The T Model module

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import warnings

from matplotlib import pyplot as plt
import numpy as np
import pandas as pd

from pyrealm.core.experimental import ExperimentalFeatureWarning
from pyrealm.demography.flora import Flora
from pyrealm.demography.cohorts import create_cohorts, cohort_id_generator
from pyrealm.demography.tmodel import (
    StemAllocation,
    StemAllometry,
    GrowthIncrements,
    calculate_whole_crown_gpp,
)

warnings.filterwarnings(
    "ignore",
    category=ExperimentalFeatureWarning,
)

The T Model also predicts how gross primary productivity (GPP) will be allocated to respiration, turnover and growth for stems with a given PFT and allometry using the StemAllometry() class. We first need a set of cohorts and their stem allometry:

# Create a flora with 3 PFTs with different maximum heights
flora = Flora(name=["short", "medium", "tall"], h_max=[10, 20, 30])

# Create an id generator.
cid_generator = cohort_id_generator(mode="str")

# Create the cohorts
cohorts = create_cohorts(
    flora=flora,
    cid_generator=cid_generator,
    pft_name=np.array(["short", "medium", "tall"]),
    dbh_value=np.array([0.1, 0.1, 0.1]),
    n_individuals=np.array([1, 1, 1]),
)

allometry = StemAllometry(cohorts=cohorts)

Carbon Allocation

This requires an estimate of the GPP available to a stem. The original implementation of the T Model implemented this (Equation 12, Li et al., 2014) using an estimate of the potential GPP per square metre (\(P_0\)), scaled up to the crown area of the stem (\(A_c\)) and using the Beer-Lambert equation to estimate the proportion of potential GPP captured by the crown as a function of the canopy light extinction coefficient (\(k\)) and the canopy leaf area index (\(L\)):

\[ \textrm{GPP} = P_0 A_c (1 - e^{-kL}) \]

This is implemented in the function calculate_whole_crown_gpp:

whole_crown_gpp = calculate_whole_crown_gpp(
    potential_gpp=np.array([55]),
    crown_area=allometry.crown_area,
    par_ext=cohorts.par_ext,
    lai=cohorts.lai,
)
print(whole_crown_gpp)

0    59.232054
1    75.943478
2    83.004957
dtype: float64

Those realised stem GPP values can then be provided to the StemAllocation class:

allocation = StemAllocation(
    cohorts=cohorts,
    allometry=allometry,
    whole_crown_gpp=whole_crown_gpp.to_numpy(),
)
allocation

StemAllocation: Values for 3 cohorts

The to_dataframe() method can be used to export data for exploration.

allocation.to_dataframe().transpose()

	0	1	2
cohort_ids	C_000000	C_000001	C_000002
whole_crown_gpp	59.232054	75.943478	83.004957
sapwood_respiration	0.197715	0.28648	0.322778
foliage_respiration	5.923205	7.594348	8.300496
fine_root_respiration	0.50701	0.650055	0.7105
foliage_turnover	0.058332	0.07479	0.081744
fine_root_turnover	0.533965	0.684615	0.748272
branch_turnover	0.0	0.0	0.0
npp	31.562474	40.447557	44.20271

The allocation values shown above can then be used to calculate growth increments, as described in the T Model overview:

Under the original T Model, all of the NPP is allocated to biomass production and the GrowthIncrements class can be used to calculate the growth increments after accounting for turnover. The original implementation of the T Model did not include branch turnover and the default PFT parameterisation sets branch turnover to zero.

growth = GrowthIncrements(
    cohorts=cohorts, allometry=allometry, stem_allocation=allocation
)
growth

GrowthIncrements: Values for 3 cohorts

growth.to_dataframe().transpose()

	0	1	2
cohort_ids	C_000000	C_000001	C_000002
delta_dbh	0.208607	0.191874	0.186059
delta_stem_mass	28.453546	36.31641	39.632111
delta_foliage_mass	0.744565	0.997557	1.106681
delta_fine_root_mass	1.772066	2.374186	2.633901

If you want to incorporate other costs into NPP - decreasing carbon available for biomass production - the GrowthIncrements class has an optional biomass_production argument:

# Reduce estimated NPP by 10% to allocate carbon to other costs
biomass_production = allocation.npp * 0.9
reduced_growth = GrowthIncrements(
    cohorts=cohorts,
    allometry=allometry,
    stem_allocation=allocation,
    biomass_production=biomass_production,
)
reduced_growth.to_dataframe().transpose()

	0	1	2
cohort_ids	C_000000	C_000001	C_000002
delta_dbh	0.187347	0.172319	0.167097
delta_stem_mass	25.553774	32.615281	35.593057
delta_foliage_mass	0.668685	0.895893	0.993895
delta_fine_root_mass	1.59147	2.132224	2.365471

Allocation profiles

As with the StemAllometry, the StemAllocation class can be used to generate a profile of the allocation predictions for different estimates of potential GPP. The profile=True option is used to indicate that - instead of providing a single GPP estimate for each cohort - you want predictions at each GPP estimate for each cohort.

# Calculate the stem GPP from potential GPP following the Li et al model
whole_crown_gpp_profile = np.arange(30, 100)

# Calculate the T Model allocation of those GPP values
allocation_profile = StemAllocation(
    cohorts=cohorts,
    allometry=allometry,
    whole_crown_gpp=whole_crown_gpp_profile,
    profile=True,
)
allocation_profile

StemAllocation: Profiles for 3 cohorts at 70 GPP values.

fig, axes = plt.subplots(ncols=2, nrows=3, sharex=True, figsize=(10, 12))

plot_details = [
    ("sapwood_respiration", "sapwood_respiration"),
    ("foliage_respiration", "foliage_respiration"),
    ("fine_root_respiration", "fine_root_respiration"),
    ("npp", "npp"),
    ("foliage_turnover", "foliage_turnover"),
    ("fine_root_turnover", "fine_root_turnover"),
]

axes = axes.flatten()

for ax, (var, ylab) in zip(axes, plot_details):
    ax.plot(whole_crown_gpp_profile, getattr(allocation_profile, var), label=flora.name)
    ax.set_xlabel("GPP (m)")
    ax.set_ylabel(ylab)

    if var == "whole_crown_gpp":
        ax.legend(frameon=False)

Again, with GPP profiles, the to_dataframe() method stacks predictions into columns identified by pairings of cohort ID and DBH.

allocation_profile.to_dataframe().head(6)[["cohort_ids", "whole_crown_gpp", "npp"]]

	cohort_ids	whole_crown_gpp	npp
0	C_000000	30.0	15.777165
1	C_000001	30.0	15.638079
2	C_000002	30.0	15.580033
3	C_000000	31.0	16.317165
4	C_000001	31.0	16.178079
5	C_000002	31.0	16.120033