Carbon Offsets & Removals
=========================

**Implementation status:** Fixed (DL-012: capacity-constrained net is the
default; DL-027: applied to residual emissions). Sectoral CORSIA subset
**Equivalent on a simplified base** (coverage matrix rows *Offsets &
Removals*, *CORSIA*)
**Source:** ``src/engine/removals.ts:offsetBlend``,
``src/engine/cascade.ts:computeLCA`` (offsets wedge + CORSIA block)
**Test evidence:** ``tests/removal-capacity.spec.ts``,
``tests/corsia-parity.spec.ts``

Two offset modes
----------------

``offset_mode`` (DL-012) selects how the offsets wedge enters net
emissions:

* ``'constrained'`` (default): the wedge is the **capacity-capped physical
  removal output** plus traditional offsets, in MtCO₂, converted ÷1000 to
  GtCO₂. Net emissions can never be reduced by more removal than the
  deployed capacity allows.
* ``'percent'``: the legacy unconstrained behaviour — a flat percentage of
  gross — retained only to reproduce the frozen parity baseline.

Since DL-027 the constrained base is **residual** emissions (after the
aircraft, operations and energy wedges), matching the CASCADE accounting
order (cf. CASCADE *Carbon Offsets & Removals*, emissions-reductions
equations):

.. math::

   G_{res} = G_{gross} - \Delta_{ac} - \Delta_{ops} - \Delta_{en},
   \qquad
   G_{net} = \max\!\big(0,\; G_{res} - (R_{rem} + R_{trad})/1000\big)

Removal pathways
----------------

Total offset demand at year :math:`y` ramps with an S-curve adoption
:math:`s(t)`, :math:`t = (y-2019)/31`:

.. math::

   D_{total}(y) = G_{base}(y) \times 1000 \times
   \frac{X_{off}}{100} \times s(t) \qquad [\mathrm{MtCO_2}]

allocated across traditional offsets and four removal pathways (nature,
biomass/BECCS, mineralisation, DACCS) by normalised scenario shares. Each
pathway :math:`k` has its own adoption curve, a Wright's-law-style cost
trajectory and a capacity ramp:

.. math::

   C_k(y) = C_{k,2050} + (C_{k,2025} - C_{k,2050})
   \left(\frac{2050 - y}{25}\right)^{lr}

.. math::

   Cap_k(y) = Cap_{k,2050}\left(\frac{y - 2019}{31}\right)^{1.8}

.. math::

   R_k(y) = \min\!\big(D_k(y),\; Cap_k(y)\big)

Defaults (editable; cost sources: Fuss et al. 2018, Keith et al. 2018,
IEA NZE; capacity potentials: IPCC AR6 WGIII Ch. 12 :cite:`ipcc_ar6`):

.. list-table::
   :header-rows: 1

   * - Pathway
     - Cost 2025 ($/t)
     - Cost 2050 ($/t)
     - Capacity 2050 (Mt/yr)
     - Energy (GJ/t)
   * - Nature-based
     - 15
     - 10
     - 3,500
     - 0.5
   * - Biomass (BECCS)
     - 150
     - 80
     - 2,000
     - 3.5
   * - Mineralisation
     - 80
     - 40
     - 1,000
     - 6.0
   * - DACCS
     - 400
     - 100
     - 5,000
     - 8.0

Total cost :math:`\sum_k R_k \times C_k` is reported in $B/yr with the
weighted-average $/t; the Gt/Mt/$ unit chain is pinned by tests.

The σ-cap note
--------------

CASCADE's σ(t) renormalisation caps total offset demand so net stays
non-negative. Under HyFlux's parameterisation this normalisation is
**vacuous**: the total offset share :math:`X_{off} + \sum_k X_k \le 100\%`
by construction and the base is residual emissions, so net is provably
≥ 0 without the clamp ever engaging — tested across scenarios (DL-027).

CORSIA subset
-------------

The sectoral accounting subset is implemented (cf. CASCADE *CORSIA*,
sector-emissions-baseline / sectoral-growth-factor equations):

.. math::

   SEB = 0.85 \times G_{2019} = 0.85 \times 0.92\ \mathrm{Gt}

.. math::

   SGF(y) = \max\!\left(0,\; \frac{G(y) - SEB}{G(y)}\right), \qquad
   \Delta_{CORSIA}(y) = G(y) \times SGF(y)

This subset is **Equivalent on a simplified base**: eligibility uses total
gross with no route-scope filter (cf. CASCADE's own documented
route-homogeneous simplification).

Documented CORSIA gaps (updated 2026-08-02)
-------------------------------------------

* Operator-level accounting (OEB, OGF, the w(t) phase weighting schedule
  1.0 to 2032 / 0.85 from 2033–35, operator emission reductions, and the
  CGI operator analogues) is **implemented standalone** in
  ``src/engine/routes/corsia-operator.ts`` (DL-045/046,
  ``tests/corsia-operator.spec.ts``), with the sectoral-vs-operator-sum
  aggregation identities and the printed-vs-floored SGF divergence made
  measurable in ``src/engine/corsia-aggregation.ts`` (DL-137,
  ``tests/suite-n-corsia-tensor.spec.ts``). It is **not wired into**
  ``computeLCA``: the operator set is synthetic (one per origin state,
  allocating emissions, not flights), so the block stays at shadow stage
  under the DL-138 integration registry.
* Automatic offset wiring for 2024–2035 and the CGI extension to 2100 are
  **implemented** (DL-044: ``cgi_enabled`` / ``cgi_gamma_end``,
  constrained offset mode only; ``tests/horizon-2100.spec.ts``) — see
  :doc:`trafficGrowth`.
* Still open: the σ(t) / σ_removals(t) renormalisation pair (argued
  vacuous under HyFlux's parameterisation, but not implemented — an
  over-100 % offsets+removals combination is not renormalised the way
  CASCADE renormalises it), and a consumption model for the removals
  resource parameters (C_biomass, ε_biomass, ε_mineral, ε_daccs).

Known deviations / limitations
------------------------------

* Legacy ``'percent'`` mode applies the wedge to gross (frozen); the
  historical gross-vs-residual deviation is closed in the default
  constrained mode (DL-027).
* Removal energy demand (``energyGJ`` per pathway) is computed but not
  consumed by the energy-demand roll-up — pinned open item.
* Traditional offsets (VER/CER) carry no cost or capacity model.