Traffic Growth
==============

**Implementation status:** Partial (coverage matrix row *Traffic Growth*).
Production: global CAGR (single, two-period or multi-segment) + COVID
factors, two-track headline model per DL-022 — no route/regional
differentiation in the wedge path. The rest of the page — the cubic
Hermite linking family (eq. 2–9), the flight-count projection (eq. 10),
the region-pair CAGR form (eq. 13) and the per-route fuel-mass series
(eq. 15) — is implemented standalone in
``src/engine/traffic-growth-full.ts`` (DL-137, Stage-1 shadow; import
guards keep it unreachable from production entry points). Every result
declares its traffic basis per DL-139/DL-165 (root year, root value,
growth rate, COVID treatment, recovery assumption).
**Source:** ``src/engine/cascade.ts:computeLCA`` (``growthMultAt``,
``grossAt``); ``src/engine/traffic-growth-full.ts`` (full page, shadow)
**Test evidence:** ``tests/traffic-model.spec.ts``,
``tests/end-year.spec.ts``, ``tests/horizon-2100.spec.ts``,
``tests/suite-l-traffic-growth-full.spec.ts``,
``tests/traffic-dataset-provenance.spec.ts``

Compound growth
---------------

Growth is applied to the 2019 baseline (cf. CASCADE *Traffic Growth*,
eqs. 11–14). For a single compound annual growth rate:

.. math::

   M(y) = \left(1 + \frac{g}{100}\right)^{y - 2019}

with :math:`g` the scenario CAGR (default 3.5 %/yr). Two refinements are
implemented. A two-period form switches CAGR at a break year:

.. math::

   M(y) = (1+g_1/100)^{y_b - 2019}\,(1+g_2/100)^{y - y_b},
   \qquad y > y_b

and a multi-segment form (``cagrPeriods``, up to 12 periods, overriding the
simpler forms when present) compounds segment by segment:

.. math::

   M(y) = \prod_{s \in S} (1 + g_s/100)^{\,\min(e_s, y) - \max(s_s, 2019)}
   \quad\text{for segments with } \min(e_s,y) > \max(s_s,2019)

COVID demand shock
------------------

Calendar years 2020–2023 are scaled by demand-recovery factors
(``constants.ts:COVID_FACTORS``), calibrated to the global traffic collapse
and recovery:

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

   * - Year
     - Factor
   * - 2019
     - 1.0
   * - 2020
     - 0.3941
   * - 2021
     - 0.4631
   * - 2022
     - 0.7168
   * - 2023
     - 0.9424

Gross BAU emissions at year :math:`y` are then:

.. math::

   G_{gross}(y) = 0.92\ \mathrm{Gt} \times M(y) \times f_{covid}(y),
   \qquad f_{covid}(y) = 1\ \text{outside 2020–2023}

so the 2021 gross value falls **below** the 2019 baseline (pinned by test).
At defaults the 2050 value is :math:`0.92 \times 1.035^{31} \approx 2.67`
GtCO₂.

Two-track headline model (DL-022)
---------------------------------

Historically the headline scalar and the time-series sweep used different
BAU models (2.82 Gt anchor vs 2.67 Gt compounded — DEFECT-NEW-1). DL-022
unified both behind the shared growth machinery and introduced
``traffic_model``:

* ``'cascade_series'`` (default): headline ≡ time-series, as above.
* ``'legacy_anchor'``: the frozen v3.3 scalar
  :math:`G = 2.82 \cdot (g/3.5) \cdot y_f \cdot f_{covid} + 0.92(1-y_f)`,
  retained only so the frozen parity baseline stays reproducible.

Test evidence (8 tests) pins the headline≡series identity, the
:math:`0.92 \times 1.035^{31}` value, the legacy anchor, monotonicity in
both modes, the COVID shock below baseline, and conservation
:math:`0 \le G_{net} \le G_{gross}`.

Extended horizon: ``end_year`` 2050 / 2075 / 2100 (DL-044)
----------------------------------------------------------

The scenario horizon is selectable via ``end_year`` (``2050 | 2075 | 2100``,
default 2050; URL-state v2 accepts only these three values as
``enum_end_year``, and the engine defensively clamps any out-of-set value
into [2050, 2100]). Extending the horizon must never reshape the legacy
window, so the rule is **hold-not-stretch**: a ``Y_SAT = 2050`` constant
anchors every curve normalisation (adoption S-curves saturate at 2050, the
SBTi pathway — defined to 2050 only — holds its 2050 floor), while
``end_year`` only extends the sweep loop. Traffic growth keeps compounding
beyond 2050 at the last-period CAGR (the two-period machinery defaults
:math:`g_2 = g_1`, so the extension is continuous):

.. math::

   G_{gross}(2100) = G_{gross}(2050)\,(1 + g/100)^{50}
   \qquad \text{(single-CAGR default)}

Acceptance properties, all pinned by test:

* **Frozen-baseline bit-identity** — ``end_year: 2050`` (or omitted)
  reproduces the legacy engine exactly (physics-signature equality); both
  frozen two-track baselines are untouched by construction.
* **Prefix invariance** — the first 32 slices (2019–2050) of a 2100 run are
  exactly the 2050 run.
* **Hold-flat** — adoption/saturation curves, SAF and methane blends,
  removal cost/capacity and SBTi hold their 2050 values beyond 2050 (no
  silent stretch); the aircraft-wedge/gross ratio is flat once fleet
  renewal completes.
* **KPI stability** — the 2050-anchored KPIs (``net2050``,
  ``grossBau2050``, ``sbti2050``, ``gapToSbti``) never move with
  ``end_year``; ``endYear`` / ``netEnd`` / ``grossEnd`` expose the horizon
  end. A 2100 run has 82 slices (2019–2100), conservation
  :math:`G_{gross} = G_{net} + \sum \text{reductions}` holds every year,
  and cumulative net emissions are monotone non-decreasing.

DL-044 also wires the RST **Custom Global Initiative (CGI)** offsets mode
(``cgi_enabled``, ``cgi_gamma_end`` clamped to [0, 0.85]): offsets are
auto-set to hold eligible emissions at the CORSIA baseline
:math:`0.85\,G_{2019}` for 2024–2035, then follow a linear CGI baseline to
:math:`\gamma_{end}\,G_{2019}` at ``end_year`` (continuity at 2036 exact
by construction). Constrained offset mode only — the frozen ``'percent'``
track ignores CGI, and the user offsets ambition is inert while CGI is
active (per the RST). See :doc:`scenarios` for the URL-state surface.

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

* CASCADE's cubic-Hermite shock-recovery blend is implemented standalone
  (``traffic-growth-full.ts``, DL-137) but **cannot reproduce CASCADE's
  curve**: the spline-width parameter α is never given a value anywhere in
  the 27-file corpus, so it is a required caller argument with no default
  (``HERMITE_ALPHA_UNVALUED_NOTE``), and the printed eq. 8/9 use an
  absolute-year exponent that overflows as printed (reproduced under
  ``CASCADE_PARITY`` as a diagnostic, corrected under
  ``CURRENT_EVIDENCE``). The production path applies the flat factor
  table; the 2019-rooted vs 2023-rebased readings differ by 21.77 % from
  2032 onward, which is why every result names its basis (DL-139/165).
* No route-, region- or market-segment-differentiated growth in
  production. The region-pair CAGR form (eq. 13) exists in the shadow
  module, and since DL-166 it has a **sourced value**: Boeing's own
  published CMO 2026 forecast-data workbook (all 39 region-pair RPK flow
  rows, transcribed programmatically with attribution) plus Airbus GMF
  2026 world figures ship in ``src/data/market-outlooks.ts``
  (``tests/market-outlooks.spec.ts``), and the ``boeing_cmo_2026``
  library scenario applies the published world CAGR. CASCADE's own
  internal CMO/WACF configuration remains unheld beyond its two public
  endpoint anchors (see the Boeing-CMO root, :doc:`scenarios`).
* The ambition table's traffic levels (``AMBITION.traffic`` =
  2.4/2.9/3.4/3.7/4.0 %/yr) are available but the headline CAGR remains a
  direct user input in most flows.