# -*- coding: utf-8 -*-
# =============================================================================
# This file is part of WaterGAP.
# WaterGAP is an opensource software which computes water flows and storages as
# well as water withdrawals and consumptive uses on all continents.
# You should have received a copy of the LGPLv3 License along with WaterGAP.
# if not see <https://www.gnu.org/licenses/lgpl-3.0>
# =============================================================================
"""Daily Leaf Area Index (LAI) Function."""
# =============================================================================
# This module computes leaf area index based on section 4.2.3 of
# (Müller Schmied et al. (2021)).
# =============================================================================
import numpy as np
from numba import njit
[docs]
@njit(cache=True)
def get_leaf_area_index(temperature, growth_status, days, initial_days,
cum_precipitation, precipitation,
leaf_area_index, min_leaf_area_index,
max_leaf_area_index, land_cover, humid_arid):
"""
Compute daily leaf area index per grid cells.
Parameters
----------
temperature : float
Daily temperature climate forcing, Units: [K]
growth_status : float
Growth status per grid cell shows whether a specific land cover
is (not) growing (value=0) or fully grown (value=1).
Initially all landcovers are not growing
This variable gets updated per time step.
days : float
Days since start of leaf area index profile (counter for days with
growing conditions), Units: [day]
This variable gets updated per time step.
initial_days : float
Landcover specific initial days
cum_precipitation : float
Cummulative precipitation per time step, Units: [mm/d]
precipitation : float
Daily precipitation climate forcing, Units: [mm/d] or [kg m-2 s-1]
Units are converted from kg m-2 s-1 to mm/d
leaf_area_index : float
leaf_area_index, Units: [-]
min_leaf_area_index : float
Minimum Leaf area index over all grid cell, Units: [-]
max_leaf_area_index : float
Maximum Leaf area index over all grid cell, Units: [-]
land_cover : float
Land_cover class based on [1]_, Units: [-]
humid_arid : float
Humid-arid calssification based on [1]_, Units: [-]
Returns
-------
leaf_area_index : float
Daily leaf area index, Units: [-]
days : float
Day since start for current day, Units: [day]
cum_precipitation : float
Cummulative precipitation for current day, units: [mm/d]
growth_status : float
Growth status per grid cell for current day, Units: [-]
Notes
-----
A day is defined as part of the growing season when daily temperature is
above 8◦C(281.15 K) for a land-cover-specific number of initial days
(Table C1) and cumulative precipitation from the day when growing season
starts reaches at least 40 mm [1]_.
In the beginning of the growing season, LAI increases linearly for 30 days
until it reaches maximum LAI. For (semi)arid cells, at least 0.5 mm of
daily precipitation is required to keep the growing season ongoing.
LAI then stays constant for the stated land-cover-specific number of days
and when growing season conditions are not fulfilled anymore, a senescence
phase is initiated and LAI linearly decreases to minimum within the next 30
days
References
----------
.. [1] Müller Schmied, H., Cáceres, D., Eisner, S., Flörke, M.,
Herbert, C., Niemann, C., Peiris, T. A., Popat, E.,
Portmann, F. T., Reinecke, R., Schumacher, M., Shadkam, S.,
Telteu, C.E., Trautmann, T., & Döll, P. (2021).
The global water resources and use model WaterGAP v2.2d: model
description and evaluation. Geoscientific Model Development,
14(2), 1037–1079. https://doi.org/10.5194/gmd-14-1037-2021
"""
if not np.isnan(land_cover):
# ======================
# Growing Phase
# ======================
# Plant can only start growing if daily temperature is above
# 8◦C(281.15 K) for a land-cover-specific number of initial days (See
# Table C1 in (Müller Schmied et al. 2021). Note that 'days' variable
# is a counter for days with growing conditions
# Initially growth staus is zero (landcover is not growing yet).
if temperature > 281.15:
if growth_status == 0:
if days >= initial_days:
# Growing season starts and days is defined as part of
# the growing season. precipiation also accumulates
days = days + 1
cum_precipitation += precipitation
if cum_precipitation > 40:
# Landcover grows linearly till it gets to maximum LAI
# (at initial + 30 days) then growth status changes.
if days >= initial_days + 30:
growth_status = 1
leaf_area_index = max_leaf_area_index
else:
leaf_area_index = (min_leaf_area_index +
((max_leaf_area_index -
min_leaf_area_index)/30.0) *
(days - initial_days))
else:
# Landcover could not grow but temperature condition is
# reached therefore LAI is minimum. The days variable
# is set to landcover specific initial days till
# cumulative precipitation is reached (thus growing
# season is reached)
days = initial_days
leaf_area_index = min_leaf_area_index
else:
# Landcover specific initial days is not reached but
# temperature specification is reached therefore LAI is
# minimum.
days = days + 1
cum_precipitation += precipitation
leaf_area_index = min_leaf_area_index
else:
# Leaf Area index has reached maximum (growth status is 1 ) and
# will deacrease. When in the decreasing phase, temperature
# specification may be reached and hence this part of the code
# still continues the decreasing phase till 30 days is reached.
if days <= 30:
days = days-1
# if land_cover_type is '1' or '2' we have evergreen plants
# and LAI will never completely degrade and hence growth
# status is switched at once.
if land_cover <= 2:
growth_status = 0
if days <= 0:
days = 0
growth_status = 0
cum_precipitation = 0
leaf_area_index = (max_leaf_area_index -
((max_leaf_area_index -
min_leaf_area_index)/30.0) *
(30 - days))
else:
# Leaf area index has reached maximum (growth status is 1 )
# but temperature specification is met. LAI then stays
# constant (at maximum) for the stated land-cover-specific
# number of days.
# Also, if land is arid and precipitation is below 0.5mm
# the days variable decreases
if humid_arid == 1 and precipitation < 0.5:
days = days-1
else:
# Note!! when growth status is 1, "days" only decreases
# when temperature is < 281.15 (see no growing phase
# lines from 247-257) except for arid regions with
# precipitation below 0.5mm which decreases whether
# temperature condition is met or not.
days = initial_days + 30
leaf_area_index = max_leaf_area_index
# ======================
# NO Growing Phase
# ======================
else:
if growth_status == 0:
if days > initial_days:
days = days + 1
cum_precipitation += precipitation
if cum_precipitation > 40:
# Here temperature is less than 281.15K but landcover
# is already growing.This part of the code
# still continues the growing phase till landcover
# specific initial days + 30 is reached.
if days >= initial_days + 30:
growth_status = 1
leaf_area_index = max_leaf_area_index
else:
leaf_area_index = (min_leaf_area_index +
((max_leaf_area_index -
min_leaf_area_index)/30.0) *
(days - initial_days))
else:
days = initial_days
leaf_area_index = min_leaf_area_index
else:
cum_precipitation += precipitation
leaf_area_index = min_leaf_area_index
else:
# Leaf Area index has reached maximum (growth status = 1) and
# will deacrease when growing season conditions are not
# fulfilled anymore.
# Here days variable decreases from 30 to 0 days
if days <= 30:
days = days-1
if days <= 0:
days = 0
growth_status = 0
cum_precipitation = 0
leaf_area_index = (max_leaf_area_index -
((max_leaf_area_index -
min_leaf_area_index)/30.0) *
(30 - days))
else:
# Leaf Area index has reached maximum (growth status is 1 )
# but temperature specification is not met. LAI then stays
# constant (at maximum) for the stated land-cover-specific
# number of days. Here the days variable decreases
# (note the difference from the growing pahse)
days = days-1
leaf_area_index = max_leaf_area_index
return leaf_area_index, days, cum_precipitation, growth_status
