Keep carbon mass currencies and budget residuals distinct

Define the evidence question

An annual carbon budget compares emissions, atmospheric accumulation and land/ocean sinks over a defined interval. Independent estimates need not close exactly because they contain uncertainty and potentially omitted processes. Conservation still holds physically; the residual describes an incomplete observational accounting.

Reconstruct the observation or physical model

The fictional packet supplies emissions E, land sink L, ocean sink 3 and independently estimated atmospheric growth 5 Gt C/year. The imbalance is E−5−L−3. A growth inferred by closing the other terms is E−L−3, which should not be mislabeled as the independently observed growth. The two differ by the residual.

Separate the competing interpretations

Carbon mass and carbon-dioxide mass are different currencies: each mole of CO₂ contains 12 mass units of carbon in 44 total, so Gt C converts by 44/12. The annual airborne fraction here is observed growth 5 divided by emissions E. It is not the fraction of one emission remaining forever and can vary with sink behavior and accounting.

Challenge uncertainty and identification

Land-use emissions, fossil emissions, cement processes, aquatic transfers and sink definitions require consistent boundaries in real budgets. Current global values are deliberately not used. A residual alone does not locate a missing sink, prove a specific feedback or justify a precise remaining warming budget.

Worked original packet

At emissions 10 and land sink 2, implied atmospheric growth is 5 and imbalance zero. Observed-growth airborne fraction 0.5; emissions correspond to 36.667 Gt CO₂/year. These are invented values illustrating units and closure.

Investigation

Keep emissions fixed and vary the land estimate. Compare inferred growth with the unchanged independent growth estimate; identify evidence needed to determine which flux or boundary caused the mismatch.

Changed-case transfer

At emissions 9 and land sink 3, compute implied growth, imbalance, airborne fraction and CO₂-mass emissions.

Feedback

Implied growth 3, imbalance 9−5−3−3=−2 Gt C/year; observed-growth airborne fraction 5/9≈0.556. Emissions 9×44/12=33 Gt CO₂/year. Negative residual is an accounting discrepancy, not a newly observed negative emission.

Sources and evidence boundary

Original prose, numerical packets and exercises. Primary method/mechanism source, checked 30 October 2026. No current measured climate values, personal risk estimates, exposure limits or regulatory conclusions are inferred from these fictional cases. Retain first reasoning and critique in the course workspace. No physical pollutant exposure or environmental intervention is requested.