Mortality

Author:

Eren Bilir

Date:

November 2024

depth:

3

CARDAMOM Vegetation Mortality Overview

DALEC:sub:CWE contains multiple new sources of vegetation mortality (carbon starvation, stem cavitation, deforestation, cropping). These build from existing sources (fire vaporization and injury mortality, background mortality). Conceptually, these are separated into deforestation, fire vaporization, environmentally-driven mortality, and background mortality.

Non-fire deforestation and degradation (DD), as well as crop harvest, are implemented as model drivers, based on datasets of human non-fire DD :cite:Xu2021 or crop yield. DD and crop fluxes are fully removed from the grid and not re-distributed or respired, but are instead assumed to be sequestered into long-lived commercial use. Cropping is implemented similarly to DD, although with differing seasonality of flux and proportion of straw residue that is shifted from live to dead pools.

Vegetation C removals due to fire are prognostic, with fire ignitions driven by estimates of burned area :cite:GFED and total emissions constrained by inversions of atmospheric CO observations :cite:MOPPIT. The fire emissions correspond to the fire vaporization term within the mortality scheme. In addition to generating instantaneous emissions, mortality due to fire injury generates a C flux from live to dead pools which are then subject to decomposition and heterotrophic respiration. Fire-injury mortality is folded into the environmentally-driven mortality term.

Environmentally-driven mortality within CARDAMOM is formulated as a combination of carbon starvation, stem cavitation, and fire injury. These are aggregated to maintain consistent response thresholds for each environmentally-linked mortality source even under events that trigger multiple mortality sources (e.g., a drought and fire occurring simultaneously), and are therefore not separated in the model output. Carbon starvation is represented as a function of non-structural carbohydrate depletion, and stem cavitation is represented as a function of soil moisture with an optimized response threshold.

Background mortality represents all other sources of mortality that can be assumed to remain consistently proportionate to live pool sizes on multi-decadal time-scales. This chiefly includes the age-related senescence of tissues but can also include mean rates of tissue loss from other sources, for example, herbivory, C loss to mycorrhizae, reproductive losses, etc.

Deforestation, Degradation, and Cropping Implementation

The DD and crop yield fluxes are imposed by model drivers as absolute quantities. For DD, annual fluxes 2000–2019 are sourced from :cite:Xu2021. For cropping, the data source is USDA annual harvest totals, which exist over the United States only, and are available only 2016–2018. Because the driver quantities are required for the entire time span of a run, the data availability is limiting. For longer runs, current practice is to impose the mean 2000–2019 deforestation for each additional year needed and to recycle 2016–2018 crop totals sequentially to generate more data.

The annual DD flux is converted to a monthly flux driver (DIST[n]) via distributing the flux evenly over 12 months. For cropping, the harvest totals are distributed by imposing the entire harvest in the month of August (YIELD[n]). Cropping additionally generates a straw residue (C*_yield2lit[n]) of equal size to the harvest total. Crop and deforestation removals are imposed on all live C pools in equal proportion by calculating a disturbance mortality factor (DMF) or crop yield factor (CROPYIELD_factor) representing the proportion of live biomass impacted by the deforestation or cropping:

\[\]

text{DMF} = frac{text{DIST}[n]}{text{TotalABGB}}

\[\]

text{CROPYIELD_factor} = frac{text{YIELD}[n]}{text{TotalABGB}}

where

\[\]

text{TotalABGB} = text{C}{fol} + text{C}{lab} + text{C}{roo} + text{C}{woo}

This is then used to generate the pool-specific aggregate disturbance flux (dist_C*[n]), representing the entire removal:

\[\]

text{dist_C*[n]}=frac{text{C*[n]}times(2timestext{CROPYIELD_factor}+text{DMF})}{dt}

as well as the straw generated by cropping:

\[\]

text{C_yield2lit[n]}=frac{text{C[n]}times(text{CROPYIELD_factor})}{dt}

Fire Implementation

Fires are ignited using GFED burned area as a model driver (BURNED_AREA), but the C cycle impacts are prognostic. Fires result in two forms of mortality fluxes:

A C flux from live pools to the atmosphere (fire vaporization flux f_C*[n], where * represents each live pool).

A C flux from live pools to dead pools. This second flux is not a separately resolved model output but is folded into the environmental mortality aggregation.

The fire vaporization flux is calculated using three distinct combustion factors (cf_ligneous, cf_foliar, and cf_DOM) that are applied to each pool as follows:

\[\]

text{CF}{C_{lab}} = text{cf}{ligneous} text{CF}{C_{fol}} = text{cf}{foliar} text{CF}{C_{roo}} = text{cf}{ligneous} text{CF}{C_{woo}} = text{cf}{ligneous} text{CF}{C_{cwd}} = text{cf}{ligneous} text{CF}{C_{lit}} = frac{text{cf}{foliar} + text{cf}{ligneous}}{2} text{CF}{C_{som}} = text{cf}_{DOM}

The pool-specific combustion factors, CF_{C*}, are then applied to determine the fire vaporization flux f_C*[n]:

\[\]

text{f}_{C*[n]} = frac{C*[n] times text{BURNED_AREA}[n] times text{CF}_{C*}}{dt}.

The fire injury C flux from live to dead pools is calculated with a resilience parameter that is imposed on all pools. The fire injury C flux is not resolved as a stand-alone flux– see the section on the aggregate mortality formulation for the implementation. Here, we present the derivation of a fire injury factor that represents the fraction of the remaining C pool that is subject to fire injury mortality:

\[\]

text{Fire_injury_factor}_{C*}[n] = text{BURNED_AREA}[n] times (1 - text{resilience}).

C Starvation Implementation

Carbon starvation mortality is implemented as a function of non-structural carbohydrate (NSC) supply relative to sequential demands from respiration and growth. Supply/demand is assessed at three stages within each model integration step:

Respiration demand of leaves.

Respiration demand of wood and roots.

Tissue growth demand.

The first two stages determine carbon starvation fluxes and are described below.

Step 1: NSC vs. Leaf Respiration Demand

NSC supply at the leaf is assumed to include all newly generated photosynthate at that timestep, as well as all stored NSC from previous timesteps:

\[\]

text{GPP} + text{NSC}

The respiration demand at the leaf is computed as a “potential respiration” flux that includes both the respiration cost of the non-light-mediated photosynthesis reactions (“dark reactions”) as well as the tissue maintenance respiration cost of the leaves:

\[\]

text{pot_resp}_{leaf}

Then, the proportion of respiration demand that is not met (leaf_mortality_factor) is computed as an exponential function:

\[\]

text{leaf_mortality_factor}[n] = e^{- frac{(text{GPP} + text{NSC})[n]}{text{pot_resp}_{leaf}[n]}}.

This determines the proportion of the leaf pool that is subject to starvation. This proportion ultimately feeds into the aggregate mortality formulation.

Step 2: NSC vs. Wood and Root Respiration Demand

NSC supply available to wood and root tissues is represented by the interim NSC pool, which represents the remaining NSC after new photosynthate is absorbed and leaf respiration demands are addressed:

\[\]

text{NSC}_{int}

Respiration demand includes the potential maintenance respiration costs of wood and root tissues:

\[\]

text{pot_resp}_{nonleaf}

Then, the proportion of respiration demand that is not met (nonleaf_mortality_factor) is computed as an exponential function:

\[\]

text{nonleaf_mortality_factor}[n] = e^{- frac{text{NSC}_{int}[n]}{text{pot_resp}_{nonleaf}[n]}}.

<<<<<<< HEAD Stem Cavitation Implementation

Stem cavitation is implemented as a sigmoidal (beta) function of soil moisture availability. This approximation, which does not consider atmospheric demand as a driver of cavitation, is designed for a coarse timestep, e.g., monthly. A single logistic growth rate (β_{HMF}) and response threshold (Ψ_{50HMF}) are used to derive a hydraulic mortality fraction (HMF_total) across two soil layers:

\[\]

text{L1}{HMF}[n] = frac{text{LF}{LY1}[n]}{1 + e^{beta_{HMF} big(frac{-Psi_{LY1}[n]}{Psi_{50HMF}} - 1big)}}

\[\]

text{L2}{HMF}[n] = frac{text{LF}{LY2}[n]}{1 + e^{beta_{HMF} big(frac{-Psi_{LY2}[n]}{Psi_{50HMF}} - 1big)}}

\[\]

text{HMF}{total}[n] = 1 - frac{text{L1}{HMF}[n] times text{Z}{LY1} + text{RF} times text{L2}{HMF}[n] times text{Z}{LY2}}{text{Z}{LY1} + text{RF} times text{Z}_{LY2}}

Aggregate Mortality Formulation

\[\]

text{AMF}{C*}[n] = 1 - (1 - text{nonleaf_mortality_factor}[n]) times (1 - text{Fire_injury_factor}{C*}[n]) times (1 - text{HMF}_{total}[n])

\[\]

text{AMF}{C{leaf}}[n] = 1 - (1 - text{leaf_mortality_factor}[n]) times (1 - text{Fire_injury_factor}{C*}[n]) times (1 - text{HMF}{total}[n])

Background Mortality Implementation

Background mortality (BGM_{C*}, where * denotes all living C pools) is computed using a pool-specific “turnover rate” parameter (τ_{C*}):

\[\]

text{BGM}{C*} = text{C}^*[n] times tau{C*}

This flux represents the C turnover rate in the pool in the absence of all other mortality.

Bibliography

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