"""The ``models.soil.uptake`` module contains functions that are used to
capture the uptake competition for the various microbial groups in the simulation.
""" # noqa: D205
from dataclasses import dataclass
import numpy as np
from numpy.typing import NDArray
from virtual_ecosystem.models.soil.env_factors import (
calculate_carbon_use_efficiency,
calculate_temperature_effect_on_microbes,
)
from virtual_ecosystem.models.soil.microbial_groups import MicrobialGroupConstants
from virtual_ecosystem.models.soil.model_config import SoilConstants
[docs]
@dataclass
class NetNutrientConsumption:
"""Net consumption of each labile due to microbial activity.
The labile inorganic pools can have negative consumptions because microbes can
mineralise inorganic nutrients from nutrients in organic form.
"""
carbon: NDArray[np.floating]
"""Uptake of low molecular weight carbon [kg{C} m^-3 day^-1]."""
organic_nitrogen: NDArray[np.floating]
"""Uptake of dissolved organic nitrogen [kg{N} m^-3 day^-1]."""
ammonium: NDArray[np.floating]
"""Uptake of ammonium [kg{N} m^-3 day^-1]."""
nitrate: NDArray[np.floating]
"""Uptake of nitrate [kg{N} m^-3 day^-1]."""
organic_phosphorus: NDArray[np.floating]
"""Uptake of dissolved organic phosphorus [kg{P} m^-3 day^-1]."""
inorganic_phosphorus: NDArray[np.floating]
"""Uptake of labile inorganic phosphorus [kg{P} m^-3 day^-1]."""
[docs]
@dataclass
class MaxUptakeRates:
"""Maximum rate at which each nutrient can be taken up by the microbial group."""
carbon: NDArray[np.floating]
"""Maximum uptake of low molecular weight carbon [kg{C} m^-3 day^-1]."""
organic_nitrogen: NDArray[np.floating]
"""Maximum uptake rate of organic nitrogen [kg{N} m^-3 day^-1].
This nitrogen is taken up along with the :term:`LMWC` uptake.
"""
organic_phosphorus: NDArray[np.floating]
"""Maximum uptake rate of organic phosphorus [kg{P} m^-3 day^-1].
This phosphorus is taken up along with the :term:`LMWC` uptake.
"""
ammonium: NDArray[np.floating]
"""Maximum uptake rate of ammonium [kg{N} m^-3 day^-1]."""
nitrate: NDArray[np.floating]
"""Maximum uptake rate of nitrate [kg{N} m^-3 day^-1]."""
inorganic_phosphorus: NDArray[np.floating]
"""Maximum uptake rate of labile inorganic phosphorus [kg{P} m^-3 day^-1]."""
[docs]
def calculate_nutrient_uptake_rates(
soil_c_pool_lmwc: NDArray[np.floating],
soil_n_pool_don: NDArray[np.floating],
soil_n_pool_ammonium: NDArray[np.floating],
soil_n_pool_nitrate: NDArray[np.floating],
soil_p_pool_dop: NDArray[np.floating],
soil_p_pool_labile: NDArray[np.floating],
microbial_pool_size: NDArray[np.floating],
external_carbon_supply: NDArray[np.floating] | None,
water_factor: NDArray[np.floating],
pH_factor: NDArray[np.floating],
soil_temp: NDArray[np.floating],
constants: SoilConstants,
functional_group: MicrobialGroupConstants,
) -> tuple[NDArray[np.floating], NetNutrientConsumption]:
"""Calculate the rate at which microbes uptake each nutrient.
These rates are found based on the assumption that microbial stoichiometry is
inflexible, i.e. assuming that the rate of uptake of all nutrients (carbon, nitrogen
and phosphorus) needed for growth will be set by the least available nutrient. The
carbon case is more complex as carbon gets used both for biomass synthesis and
respiration. In this case, we calculate the carbon use efficiency and use this to
find the maximum amount of carbon available for biomass synthesis. Once the most
limiting nutrient uptake stream is found it is straightforward to find the demand
for other nutrients. This is because the microbial biomass stoichiometry can only
remain the same if nutrients are taken up following the same stoichiometry (with an
adjustment made for carbon use efficiency).
Biomass synthesis is split between the synthesis of new cellular biomass and the
production of extracellular enzymes. We assume that extracellular enzymes are always
produced in fixed proportion to the rate at which new biomass is synthesised. As
such, we calculate the nutrient costs of synthesising new biomass based on a
weighted (by relative investment in production) average of the stoichiometry of the
different enzymes and the microbial group itself.
The balance of mineralisation and immobilisation rates of inorganic nitrogen and
phosphorus are also calculated in this function. This is done by calculating the
difference between the demand for nitrogen and phosphorus and their uptake due to
organic matter uptake. If more is taken up as a component of organic matter than is
needed then nutrients are mineralised, i.e. mass is added to the relevant inorganic
nutrient pool. Conversely, if more is required to meet demand uptake occurs from the
relevant inorganic nutrient pool (this is termed immobilisation). Two forms
inorganic nitrogen can be taken up by microbes, ammonium and nitrate. The rate at
which these are taken up is determined by the ratio of their uptake rates. When
inorganic nitrogen is mineralised the ratio of ammonium to nitrate mineralised is
determined by a fixed ratio defined in the model constants.
Symbiotic microbes depend on their symbiotic plant partners for their carbon
requirements. They uptake the nitrogen and phosphorus they need to grow from the
soil, preferentially taking inorganic nutrients. A fixed (but configurable) fraction
of their uptake is supplied to their symbiotic partners. If more carbon is supplied
than the microbes can use the surplus is added to the soil as :term:`LMWC`.
Args:
soil_c_pool_lmwc: Low molecular weight carbon pool [kg{C} m^-3]
soil_n_pool_don: Dissolved organic nitrogen pool [kg{N} m^-3]
soil_n_pool_ammonium: Soil ammonium pool [kg{N} m^-3]
soil_n_pool_nitrate: Soil nitrate pool [kg{N} m^-3]
soil_p_pool_dop: Dissolved organic phosphorus pool [kg{P} m^-3]
soil_p_pool_labile: Labile inorganic phosphorus pool [kg{P} m^-3]
microbial_pool_size: Amount of biomass for functional of interest [kg{C} m^-3]
external_carbon_supply: Additional supply of carbon to the microbial group from
external sources (i.e. partner plants) [kg{C} m^-3 day^-1]
water_factor: A factor capturing the impact of soil water potential on microbial
rates [unitless]
pH_factor: A factor capturing the impact of soil pH on microbial rates
[unitless]
soil_temp: soil temperature for each soil grid cell [Celsius]
constants: Set of constants for the soil model.
functional_group: A data class containing the parameters defining the microbial
functional group
Returns:
A tuple containing the rate at which microbial (cellular) biomass is generated
due to nutrient uptake, as well as a dataclass containing the rate at which
carbon, nitrogen and phosphorus get taken up.
Raises:
ValueError: If an external carbon supply is provided without a corresponding
demand for nitrogen and phosphorus exchange
"""
# Calculate carbon use efficiency as it is used in multiple subsequent functions
carbon_use_efficiency = calculate_carbon_use_efficiency(
soil_temp=soil_temp,
reference_cue_logit=constants.reference_cue_logit,
cue_reference_temp=constants.cue_reference_temp,
logit_cue_with_temp=constants.logit_cue_with_temperature,
)
max_uptake_rates = calculate_maximum_uptake_rates(
soil_c_pool_lmwc=soil_c_pool_lmwc,
soil_n_pool_don=soil_n_pool_don,
soil_n_pool_ammonium=soil_n_pool_ammonium,
soil_n_pool_nitrate=soil_n_pool_nitrate,
soil_p_pool_dop=soil_p_pool_dop,
soil_p_pool_labile=soil_p_pool_labile,
microbial_pool_size=microbial_pool_size,
water_factor=water_factor,
pH_factor=pH_factor,
soil_temp=soil_temp,
functional_group=functional_group,
)
actual_carbon_gain = calculate_actual_carbon_gain(
max_uptake_rates=max_uptake_rates,
external_carbon_supply=external_carbon_supply,
carbon_use_efficiency=carbon_use_efficiency,
functional_group=functional_group,
)
if external_carbon_supply is not None:
consumption_rates = find_net_nutrient_consumptions_symbiotic(
max_uptake_rates=max_uptake_rates,
actual_carbon_gain=actual_carbon_gain,
external_carbon_supply=external_carbon_supply,
carbon_use_efficiency=carbon_use_efficiency,
functional_group=functional_group,
)
else:
consumption_rates = find_net_nutrient_consumptions_free_living(
max_uptake_rates=max_uptake_rates,
actual_carbon_gain=actual_carbon_gain,
carbon_use_efficiency=carbon_use_efficiency,
functional_group=functional_group,
ammonium_mineralisation_proportion=constants.ammonium_mineralisation_proportion,
)
# TODO - the quantities calculated above can be used to calculate the carbon
# respired instead of being uptaken. This isn't currently of interest, but will be
# in future
# Carbon gain needs to be divided by the proportional enzyme production as it
# represents biomass gain and enzyme production.
return (
actual_carbon_gain
/ (
1
+ sum(functional_group.enzyme_production.values())
+ functional_group.reproductive_allocation
),
consumption_rates,
)
[docs]
def find_net_nutrient_consumptions_free_living(
max_uptake_rates: MaxUptakeRates,
actual_carbon_gain: NDArray[np.floating],
carbon_use_efficiency: NDArray[np.floating],
functional_group: MicrobialGroupConstants,
ammonium_mineralisation_proportion: float,
) -> NetNutrientConsumption:
"""Find net consumption of each nutrient class for a free-living microbial group.
These net consumptions can be negative as microbes can mineralise nutrients from
organic matter.
We assume that organic matter is always taken up at the maximum possible rate. This
is because organic matter contains carbon, nitrogen and phosphorus and one of these
will always be limiting growth. Any excess uptake through organic matter gets
returned (this represents overflow metabolism). If the microbial group is heavily
carbon limited nutrients will be returned to the soil in an inorganic form,
conversely if it is less carbon limited the excess nutrients will be returned in an
organic form. If the demand for nitrogen or phosphorus exceeds the amount provided
through organic matter uptake, inorganic nutrients are uptaken.
Args:
max_uptake_rates: Maximum uptake rates for each nutrient class [kg m^-3 day^-1]
actual_carbon_gain: The rate at which carbon is assimilated to biomass [kg C
m^-3 day^-1]
carbon_use_efficiency: Carbon use efficiency of the microbial group (varies with
temperature) [unitless]
functional_group: A data class containing the parameters defining the microbial
functional group.
ammonium_mineralisation_proportion: Proportion of microbially mineralised
nitrogen that takes the form of ammonium [unitless]
Returns:
The net consumption/production of each nutrient class [kg m^-3 day^-1].
"""
# Determine how limiting carbon is (as a proportion). The zero carbon uptake case is
# handled by assuming that carbon limitation is total in this case.
carbon_limitation = np.divide(
actual_carbon_gain,
max_uptake_rates.carbon * carbon_use_efficiency,
out=np.ones_like(max_uptake_rates.carbon, dtype=float),
where=(max_uptake_rates.carbon > 0),
)
# Calculate biomass demands for nitrogen and phosphorus
nitrogen_demand = (
actual_carbon_gain / functional_group.synthesis_nutrient_ratios["nitrogen"]
)
phosphorus_demand = (
actual_carbon_gain / functional_group.synthesis_nutrient_ratios["phosphorus"]
)
# Next find if organic uptake satisfies demands for phosphorus and nitrogen
nitrogen_inorganic_demand = nitrogen_demand - max_uptake_rates.organic_nitrogen
phosphorus_inorganic_demand = (
phosphorus_demand - max_uptake_rates.organic_phosphorus
)
# Calculate how much of the organic nitrogen and phosphorus should be returned in an
# organic form
organic_nitrogen_return = np.where(
nitrogen_inorganic_demand < 0,
-nitrogen_inorganic_demand * (1 - carbon_limitation),
0.0,
)
organic_phosphorus_return = np.where(
phosphorus_inorganic_demand < 0,
-phosphorus_inorganic_demand * (1 - carbon_limitation),
0.0,
)
# Find how much inorganic nitrogen and phosphorus is taken up or released
inorganic_nitrogen_change = np.where(
nitrogen_inorganic_demand >= 0,
nitrogen_inorganic_demand,
nitrogen_inorganic_demand * carbon_limitation,
)
inorganic_phosphorus_change = np.where(
phosphorus_inorganic_demand >= 0,
phosphorus_inorganic_demand,
phosphorus_inorganic_demand * carbon_limitation,
)
# For immobilisation of nitrogen, the proportion of ammonium and nitrate taken up
# follows the proportion of the maximum uptake rates (if either is above zero)
ammonium_uptake_proportion = np.divide(
max_uptake_rates.ammonium,
max_uptake_rates.ammonium + max_uptake_rates.nitrate,
out=np.zeros_like(max_uptake_rates.ammonium, dtype=float),
where=(max_uptake_rates.ammonium > 0) | (max_uptake_rates.nitrate > 0),
)
# Whether the uptake proportion or the mineralisation proportion is relevant depends
# whether inorganic nitrogen is being taken up or not
ammonium_to_nitrate_proportion = np.where(
inorganic_nitrogen_change > 0,
ammonium_uptake_proportion,
ammonium_mineralisation_proportion,
)
ammonium_change = inorganic_nitrogen_change * ammonium_to_nitrate_proportion
nitrate_change = inorganic_nitrogen_change * (1 - ammonium_to_nitrate_proportion)
return NetNutrientConsumption(
organic_nitrogen=max_uptake_rates.organic_nitrogen - organic_nitrogen_return,
organic_phosphorus=(
max_uptake_rates.organic_phosphorus - organic_phosphorus_return
),
carbon=actual_carbon_gain / carbon_use_efficiency,
ammonium=ammonium_change,
nitrate=nitrate_change,
inorganic_phosphorus=inorganic_phosphorus_change,
)
[docs]
def find_net_nutrient_consumptions_symbiotic(
max_uptake_rates: MaxUptakeRates,
actual_carbon_gain: NDArray[np.floating],
external_carbon_supply: NDArray[np.floating],
carbon_use_efficiency: NDArray[np.floating],
functional_group: MicrobialGroupConstants,
) -> NetNutrientConsumption:
"""Find net consumption of each nutrient class for a symbiotic microbial group.
We assume that inorganic nutrients are preferentially taken up, as the symbiotic
microbes are reliant on their hosts for carbon. If the demand for nitrogen or
phosphorus exceeds the amount provided through inorganic matter uptake, organic
nutrients are uptaken. Though this implies a corresponding uptake of carbon, we do
not track it as we are assuming that the symbiotic partners cannot make use of this
carbon at all, and so immediately release it. If more carbon is supplied (by
symbiotic plant partners) than the microbes make use of the surplus carbon is added
to the soil as :term:`LMWC`.
Args:
max_uptake_rates: Maximum uptake rates for each nutrient class [kg m^-3 day^-1]
actual_carbon_gain: The rate at which carbon is assimilated to biomass [kg C
m^-3 day^-1]
external_carbon_supply: Additional supply of carbon to the microbial group from
symbiotic partner plants [kg{C} m^-3 day^-1]
carbon_use_efficiency: Carbon use efficiency of the microbial group (varies with
temperature) [unitless]
functional_group: A data class containing the parameters defining the microbial
functional group.
Returns:
The net consumption/production of each nutrient class [kg m^-3 day^-1].
"""
# Calculate total demands for nitrogen and phosphorus by dividing amount uptaken for
# assimilation by the fraction of the total uptake that this represents
nitrogen_demand = (
actual_carbon_gain / functional_group.synthesis_nutrient_ratios["nitrogen"]
) / (1 - functional_group.symbiote_nitrogen_uptake_fraction)
phosphorus_demand = (
actual_carbon_gain / functional_group.synthesis_nutrient_ratios["phosphorus"]
) / (1 - functional_group.symbiote_phosphorus_uptake_fraction)
# Inorganic nutrients are preferentially taken up, so calculate how much of each of
# these are taken up
inorganic_nitrogen_demand = np.where(
nitrogen_demand >= max_uptake_rates.ammonium + max_uptake_rates.nitrate,
max_uptake_rates.ammonium + max_uptake_rates.nitrate,
nitrogen_demand,
)
inorganic_phosphorus_demand = np.where(
phosphorus_demand >= max_uptake_rates.inorganic_phosphorus,
max_uptake_rates.inorganic_phosphorus,
phosphorus_demand,
)
# Organic nutrients are then taken up if the demand can't be satisfied by inorganic
# uptake alone.
organic_nitrogen_demand = nitrogen_demand - inorganic_nitrogen_demand
organic_phosphorus_demand = phosphorus_demand - inorganic_phosphorus_demand
# For inorganic nitrogen uptake, the proportion of ammonium and nitrate taken up
# follows the proportion of the maximum uptake rates (if either is above zero)
ammonium_uptake_proportion = np.divide(
max_uptake_rates.ammonium,
max_uptake_rates.ammonium + max_uptake_rates.nitrate,
out=np.zeros_like(max_uptake_rates.ammonium, dtype=float),
where=(max_uptake_rates.ammonium > 0) | (max_uptake_rates.nitrate > 0),
)
ammonium_uptake = inorganic_nitrogen_demand * ammonium_uptake_proportion
nitrate_uptake = inorganic_nitrogen_demand * (1 - ammonium_uptake_proportion)
# Finally need to find how much additional carbon has been provided
surplus_carbon_supply = external_carbon_supply - (
actual_carbon_gain / carbon_use_efficiency
)
return NetNutrientConsumption(
organic_nitrogen=organic_nitrogen_demand,
organic_phosphorus=organic_phosphorus_demand,
carbon=-surplus_carbon_supply,
ammonium=ammonium_uptake,
nitrate=nitrate_uptake,
inorganic_phosphorus=inorganic_phosphorus_demand,
)
[docs]
def calculate_actual_carbon_gain(
max_uptake_rates: MaxUptakeRates,
external_carbon_supply: NDArray[np.floating] | None,
carbon_use_efficiency: NDArray[np.floating],
functional_group: MicrobialGroupConstants,
) -> NDArray[np.floating]:
"""Calculate the rate at which carbon is assimilated by microbes.
The limitation that each nutrient places on carbon assimilation is determined. For
carbon this is based on carbon use efficiency, but in the case of nitrogen and
phosphorus this is determined based on biomass stoichiometry (i.e. you can't add
more carbon to biomass if you are deficient in nitrogen). This is used to calculate
the actual rate at which carbon is assimilated to biomass.
In the symbiotic case, microbes can only use the carbon is supplied by their plant
partners to grow. In return for this, symbiotic microbes must provide a fraction of
the nutrients they uptake back to the plants. This means that they can only
assimilate a fraction of the nutrients that they uptake as biomass, which generally
reduces maximum carbon assimilation rates.
Args:
max_uptake_rates: Maximum uptake rates for each nutrient class [kg m^-3 day^-1]
external_carbon_supply: Additional supply of carbon to the microbial group from
external sources (i.e. partner plants) [kg{C} m^-3 day^-1]
carbon_use_efficiency: Carbon use efficiency of the microbial group (varies with
temperature) [unitless]
functional_group: A data class containing the parameters defining the microbial
functional group.
Returns:
The rate at which carbon is assimilated to biomass [kg m^-3 day^-1].
"""
# In symbiotic cases only external carbon is used, and in free-living cases there is
# no external carbon supplied
if external_carbon_supply is not None:
carbon_gain_max = external_carbon_supply * carbon_use_efficiency
else:
carbon_gain_max = max_uptake_rates.carbon * carbon_use_efficiency
nitrogen_gain_max = (
max_uptake_rates.organic_nitrogen
+ max_uptake_rates.ammonium
+ max_uptake_rates.nitrate
) * (1 - functional_group.symbiote_nitrogen_uptake_fraction)
phosphorus_gain_max = (
max_uptake_rates.organic_phosphorus + max_uptake_rates.inorganic_phosphorus
) * (1 - functional_group.symbiote_phosphorus_uptake_fraction)
# Find the maximum rate of carbon assimilation based on nitrogen and phosphorus
# uptake rates, and biomass stoichiometric ratios
nitrogen_limit = (
functional_group.synthesis_nutrient_ratios["nitrogen"] * nitrogen_gain_max
)
phosphorus_limit = (
functional_group.synthesis_nutrient_ratios["phosphorus"] * phosphorus_gain_max
)
# Find actual rate of carbon gain based on most limiting uptake rate, then find
# nutrient gain and total carbon consumption based on this
return np.minimum.reduce([carbon_gain_max, nitrogen_limit, phosphorus_limit])
[docs]
def calculate_maximum_uptake_rates(
soil_c_pool_lmwc: NDArray[np.floating],
soil_n_pool_don: NDArray[np.floating],
soil_n_pool_ammonium: NDArray[np.floating],
soil_n_pool_nitrate: NDArray[np.floating],
soil_p_pool_dop: NDArray[np.floating],
soil_p_pool_labile: NDArray[np.floating],
microbial_pool_size: NDArray[np.floating],
water_factor: NDArray[np.floating],
pH_factor: NDArray[np.floating],
soil_temp: NDArray[np.floating],
functional_group: MicrobialGroupConstants,
) -> MaxUptakeRates:
"""Calculate the maximum uptake rate for each category of nutrient.
Categories are, carbon, organic nitrogen and phosphorus, inorganic nitrogen
(ammonium and nitrate), and inorganic phosphorus.
Args:
soil_c_pool_lmwc: Low molecular weight carbon pool [kg{C} m^-3]
soil_n_pool_don: Dissolved organic nitrogen pool [kg{N} m^-3]
soil_n_pool_ammonium: Soil ammonium pool [kg{N} m^-3]
soil_n_pool_nitrate: Soil nitrate pool [kg{N} m^-3]
soil_p_pool_dop: Dissolved organic phosphorus pool [kg{P} m^-3]
soil_p_pool_labile: Labile inorganic phosphorus pool [kg{P} m^-3]
microbial_pool_size: Amount of biomass for functional of interest [kg{C} m^-3]
lmwc_c_n_ratio: Carbon to nitrogen ratio of the low molecular weight carbon pool
[unitless]
lmwc_c_p_ratio: Carbon to phosphorus ratio of the low molecular weight carbon
pool [unitless]
water_factor: A factor capturing the impact of soil water potential on microbial
rates [unitless]
pH_factor: A factor capturing the impact of soil pH on microbial rates
[unitless]
soil_temp: soil temperature for each soil grid cell [Celsius]
constants: Set of constants for the soil model.
functional_group: A data class containing the parameters defining the microbial
functional group
Returns:
The maximum rate at which each category of nutrient can be taken up by the
microbial group of interest.
"""
# Calculate highest possible microbial uptake rates for organic matter and inorganic
# forms of nitrogen and phosphorus
carbon_uptake_rate_max = calculate_highest_achievable_nutrient_uptake(
labile_nutrient_pool=soil_c_pool_lmwc,
microbial_pool_size=microbial_pool_size,
water_factor=water_factor,
pH_factor=pH_factor,
soil_temp=soil_temp,
max_uptake_rate=functional_group.max_uptake_rate_labile_C,
half_saturation_constant=functional_group.half_sat_labile_C_uptake,
activation_energy_uptake=functional_group.activation_energy_uptake_rate,
activation_energy_uptake_saturation=functional_group.activation_energy_uptake_saturation,
reference_temperature=functional_group.reference_temperature,
)
ammonium_uptake_rate_max = calculate_highest_achievable_nutrient_uptake(
labile_nutrient_pool=soil_n_pool_ammonium,
microbial_pool_size=microbial_pool_size,
water_factor=water_factor,
pH_factor=pH_factor,
soil_temp=soil_temp,
max_uptake_rate=functional_group.max_uptake_rate_ammonium,
half_saturation_constant=functional_group.half_sat_ammonium_uptake,
activation_energy_uptake=functional_group.activation_energy_uptake_rate,
activation_energy_uptake_saturation=functional_group.activation_energy_uptake_saturation,
reference_temperature=functional_group.reference_temperature,
)
nitrate_uptake_rate_max = calculate_highest_achievable_nutrient_uptake(
labile_nutrient_pool=soil_n_pool_nitrate,
microbial_pool_size=microbial_pool_size,
water_factor=water_factor,
pH_factor=pH_factor,
soil_temp=soil_temp,
max_uptake_rate=functional_group.max_uptake_rate_nitrate,
half_saturation_constant=functional_group.half_sat_nitrate_uptake,
activation_energy_uptake=functional_group.activation_energy_uptake_rate,
activation_energy_uptake_saturation=functional_group.activation_energy_uptake_saturation,
reference_temperature=functional_group.reference_temperature,
)
inorganic_phosphorus_uptake_rate_max = calculate_highest_achievable_nutrient_uptake(
labile_nutrient_pool=soil_p_pool_labile,
microbial_pool_size=microbial_pool_size,
water_factor=water_factor,
pH_factor=pH_factor,
soil_temp=soil_temp,
max_uptake_rate=functional_group.max_uptake_rate_labile_p,
half_saturation_constant=functional_group.half_sat_labile_p_uptake,
activation_energy_uptake=functional_group.activation_energy_uptake_rate,
activation_energy_uptake_saturation=functional_group.activation_energy_uptake_saturation,
reference_temperature=functional_group.reference_temperature,
)
# Find maximum possible uptake rates for organic nitrogen and phosphorus, based on
# LMWC pool stoichiometry (in cases where either the carbon or nutrient component is
# negative, uptake is forced to cease)
organic_nitrogen_uptake_rate_max = np.divide(
soil_n_pool_don * carbon_uptake_rate_max,
soil_c_pool_lmwc,
out=np.zeros_like(carbon_uptake_rate_max, dtype=float),
where=(soil_n_pool_don > 0) & (soil_c_pool_lmwc > 0),
)
organic_phosphorus_uptake_rate_max = np.divide(
soil_p_pool_dop * carbon_uptake_rate_max,
soil_c_pool_lmwc,
out=np.zeros_like(carbon_uptake_rate_max, dtype=float),
where=(soil_p_pool_dop > 0) & (soil_c_pool_lmwc > 0),
)
return MaxUptakeRates(
carbon=carbon_uptake_rate_max,
organic_nitrogen=organic_nitrogen_uptake_rate_max,
organic_phosphorus=organic_phosphorus_uptake_rate_max,
ammonium=ammonium_uptake_rate_max,
nitrate=nitrate_uptake_rate_max,
inorganic_phosphorus=inorganic_phosphorus_uptake_rate_max,
)
[docs]
def calculate_highest_achievable_nutrient_uptake(
labile_nutrient_pool: NDArray[np.floating],
microbial_pool_size: NDArray[np.floating],
water_factor: NDArray[np.floating],
pH_factor: NDArray[np.floating],
soil_temp: NDArray[np.floating],
max_uptake_rate: float,
activation_energy_uptake: float,
half_saturation_constant: float,
activation_energy_uptake_saturation: float,
reference_temperature: float,
) -> NDArray[np.floating]:
"""Calculate highest achievable uptake rate for a specific nutrient.
This function starts by calculating the impact that environmental factors have on
the rate and saturation constants for microbial uptake. These constants are then
used to calculate the maximum possible uptake rate for the specific nutrient and
microbial group in question.
Args:
labile_nutrient_pool: Mass of nutrient that is in a readily uptakeable (labile)
form [kg{nutrient} m^-3]
microbial_pool_size: Size of microbial biomass (carbon) pool of interest
[kg{C} m^-3]
water_factor: A factor capturing the impact of soil water potential on microbial
rates [unitless]
pH_factor: A factor capturing the impact of soil pH on microbial rates
[unitless]
soil_temp: soil temperature for each soil grid cell [Celsius]
max_uptake_rate: Maximum possible uptake rate of the nutrient (at reference
temperature) [day^-1]
activation_energy_uptake: Activation energy for nutrient uptake for the
microbial group in question [J Kelvin^-1].
half_saturation_constant: Half saturation constant for nutrient uptake (at
reference temperature) [kg{nutrient} m^-3]
activation_energy_uptake_saturation: Activation energy for nutrient uptake
saturation for the microbial group in question [J Kelvin^-1].
reference_temperature: The reference temperature of the Arrhenius equation
[Celsius]
Returns:
The maximum uptake rate by the soil microbial biomass for the nutrient in
question.
"""
# Calculate impact of temperature on the rate and saturation constants
temp_factor_rate = calculate_temperature_effect_on_microbes(
soil_temperature=soil_temp,
activation_energy=activation_energy_uptake,
reference_temperature=reference_temperature,
)
temp_factor_saturation = calculate_temperature_effect_on_microbes(
soil_temperature=soil_temp,
activation_energy=activation_energy_uptake_saturation,
reference_temperature=reference_temperature,
)
# Rate and saturation constants are then adjusted based on these environmental
# conditions
rate_constant = max_uptake_rate * temp_factor_rate * water_factor * pH_factor
saturation_constant = half_saturation_constant * temp_factor_saturation
# Calculate both the rate of carbon uptake, and the rate at which this carbon is
# assimilated into microbial biomass.
uptake_rate = rate_constant * (
(labile_nutrient_pool * microbial_pool_size)
/ (labile_nutrient_pool + saturation_constant)
)
# Uptake rate is only valid if both the nutrient pool and the microbial pool are
# positive, otherwise uptake rate should be zero
return np.where(
(microbial_pool_size >= 0.0) & (labile_nutrient_pool >= 0.0), uptake_rate, 0.0
)
