Auxiliary
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 2024-11-12 13:40:23.
Degree-day PET
Version: 1.0.0
File: modules/pet.txt
Description
This is a very simple potential evapotranspiration model that uses a linear relationship between PET and air temperature.
Authors: Magnus D. Norling
External symbols
| Name | Symbol | Type |
|---|---|---|
| Atmosphere | air | compartment |
| Soil | soil | compartment |
| Potential evapotranspiration | pet | property |
| Temperature | temp | property |
Parameters
| Name | Symbol | Unit | Description |
|---|---|---|---|
| Potential evapotranspiration | Distributes like: soil | ||
| Degree-day factor for evapotranspiration | ddf_pet | mm °C⁻¹ day⁻¹ | |
| Minimal temperature for evapotranspiration | pet_min_t | °C |
State variables
Potential evapotranspiration
Location: soil.pet
Unit: mm day⁻¹
Value:
\[\mathrm{max}\left(0,\, \mathrm{ddf\_pet}\cdot \left(\mathrm{air}.\mathrm{temp}-\mathrm{pet\_min\_t}\right)\right)\]HBVSnow
Version: 1.0.0
File: modules/hbv_snow.txt
Description
This is an adaption of the snow module from HBV-Nordic (Sælthun 1995)
Authors: Magnus D. Norling
External symbols
| Name | Symbol | Type |
|---|---|---|
| Atmosphere | air | compartment |
| Snow | snow | quantity |
| Snow layer | snow_box | compartment |
| Water | water | quantity |
| Temperature | temp | property |
| Precipitation | precip | property |
| water_target | loc |
Parameters
| Name | Symbol | Unit | Description |
|---|---|---|---|
| Snow | Distributes like: snow_box | ||
| Degree-day factor for snowmelt | ddf_melt | mm °C⁻¹ day⁻¹ | Linear correlation between rate of snow melt and air temperature |
| Temperature at which precip falls as snow | t_snow | °C | |
| Temperature at which snow melts | t_melt | °C | |
| Refreeze efficiency | refr_eff | Speed of refreeze of liquid water in snow relative to speed of melt at the opposite temperature differential | |
| Liquid water fraction | snow_liq | How many mm liquid water one mm of snow (water equivalents) can hold before the water is released | |
| Initial snow depth (water equivalents) | init_snow | mm |
State variables
Air temperature
Location: air.temp
Unit: °C
This series is externally defined. It may be an input series.
Precipitation
Location: air.precip
Unit: mm day⁻¹
This series is externally defined. It may be an input series.
Snow depth
Location: snow_box.snow
Unit: mm
Initial value:
\[\mathrm{init\_snow}\]Snow water
Location: snow_box.water
Unit: mm
Fluxes
Precipitation falling as snow
Source: out
Target: snow_box.snow
Unit: mm day⁻¹
Value:
\[\mathrm{air}.\mathrm{precip}\cdot \left(\mathrm{air}.\mathrm{temp}\leq \mathrm{t\_snow}\right)\]Precipitation falling as rain
Source: out
Target: snow_box.water
Unit: mm day⁻¹
Value:
\[\mathrm{air}.\mathrm{precip}\cdot \left(\mathrm{air}.\mathrm{temp}>\mathrm{t\_snow}\right)\]Melt
Source: snow_box.snow
Target: snow_box.water
Unit: mm day⁻¹
Value:
\[\mathrm{max}\left(0,\, \mathrm{ddf\_melt}\cdot \left(\mathrm{air}.\mathrm{temp}-\mathrm{t\_melt}\right)\right)\]Refreeze
Source: snow_box.water
Target: snow_box.snow
Unit: mm day⁻¹
Value:
\[\mathrm{max}\left(0,\, \mathrm{refr\_eff}\cdot \mathrm{ddf\_melt}\cdot \left(\mathrm{t\_melt}-\mathrm{air}.\mathrm{temp}\right)\right)\]Melt runoff
Source: snow_box.water
Target: water_target
Unit: mm day⁻¹
Value:
\[\mathrm{max}\left(0,\, \mathrm{water}-\mathrm{snow}\cdot \mathrm{snow\_liq}\right)\cdot 1 \mathrm{day}^{-1}\,\]Simply soil temperature
Version: 0.1.0
File: modules/simplysoiltemp.txt
Description
This is a simplification of the soil temperature model developed for the INCA models.
Rankinen K. T. Karvonen and D. Butterfield (2004), A simple model for predicting soil temperature in snow covered and seasonally frozen soil; Model description and testing, Hydrol. Earth Syst. Sci., 8, 706-716, https://doi.org/10.5194/hess-8-706-2004
Soil temperature is computed at a depth of 15 cm.
Authors: Leah A. Jackson-Blake, Magnus D. Norling
External symbols
| Name | Symbol | Type |
|---|---|---|
| Atmosphere | air | compartment |
| Snow | snow | quantity |
| Soil | soil | compartment |
| Snow layer | snow_box | compartment |
| Temperature | temp | property |
Constants
| Name | Symbol | Unit | Value |
|---|---|---|---|
| Soil temperature depth | st_depth | cm | 15 |
Parameters
| Name | Symbol | Unit | Description |
|---|---|---|---|
| Soil temperature general | |||
| Snow depth / soil temperature factor | depthst | cm⁻¹ | Per cm snow water equivalents |
| Initial soil temperature | init_st | °C | |
| Soil temperature land | Distributes like: soil | ||
| Soil thermal conductivity / specific heat capacity | stc | m² Ms⁻¹ |
State variables
COUP temperature
Location: soil.coup
Unit: °C
Value:
\[\mathrm{last}\left(\mathrm{coup}\right)+\left(\frac{\mathrm{stc}}{\left(2\cdot \mathrm{st\_depth}\right)^{2}}\cdot \left(\mathrm{air}.\mathrm{temp}-\mathrm{last}\left(\mathrm{coup}\right)\right)\cdot \mathrm{time}.\mathrm{step\_length\_in\_seconds}\rightarrow \mathrm{°C}\,\right)\]Initial value:
\[\mathrm{init\_st}\]Soil temperature
Location: soil.temp
Unit: °C
Value:
\[\mathrm{coup}\cdot e^{\left(\mathrm{depthst}\cdot \mathrm{snow\_box}.\mathrm{snow}\rightarrow 1\right)}\]Initial value:
\[\mathrm{init\_st}\]RiverTemperature
Version: 0.1.1
File: modules/rivertemp.txt
Description
A simple model for river water temperature. Water from the catchment is assumed to have the same temperature as the soil. Then heat is exchanged with the atmosphere with a constant rate relative to the temperature difference.
Authors: Magnus D. Norling
External symbols
| Name | Symbol | Type |
|---|---|---|
| Atmosphere | air | compartment |
| Soil | soil | compartment |
| River | river | compartment |
| Water | water | quantity |
| Heat energy | heat | quantity |
| Temperature | temp | property |
Constants
| Name | Symbol | Unit | Value |
|---|---|---|---|
| Minimum river temperature | min_t | °C | 0.4 |
Parameters
| Name | Symbol | Unit | Description |
|---|---|---|---|
| River temperature | Distributes like: river | ||
| Air-river heat exchange coefficient | coeff | day⁻¹ |
State variables
River thermal energy
Location: river.water.heat
Unit: J
Initial value:
\[\href{stdlib.html#water-utils}{\mathrm{water\_temp\_to\_heat}}\left(\mathrm{water},\, \mathrm{max}\left(\mathrm{air}.\mathrm{temp},\, \mathrm{min\_t}\right)\right)\]River temperature
Location: river.water.temp
Unit: °C
Value:
\[\href{stdlib.html#water-utils}{\mathrm{water\_heat\_to\_temp}}\left(\mathrm{water},\, \mathrm{water}.\mathrm{heat}\right)\]Fluxes
River heat from land
Source: out
Target: river.water.heat
Unit: J day⁻¹
Value:
\[\mathrm{V} = \left(\mathrm{in\_flux}\left(\mathrm{water}\right)\rightarrow \mathrm{m}^{3}\,\mathrm{day}^{-1}\,\right) \\ \mathrm{t} = \mathrm{max}\left(\mathrm{min\_t},\, \mathrm{aggregate}\left(\mathrm{soil}.\mathrm{temp}\right)\right) \\ \left(\href{stdlib.html#water-utils}{\mathrm{water\_temp\_to\_heat}}\left(\left(\mathrm{V}\Rightarrow \mathrm{m}^{3}\,\right),\, \mathrm{t}\right)\Rightarrow \mathrm{J}\,\mathrm{day}^{-1}\,\right)\]River sensible heat flux
Source: out
Target: river.water.heat
Unit: J day⁻¹
Value:
\[\left(\href{stdlib.html#water-utils}{\mathrm{water\_temp\_to\_heat}}\left(\mathrm{water},\, \mathrm{max}\left(\mathrm{air}.\mathrm{temp},\, \mathrm{min\_t}\right)\right)-\mathrm{heat}\right)\cdot \mathrm{coeff}\]Atmospheric
Version: 0.1.0
File: modules/atmospheric.txt
Description
Simple module for some common atmospheric attributes for use e.g. with evapotranspiration or air-sea heat exchange modules.
The user must provide either “Daily average global radiation” or “Cloud cover” as an input series, but one of these can be computed from the other if not both are available.
Authors: Magnus D. Norling
External symbols
| Name | Symbol | Type |
|---|---|---|
| Atmosphere | air | compartment |
| Cosine of the solar zenith angle | cos_z | property |
| Actual vapour pressure | a_vap | property |
| Actual specific humidity | a_hum | property |
| Temperature | temp | property |
| Wind speed | wind | property |
| Global radiation | g_rad | property |
| Saturation vapour pressure | s_vap | property |
| Pressure | pressure | property |
| Density | dens | property |
| Downwelling longwave radiation | lwd | property |
Parameters
| Name | Symbol | Unit | Description |
|---|---|---|---|
| Location | Distributes like: air | ||
| Latitude | latitude | ° | Only used if Daily average radiation is not provided as a series |
| Longitude | longitude | ° | Only used if sub-daily precision is used. |
| GMT zone | time_zone | hr | Only used if sub-daily precision is used. |
| Elevation | elev | m | Only used if Daily average radiation is not provided as a series |
| Radiation | |||
| Cloud absorption scaling factor | crs | Used if ‘Daily average global radiation’ is not provided as a series. Scaling factor for shortwave absorption by clouds | |
| Cloud absorption power factor | crp | Used if ‘Daily average global radiation’ is not provided as a series. Power factor for shortwave absorption by clouds | |
| Use sub-daily precision | subdaily | Compute hourly averages of solar radiation. Only works correctly if the model sampling step is [hr] or lower. |
State variables
Air temperature
Location: air.temp
Unit: °C
This series is externally defined. It may be an input series.
Relative humidity
Location: air.r_hum
Unit: %
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.
Daily average global radiation on a clear sky day
Location: air.g_rad_cloud_free
Unit: W m⁻²
Value:
\[\mathrm{ext} = \href{stdlib.html#radiation}{\mathrm{daily\_average\_extraterrestrial\_radiation}}\left(\mathrm{latitude},\, \mathrm{time}.\mathrm{day\_of\_year}\right) \\ \href{stdlib.html#radiation}{\mathrm{clear\_sky\_shortwave}}\left(\mathrm{ext},\, \mathrm{elev}\right)\]Daily average global radiation
Location: air.g_rad_day
Unit: W m⁻²
Value:
\[\left(1-\mathrm{crs}\cdot \mathrm{cloud}^{\mathrm{crp}}\right)\cdot \mathrm{g\_rad\_cloud\_free}\]Global radiation
Location: air.g_rad
Unit: W m⁻²
Value:
\[\begin{cases}\begin{pmatrix}\mathrm{hour} = \mathrm{floor}\left(\left(\mathrm{time}.\mathrm{second\_of\_day}+\mathrm{time}.\mathrm{fractional\_step}\cdot \mathrm{time}.\mathrm{step\_length\_in\_seconds}\rightarrow \mathrm{hr}\,\right)\right) \\ \mathrm{hour\_a} = \href{stdlib.html#radiation}{\mathrm{hour\_angle}}\left(\mathrm{time}.\mathrm{day\_of\_year},\, \mathrm{time\_zone},\, \mathrm{hour},\, \mathrm{longitude}\right) \\ \href{stdlib.html#radiation}{\mathrm{hourly\_average\_radiation}}\left(\mathrm{g\_rad\_day},\, \mathrm{time}.\mathrm{day\_of\_year},\, \mathrm{latitude},\, \mathrm{hour\_a}\right)\end{pmatrix} & \text{if}\;\mathrm{subdaily} \\ \mathrm{g\_rad\_day} & \text{otherwise}\end{cases}\]Cosine of the solar zenith angle
Location: air.cos_z
Unit:
Value:
\[\mathrm{hour\_a} = \begin{pmatrix}\mathrm{hour} = \left(\mathrm{time}.\mathrm{second\_of\_day}+\mathrm{time}.\mathrm{fractional\_step}\cdot \mathrm{time}.\mathrm{step\_length\_in\_seconds}\rightarrow \mathrm{hr}\,\right) \\ \begin{cases}\href{stdlib.html#radiation}{\mathrm{hour\_angle}}\left(\mathrm{time}.\mathrm{day\_of\_year},\, \mathrm{time\_zone},\, \mathrm{hour},\, \mathrm{longitude}\right) & \text{if}\;\mathrm{subdaily} \\ 0 & \text{otherwise}\end{cases}\end{pmatrix} \\ \href{stdlib.html#radiation}{\mathrm{cos\_zenith\_angle}}\left(\mathrm{hour\_a},\, \mathrm{time}.\mathrm{day\_of\_year},\, \mathrm{latitude}\right)\]Cloud cover
Location: air.cloud
Unit:
Value:
\[\mathrm{sw\_ratio} = \frac{\mathrm{g\_rad\_day}}{\mathrm{g\_rad\_cloud\_free}} \\ \mathrm{cc} = 1-\mathrm{sw\_ratio} \\ \href{stdlib.html#basic}{\mathrm{clamp}}\left(\mathrm{cc},\, 0,\, 1\right)\]Air pressure
Location: air.pressure
Unit: hPa
Value:
\[\left(\href{stdlib.html#meteorology}{\mathrm{mean\_barometric\_pressure}}\left(\mathrm{elev}\right)\rightarrow \mathrm{hPa}\,\right)\]Saturation vapour pressure
Location: air.s_vap
Unit: hPa
Value:
\[\href{stdlib.html#meteorology}{\mathrm{saturation\_vapor\_pressure}}\left(\mathrm{temp}\right)\]Actual vapour pressure
Location: air.a_vap
Unit: hPa
Value:
\[\left(\mathrm{r\_hum}\rightarrow 1\right)\cdot \mathrm{s\_vap}\]Actual specific humidity
Location: air.a_hum
Unit:
Value:
\[\href{stdlib.html#meteorology}{\mathrm{specific\_humidity\_from\_pressure}}\left(\mathrm{pressure},\, \mathrm{a\_vap}\right)\]Air density
Location: air.dens
Unit: kg m⁻³
Value:
\[\href{stdlib.html#meteorology}{\mathrm{air\_density}}\left(\mathrm{temp},\, \mathrm{pressure},\, \mathrm{a\_vap}\right)\]Downwelling longwave radiation
Location: air.lwd
Unit: W m⁻²
Value:
\[\href{stdlib.html#radiation}{\mathrm{downwelling\_longwave}}\left(\mathrm{temp},\, \mathrm{a\_vap},\, \mathrm{cloud}\right)\]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 |
| Wind speed | wind | property |
| Temperature | temp | 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 indicator | indicator | property |
| Evaporation | evap | property |
| freeze_temp | loc | |
| 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 coefficient 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:
\[\mathrm{z\_surf} = 1 \mathrm{m}\, \\ \mathrm{K\_ice} = 200 \mathrm{W}\,\mathrm{m}^{-3}\,\mathrm{°C}^{-1}\, \\ \mathrm{e} = \left(\mathrm{freeze\_temp}-\mathrm{top\_water}.\mathrm{temp}\right)\cdot \mathrm{z\_surf}\cdot \mathrm{K\_ice} \\ \begin{cases}0 \mathrm{W}\,\mathrm{m}^{-2}\, & \text{if}\;\mathrm{ice}<10^{-6} \mathrm{m}\,\;\text{and}\;\mathrm{e}<0 \\ \mathrm{e} & \text{otherwise}\end{cases}\]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:
\[\mathrm{alpha} = \frac{1}{10 \mathrm{m}^{-1}\,\cdot \mathrm{ice}} \\ \begin{cases}\frac{\mathrm{alpha}\cdot \mathrm{freeze\_temp}+\mathrm{air}.\mathrm{temp}}{1+\mathrm{alpha}} & \text{if}\;\mathrm{indicator} \\ 0 \mathrm{°C}\, & \text{otherwise}\end{cases}\]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:
\[\left(\frac{\mathrm{energy}+\begin{cases}\mathrm{lambda\_ice}\cdot \frac{\left(\mathrm{freeze\_temp}\rightarrow \mathrm{K}\,\right)-\left(\mathrm{temp}\rightarrow \mathrm{K}\,\right)}{\mathrm{ice}} & \text{if}\;\mathrm{temp}\leq \mathrm{freeze\_temp}\;\text{and}\;\mathrm{indicator} \\ -\left(1-\mathrm{albedo}\right)\cdot \mathrm{air}.\mathrm{g\_rad}\cdot \mathrm{attn} & \text{if}\;\mathrm{indicator} \\ 0 & \text{otherwise}\end{cases}}{\mathrm{rho\_ice}\cdot \mathrm{l\_freeze}}\rightarrow \mathrm{m}\,\mathrm{day}^{-1}\,\right)+\left(\begin{cases}\mathrm{air}.\mathrm{precip} & \text{if}\;\mathrm{indicator}\;\text{and}\;\mathrm{air}.\mathrm{temp}\leq \mathrm{freeze\_temp} \\ 0 & \text{otherwise}\end{cases}\rightarrow \mathrm{m}\,\mathrm{day}^{-1}\,\right)\]AirSeaGas Lake
Version: 0.0.0
File: modules/airsea_gas.txt
Description
Air-sea gas exchange module (O₂, CO₂, CH₄)
Authors: François Clayer, Magnus Dahler Norling
External symbols
| Name | Symbol | Type |
|---|---|---|
| Atmosphere | air | compartment |
| CO₂ | co2 | quantity |
| O₂ saturation concentration | o2satconc | property |
| Epilimnion | basin | compartment |
| O₂ | o2 | quantity |
| CH₄ | ch4 | quantity |
| Wind speed | wind | property |
| Temperature | temp | property |
| Precipitation | precip | property |
| Pressure | pressure | property |
| ice_ind | loc | |
| top_water | loc | |
| A_surf | loc | |
| compute_dic | loc |
State variables
O₂ piston velocity
Location: basin.p_vel
Unit: cm hr⁻¹
Value:
\[\href{stdlib.html#sea-oxygen}{\mathrm{o2\_piston\_velocity}}\left(\mathrm{air}.\mathrm{wind},\, \mathrm{top\_water}.\mathrm{temp}\right)\]Fluxes
Precipitation O₂
Source: out
Target: top_water.o2
Unit: kg day⁻¹
Value:
\[\mathrm{precip\_saturation} = 0.9 \\ \mathrm{cnc} = \mathrm{precip\_saturation}\cdot \href{stdlib.html#sea-oxygen}{\mathrm{o2\_saturation\_concentration}}\left(\mathrm{air}.\mathrm{temp},\, 0\right)\cdot \mathrm{o2\_mol\_mass} \\ \left(\mathrm{air}.\mathrm{precip}\cdot \mathrm{A\_surf}\cdot \mathrm{cnc}\rightarrow \mathrm{kg}\,\mathrm{day}^{-1}\,\right)\]O₂ gas exchange at surface
Source: top_water.o2
Target: out
Unit: kg day⁻¹
Value:
\[\left(\;\text{not}\;\mathrm{ice\_ind}\cdot \mathrm{basin}.\mathrm{p\_vel}\cdot \left(\mathrm{conc}\left(\mathrm{top\_water}.\mathrm{o2}\right)-\mathrm{top\_water}.\mathrm{o2satconc}\right)\cdot \mathrm{A\_surf}\rightarrow \mathrm{kg}\,\mathrm{day}^{-1}\,\right)\]Simple river TOC
Version: 0.1.1
File: modules/simplyc.txt
Description
River particulate organic carbon.
Authors: Magnus D. Norling
External symbols
| Name | Symbol | Type |
|---|---|---|
| Total organic carbon | toc | property |
| River | river | compartment |
| Water | water | quantity |
| Organic carbon | oc | quantity |
| Particles | sed | quantity |
Parameters
| Name | Symbol | Unit | Description |
|---|---|---|---|
| Particulate carbon | |||
| Particle OC mass fraction | sed_oc | g kg⁻¹ |
State variables
River POC
Location: river.water.sed.oc
Unit: kg
River TOC
Location: river.water.toc
Unit: mg l⁻¹
Value:
\[\mathrm{conc}\left(\mathrm{oc}\right)+\mathrm{conc}\left(\mathrm{sed}.\mathrm{oc}\right)\cdot \mathrm{conc}\left(\mathrm{sed}\right)\]Fluxes
River POC mobilization
Source: out
Target: river.water.sed.oc
Unit: kg day⁻¹
Value:
\[\left(\mathrm{sed\_oc}\cdot \mathrm{in\_flux}\left(\mathrm{river}.\mathrm{water}.\mathrm{sed}\right)\rightarrow \mathrm{kg}\,\mathrm{day}^{-1}\,\right)\]Organic CNP land
Version: 0.0.0
File: modules/organic_np.txt
Parameters
| Name | Symbol | Unit | Description |
|---|---|---|---|
| Organic nutrient ratios land | |||
| OM molar C/N ratio | om_cn | The default value is the Redfield ratio | |
| OM molar C/P ratio | om_cp | The default value is the Redfield ratio |
Simple organic NP
Version: 0.0.0
File: modules/organic_np.txt
External symbols
| Name | Symbol | Type |
|---|---|---|
| River | river | compartment |
| Organic nitrogen | on | quantity |
| Water | water | quantity |
| Organic carbon | oc | quantity |
| Particles | sed | quantity |
| Organic phosphorous | op | quantity |
| Total nitrogen | tn | property |
| Total phosphorous | tp | property |
| Total dissolved phosphorous | tdp | property |
State variables
River DOP
Location: river.water.op
Unit: kg
Conc. unit: mg l⁻¹
River POP
Location: river.water.sed.op
Unit: kg
River DON
Location: river.water.on
Unit: kg
Conc. unit: mg l⁻¹
River PON
Location: river.water.sed.on
Unit: kg
Total phosphorous
Location: river.water.tp
Unit: mg l⁻¹
Total dissolved phosphorous
Location: river.water.tdp
Unit: mg l⁻¹
Total nitrogen
Location: river.water.tn
Unit: mg l⁻¹
Fluxes
DON mobilization
Source: out
Target: river.water.on
Unit: kg day⁻¹
Value:
\[\left(\frac{\mathrm{in\_flux}\left(\mathrm{oc}\right)}{\href{stdlib.html#chemistry}{\mathrm{cn\_molar\_to\_mass\_ratio}}\left(\mathrm{om\_cn}\right)}\rightarrow \mathrm{kg}\,\mathrm{day}^{-1}\,\right)\]PON mobilization
Source: out
Target: river.water.sed.on
Unit: kg day⁻¹
Value:
\[\left(\frac{\mathrm{in\_flux}\left(\mathrm{sed}.\mathrm{oc}\right)}{\href{stdlib.html#chemistry}{\mathrm{cn\_molar\_to\_mass\_ratio}}\left(\mathrm{om\_cn}\right)}\rightarrow \mathrm{kg}\,\mathrm{day}^{-1}\,\right)\]DOP mobilization
Source: out
Target: river.water.op
Unit: kg day⁻¹
Value:
\[\left(\frac{\mathrm{in\_flux}\left(\mathrm{oc}\right)}{\href{stdlib.html#chemistry}{\mathrm{cn\_molar\_to\_mass\_ratio}}\left(\mathrm{om\_cp}\right)}\rightarrow \mathrm{kg}\,\mathrm{day}^{-1}\,\right)\]POP mobilization
Source: out
Target: river.water.sed.op
Unit: kg day⁻¹
Value:
\[\left(\frac{\mathrm{in\_flux}\left(\mathrm{sed}.\mathrm{oc}\right)}{\href{stdlib.html#chemistry}{\mathrm{cp\_molar\_to\_mass\_ratio}}\left(\mathrm{om\_cp}\right)}\rightarrow \mathrm{kg}\,\mathrm{day}^{-1}\,\right)\]