\mathrm{resp}\cdot \mathrm{on}\cdot \mathrm{relrate\_n}\]DIN sediment denitrification (epi)
Source: epi.water.din
Target: out
Unit: kg day⁻¹
Value:
\[\mathrm{denit\_a}\cdot \mathrm{din}\cdot \href{stdlib.html#response}{\mathrm{q10\_adjust}}\left(\mathrm{denit},\, 20 \mathrm{°C}\,,\, \mathrm{temp},\, \mathrm{denitQ10}\right)\cdot \frac{\mathrm{area}-\mathrm{hyp}.\mathrm{area}}{365 \mathrm{day}\,\mathrm{year}^{-1}\,}\]DIN sediment denitrification (hyp)
Source: hyp.water.din
Target: out
Unit: kg day⁻¹
Value:
\[\mathrm{denit\_a}\cdot \mathrm{din}\cdot \href{stdlib.html#response}{\mathrm{q10\_adjust}}\left(\mathrm{denit},\, 20 \mathrm{°C}\,,\, \mathrm{temp},\, \mathrm{denitQ10}\right)\cdot \frac{\mathrm{area}}{365 \mathrm{day}\,\mathrm{year}^{-1}\,}\]Epilimnion photosynthetic C fixation
Source: out
Target: epi.water.phyt
Unit: kg day⁻¹
Value:
\[\mathrm{fix}\]Phytoplankton death DOC release (epi)
Source: epi.water.phyt
Target: out
Unit: kg day⁻¹
Value:
\[\mathrm{phyt}.\mathrm{death}\]Phytoplankton death DOC release (hypo)
Source: hyp.water.phyt
Target: out
Unit: kg day⁻¹
Value:
\[\mathrm{phyt}.\mathrm{death}\]Epilimnion O₂ photosynthesis
Source: out
Target: epi.water.o2
Unit: kg day⁻¹
Value:
\[\mathrm{phyt}.\mathrm{fix}\cdot \frac{\mathrm{o2\_mol\_mass}}{\mathrm{c\_mol\_mass}}\]Phytoplankton N uptake
Source: epi.water.din
Target: out
Unit: kg day⁻¹
Value:
\[\frac{\mathrm{phyt}.\mathrm{fix}}{\href{stdlib.html#chemistry}{\mathrm{cn\_molar\_to\_mass\_ratio}}\left(\mathrm{phyt\_cn}\right)}\]Phytoplankton P uptake
Source: epi.water.phos
Target: out
Unit: kg day⁻¹
Value:
\[\frac{\mathrm{phyt}.\mathrm{fix}}{\href{stdlib.html#chemistry}{\mathrm{cp\_molar\_to\_mass\_ratio}}\left(\mathrm{phyt\_cp}\right)}\]Phytoplankton C excretion
Source: epi.water.phyt
Target: epi.water.oc
Unit: kg day⁻¹
Value:
\[\mathrm{phyt}\cdot \mathrm{excr}\]Phytoplankton N excretion
Source: epi.water.phyt
Target: epi.water.on
Unit: kg day⁻¹
Value:
\[\mathrm{phyt}\cdot \frac{\mathrm{excr}}{\href{stdlib.html#chemistry}{\mathrm{cn\_molar\_to\_mass\_ratio}}\left(\mathrm{phyt\_cn}\right)}\]Phytoplankton P excretion
Source: epi.water.phyt
Target: epi.water.op
Unit: kg day⁻¹
Value:
\[\mathrm{phyt}\cdot \frac{\mathrm{excr}}{\href{stdlib.html#chemistry}{\mathrm{cp\_molar\_to\_mass\_ratio}}\left(\mathrm{phyt\_cp}\right)}\]Pytoplankton death P release (epi)
Source: out
Target: epi.water.sed.op
Unit: kg day⁻¹
Value:
\[\frac{\mathrm{phyt}.\mathrm{death}}{\href{stdlib.html#chemistry}{\mathrm{cp\_molar\_to\_mass\_ratio}}\left(\mathrm{phyt\_cp}\right)}\]Pytoplankton death P release (hyp)
Source: out
Target: hyp.water.sed.op
Unit: kg day⁻¹
Value:
\[\frac{\mathrm{phyt}.\mathrm{death}}{\href{stdlib.html#chemistry}{\mathrm{cp\_molar\_to\_mass\_ratio}}\left(\mathrm{phyt\_cp}\right)}\]EasyChem-Particulate
Version: 0.0.3
File: modules/easychem.txt
Description
Particle transport and settling for EasyChem.
Authors: Magnus D. Norling
External symbols
| Name | Symbol | Type |
|---|---|---|
| Atmosphere | air | compartment |
| Epilimnion | epi | compartment |
| Hypolimnion | hyp | compartment |
| Water | water | quantity |
| Particles | sed | quantity |
| Wind speed | wind | property |
| Surface area | area | property |
| Downstream | downstream | connection |
| sett_target | loc |
Parameters
| Name | Symbol | Unit | Description |
|---|---|---|---|
| Particles | |||
| Sediment settling velocity | sett_vel | m day⁻¹ | The net settling velocity after taking into account mixing whithin (but not between) each compartment. |
| Resuspension factor | resusp_f | Wind-proportional resuspension in epilimnion-sediment interface. | |
| Sediment concentration of fast settling | maxconc | mg l⁻¹ | With suspended sediment concentrations in the river higher than this, it is assumed to contain larger grain sizes that settle faster |
State variables
Epilimnion suspended sediments
Location: epi.water.sed
Unit: kg
Conc. unit: mg l⁻¹
Hypolimnion suspended sediments
Location: hyp.water.sed
Unit: kg
Conc. unit: mg l⁻¹
Fluxes
Epilimnion sediment settling
Source: epi.water.sed
Target: sett_target
Unit: kg day⁻¹
Value:
\[\left(\mathrm{max}\left(0 \mathrm{m}\,\mathrm{day}^{-1}\,,\, \mathrm{sett\_vel}-\left(\mathrm{air}.\mathrm{wind}\cdot \mathrm{resusp\_f}\rightarrow \mathrm{m}\,\mathrm{day}^{-1}\,\right)\right)\cdot \mathrm{conc}\left(\mathrm{sed}\right)\cdot \left(\mathrm{area}-\mathrm{hyp}.\mathrm{area}\right)\rightarrow \mathrm{kg}\,\mathrm{day}^{-1}\,\right)\]Epilimnion-hypolimnion settling
Source: epi.water.sed
Target: hyp.water.sed
Unit: kg day⁻¹
Value:
\[\left(\mathrm{sett\_vel}\cdot \mathrm{conc}\left(\mathrm{sed}\right)\cdot \mathrm{hyp}.\mathrm{area}\rightarrow \mathrm{kg}\,\mathrm{day}^{-1}\,\right)\]Hypolimnion sediment settling
Source: hyp.water.sed
Target: sett_target
Unit: kg day⁻¹
Value:
\[\left(\mathrm{sett\_vel}\cdot \mathrm{conc}\left(\mathrm{sed}\right)\cdot \mathrm{area}\rightarrow \mathrm{kg}\,\mathrm{day}^{-1}\,\right)\]Epilimnion SS inlet settling
Source: epi.water.sed
Target: sett_target
Unit: kg day⁻¹
Value:
\[\mathrm{in\_s} = \mathrm{in\_flux}\left(\mathrm{downstream},\, \mathrm{epi}.\mathrm{water}.\mathrm{sed}\right) \\ \mathrm{in\_q} = \mathrm{in\_flux}\left(\mathrm{downstream},\, \mathrm{epi}.\mathrm{water}\right) \\ \mathrm{in\_conc} = \left(\href{stdlib.html#basic}{\mathrm{safe\_divide}}\left(\mathrm{in\_s},\, \mathrm{in\_q}\right)\rightarrow \mathrm{mg}\,\mathrm{l}^{-1}\,\right) \\ \mathrm{excess} = \mathrm{in\_conc}-\mathrm{maxconc} \\ \left(\href{stdlib.html#response}{\mathrm{s\_response}}\left(\mathrm{excess},\, 0,\, \mathrm{maxconc},\, 0,\, \mathrm{excess}\cdot \mathrm{in\_q}\right)\rightarrow \mathrm{kg}\,\mathrm{day}^{-1}\,\right)\]