CarbonKeel · for verification
Calculation Master Guide
Every computation behind every page: the equations, every parameter and its source, the rules that change the result, and worked results.
Engine 2026.10.30 · built 31 October 2026 · CarbonKeel is not an accredited verifier; allowances are surrendered and FuelEU balances settled on the figures the ship's verifier accepts.
- 1How to read this guide
- 2Fuel properties and shared constants
- 3Rebuilding a ship-year from the public register
- 4EU Emissions Trading System (shipping)
- 5UK Emissions Trading Scheme (shipping) and your own fuel by scope
- 6FuelEU Maritime
- 7Carbon Intensity Indicator (CII)
- 8Energy Efficiency Existing Ship Index (EEXI)
- 9IMO Net-Zero Framework (scenario until adopted)
- 10The four-score ship card
- 11What-if levers and scenario comparison
- 12Owner and time-charterer split
- 13EU ETS statement to charterers (document)
- 14FuelEU pooling: allocation, settlement and the optimiser
- 15Allowance planner
- 16MOHA workspace: obligations, reconciliation, funding, penalty watch
- 17Poseidon Principles climate alignment
- 18SEEMP Part III plan
- 19Hull and propeller performance (ISO 19030 approach)
- 20Part-year data: annualising
- 21Appendix: parameter tables
1How to read this guide
Every figure on carbonkeel.com, in the app, the allowance planner, the MOHA workspace, the compliance documents and the reports comes from one of the deterministic calculations below. Each section gives the equations (numbered on the right), a table defining every symbol with its unit and value or source, the rules and nuances of the regulation that change the result, and a worked example whose numbers were produced by the engines themselves when this guide was built. Engine version 2026.10.30; register file thetis_mrv_2025_v67.xlsx; built 31 October 2026.
Three kinds of figure, never mixed
- Public-data estimate: rebuilt from the EU MRV register EMSA publishes (THETIS-MRV, Regulation (EU) 2015/757 Art. 21). Always labelled ESTIMATE.
- Customer-data calculation: the same rules applied to figures the customer supplies (fuel by type, distance, voyages, technical data).
- Verified compliance: done by the accredited verifier and the Administration. CarbonKeel prepares figures for them and never claims verification.
Conventions
- Masses in tonnes (t); energy in megajoules (MJ); distance in nautical miles (nm); intensities in grams per unit (g CO₂/t·nm, g CO₂e/MJ).
- Allowances (EUAs, UKAs) are whole units: where a document or a company total is due, the figure is rounded up. The ship page shows one decimal.
- Market inputs are assumptions the user can change, echoed in every result: EU allowance €85, UK allowance £40, €/£ 1.15, FuelEU pool price €110 per t CO₂e (checked 17 October 2026). The allowance planner uses EEX primary auction results instead (section 15).
2Fuel properties and shared constants
One table per fuel, used by every scheme. Each scheme uses its own column: the EU and UK ETS use tank-to-wake CO₂ and the AR5 global-warming potentials; FuelEU uses Annex II well-to-wake values with AR4 potentials; the Poseidon Principles use their own well-to-wake factors with AR6 potentials. The regimes deliberately differ, so the same fuel gives different numbers in each.
| Fuel | CF CO₂, t/t (ETS, CII, EEXI) | CH₄, t/t | N₂O, t/t | LCV, MJ/t (FuelEU) | WtW, g CO₂e/MJ (FuelEU) | WtW, g CO₂e/g (Poseidon) |
|---|
| Heavy fuel oil (HFO) | 3.114 | 5e-05 | 0.00018 | 40,500 | 91.74 | 3.84 |
| Light fuel oil (LFO) | 3.151 | 5e-05 | 0.00018 | 41,000 | 91.39 | 3.75 |
| Diesel / gas oil (MDO, MGO) | 3.206 | 5e-05 | 0.00018 | 42,700 | 90.77 | 4.01 |
| LNG | 2.750 | 0 | 0.00011 | 49,100 | 89.2 | 4.61 |
| Methanol (fossil) | 1.375 | 5e-05 | 0.00018 | 19,900 | 103.15 | 2 |
| B24 biofuel blend | 2.367 | 5e-05 | 0.00018 | 40,040 | 74.8 | 3.07 |
| B100 biofuel | 0.000 | 5e-05 | 0.00018 | 37,000 | 16.4 | 0.82 |
| LNG engine (consumer class) | Methane slip, share of fuel mass (ETS) | FuelEU WtW, g CO₂e/MJ |
|---|
| otto medium speed | 3.1% | 89.2 |
| otto slow speed | 1.7% | 82.87 |
| diesel dual fuel | 0.2% | 76.08 |
| lbsi | 2.6% | 86.94 |
Sources and nuances
- CF: 2018 IMO DCS guidelines and MEPC.364(79) (identical for oil fuels). CH₄ and N₂O factors and slip: Regulation (EU) 2015/757 Annex I Part A as amended by Delegated Regulation (EU) 2023/2776.
- Global-warming potentials: ETS (EU and UK) AR5 CH₄ 28, N₂O 265 (Delegated Reg. 2020/1044; UK Order Table C1); FuelEU AR4 25 and 298 (Annex II); Poseidon AR6 29.8 and 273 (Technical Guidance v5.2 Table 8).
- FuelEU WtW is computed from Annex II as WtT + (Cf,CO₂ + 25·Cf,CH₄ + 298·Cf,N₂O) ÷ LCV; for LNG the slipped share counts as methane, which is why the four LNG engine classes differ.
- Biofuel: B100 is counted at zero tank-to-wake CO₂ only if certified (RED); its FuelEU WtW of 16.4 is the UCOME default pathway and must be replaced by the certificate's value (Art. 10). Methanol's CH₄/N₂O use the highest value of its class.
3Rebuilding a ship-year from the public register
The EU MRV register publishes, for each ship and year, total CO₂, total fuel mass, CO₂ per distance, the CO₂ (and from 2024 the CH₄ and N₂O) of each scope (voyages between EU/EEA ports, departing, arriving, at EU/EEA berths), the verifier's ETS-scope CO₂ and fuel per transport work. It does not publish fuel types, deadweight or distance. These equations turn the filing into the voyage legs every engine reads.
Distance
$$ D = \frac{\mathrm{CO_2}_{\,total} \times 1000}{\mathrm{CO_2}/D} \tag{3.1} $$
| where |
|---|
| \(D\) | distance sailed in the year | nm | derived |
| \(\mathrm{CO_2}_{\,total}\) | total CO₂ in the filing | t | register |
| \(\mathrm{CO_2}/D\) | CO₂ per distance in the filing | kg/nm | register |
Year's fuel mix
$$ r = \frac{\mathrm{CO_2}_{\,total}}{M_{total}}, \qquad x_{MGO} = \frac{r - 3.114}{3.206 - 3.114}, \qquad x_{HFO} = 1 - x_{MGO} \tag{3.2} $$
| where |
|---|
| \(r\) | the ship's average CO₂ per tonne of fuel | t/t | derived |
| \(M_{total}\) | total fuel mass in the filing | t | register |
| \(x\) | share of fuel mass by fuel | – | derived |
Reading the ratio
- Within ±0.0015 of a single fuel's CF (3.114, 3.151, 3.206, 2.750) the ship is read as burning that fuel.
- Between 3.114 and 3.206: a blend of HFO and MGO by mass, as in (3.2). Between 2.750 and 3.114: a blend of LNG and HFO, xLNG = (3.114 − r) ÷ (3.114 − 2.750). Up to 0.05 above 3.206: MGO.
- Any other ratio, or no fuel figure: assumed HFO (LNG for an LNG carrier), stated on the result. The blend reproduces both published totals exactly.
Each scope's own mix
$$ M_s = \frac{\mathrm{N_2O}_s}{0.00018}, \qquad r_s = \frac{\mathrm{CO_2}_{\,s}}{M_s} \tag{3.3} $$
| where |
|---|
| \(M_s\) | fuel burned in scope s | t | derived |
| \(\mathrm{N_2O}_s\) | the scope's N₂O in the filing | t | register |
| \(0.00018\) | N₂O per tonne of HFO, LFO and MGO alike | t/t | Reg. 2015/757 Annex I |
| \(r_s\) | the scope's own CO₂ per tonne, read as in (3.2) | t/t | derived |
When the scope's own mix is used
- Only for a ship whose whole-year N₂O is the oil default within 1% (no LNG, default factors), and where the scope's N₂O is at least 0.0025 t (about 14 t of fuel). Otherwise the year's mix (3.2) is used.
- It matters because EU berths require 0.1% sulphur fuel, mostly gas oil: the berth scope usually reads as MGO even when the ship burns HFO at sea.
- Outside EU scope the fuel left over (Mtotal minus the fuel already placed in the EU scopes) gives the mix, so the year's fuel and CO₂ totals are still reproduced.
Fuel and distance per leg
$$ M_{s,f} = \frac{\mathrm{CO_2}_{\,s}}{\sum_f x_{s,f}\, C_{F,f}}\; x_{s,f}, \qquad D_s = D\,\frac{\mathrm{CO_2}_{\,s}}{\mathrm{CO_2}_{\,sea}} \;(D_{berth} = 0) \tag{3.4} $$
| where |
|---|
| \(M_{s,f}\) | tonnes of fuel f placed in scope s | t | derived |
| \(C_{F,f}\) | carbon factor of fuel f | t/t | section 2 |
| \(\mathrm{CO_2}_{\,sea}\) | CO₂ of the three sea scopes (all except berth) | t | register |
| \(D_s\) | distance given to scope s | nm | derived |
Calibration to the verifier
$$ k = \frac{\mathrm{CO_2}_{\,ETS,\,verifier}}{\mathrm{CO_2}_{\,between} + 0.5\,(\mathrm{CO_2}_{\,leaving} + \mathrm{CO_2}_{\,arriving}) + \mathrm{CO_2}_{\,berth}} \tag{3.5} $$
| where |
|---|
| \(k\) | calibration of our rebuild to the verifier's ETS figure | – | derived |
| \(\mathrm{CO_2}_{\,ETS,\,verifier}\) | “CO₂ to be reported under Directive 2003/87/EC” | t | register |
The EU ETS engine multiplies its rebuild by k (equation 4.4), so the bill uses the verifier's figure, which already reflects ports of call, transhipment stops, ship size and derogations the file does not show. k = 0 means the verifier reported no ETS-scope emissions (typically a ship below 5,000 GT, an offshore ship before 2027, or an exempt one): no allowances and no FuelEU result.
Deadweight estimate
$$ \text{Cargo} = 1000\;\frac{\text{fuel per distance}}{\text{fuel per transport work}}, \qquad \mathrm{DWT}_{est} = \frac{\text{Cargo}}{\lambda_{type}} \tag{3.6} $$
| where |
|---|
| \(\text{Cargo}\) | average cargo on board, laden voyages first | t | register ratio |
| \(\lambda_{type}\) | cargo as a share of deadweight on laden voyages | – | container ship 0.68, bulk carrier 0.85, oil tanker 0.85, chemical tanker 0.8, general cargo ship 0.7, refrigerated cargo carrier 0.55, gas carrier 0.6, lng carrier 0.6, combination carrier 0.85 |
| \(\mathrm{DWT}_{est}\) | first deadweight for the CII, rounded to 100 t | t | shown with a ±15% band; not offered below 3,000 t |
Worked example: PETER OLDENDORFF (IMO 9464663), 2025 filing
| Total CO₂ ÷ total fuel | 13,829.15 ÷ 4,426.56 = 3.124 t/t → 89% HFO 11% MGO by mass |
| Distance (3.1) | 32,515 nm |
| Leg: intra eea | HFO 164.18 t, MDO_MGO 28.55 t; 1,458 nm |
| Leg: extra eea | HFO 3,756.04 t, MDO_MGO 356.85 t; 31,058 nm |
| Leg: at berth eea | HFO 16.82 t, MDO_MGO 104.07 t; 0 nm |
| Rebuilt ETS-scope CO₂ | 602.76 + 0.5 × (5,346.68 + 7,493.68) + 386.02 = 7,408.97 t |
| Verifier's ETS-scope CO₂ | 7,408.97 t, so k = 1.0000 |
| Deadweight estimate (3.6) | cargo 57,443 t ÷ 0.85 = 67,600 t |
The rebuild reproduces the verifier's figure exactly for this ship. Over the whole 2025 register: exact for 67.8% of ships, within 2% for 76.5%.
4EU Emissions Trading System (shipping)
Directive 2003/87/EC as amended by Directive (EU) 2023/959; monitoring formula of Regulation (EU) 2015/757 Annex I Part A as amended by Delegated Regulation (EU) 2023/2776.
Gases, combusted mass
$$ \mathrm{CO_2} = \sum_i (M_i - M_{i,NC})\,C_{F,i}, \quad \mathrm{CH_4} = \sum_i \big[(M_i - M_{i,NC})\,EF_{CH_4,i} + M_{i,NC}\big], \quad \mathrm{N_2O} = \sum_i (M_i - M_{i,NC})\,EF_{N_2O,i} \tag{4.1} $$
| where |
|---|
| \(M_i\) | mass of fuel i used | t | customer data or section 3 |
| \(M_{i,NC}\) | fuel released unburned (slip) = slip share × M_i; LNG only | t | section 2 |
| \(EF\) | CH₄ and N₂O per tonne combusted | t/t | section 2 |
CO₂ equivalent
$$ \mathrm{CO_2e} = \mathrm{CO_2} + \delta_{y}\,(28\,\mathrm{CH_4} + 265\,\mathrm{N_2O}), \qquad \delta_y = \begin{cases} 0 & y \lt 2026 \\ 1 & y \ge 2026 \end{cases} \tag{4.2} $$
| where |
|---|
| \(y\) | emissions year | – | |
| \(28, 265\) | AR5 global-warming potentials | – | Delegated Reg. 2020/1044 |
Scope
$$ E_{scope} = \sum_{legs} \sigma_{leg}\,\mathrm{CO_2e}_{leg}, \qquad \sigma = \begin{cases} 1.0 & \text{between EU/EEA ports, at EU/EEA berth} \\ 0.5 & \text{into or out of the EU/EEA} \\ 0 & \text{otherwise} \end{cases} \tag{4.3} $$
| where |
|---|
| \(\sigma\) | scope share | – | Directive Art. 3ga |
Verifier basis
$$ E_{ETS} = k \cdot E_{scope} \tag{4.4} $$
| where |
|---|
| \(k\) | calibration to the verifier, (3.5); 1 for customer data | – | |
Allowances and cost
$$ A = E_{ETS}\;\phi_y\;(1 - \rho)\,(1 - 0.05\,\iota), \qquad \text{Cost} = A \times P_{EUA} \tag{4.5} $$
| where |
|---|
| \(\phi_y\) | share to surrender: 2024 40%, 2025 70%, 2026 onwards 100%; 0 before 2024 | – | Art. 3gb |
| \(\rho\) | share of in-scope emissions covered by a derogation (island, outermost-region, public-service routes) | 0–1 | Art. 12(3-b) to (3-d), to 31 Dec 2030; stated by the user |
| \(\iota\) | 1 for ice class IA or IA Super, else 0 | – | Art. 12(3-e), to 31 Dec 2030 |
| \(A\) | allowances due | EUA | |
| \(P_{EUA}\) | allowance price | € | input, default 85 |
Excess emissions penalty
$$ \text{Penalty} = 100 \times \text{(allowances not surrendered by 30 September)} \tag{4.6} $$
| where |
|---|
| \(100\) | excess emissions penalty per t CO₂e, indexed to EU consumer prices since 2013 (so at least €100) | €/t | Art. 16(3) |
Rules and nuances
- Surrender by 30 September of the following year (Art. 12(2a)); verified emissions by 31 March. The penalty does not replace the allowances: they are still owed, the company is named, and after two consecutive failures a ship can be refused entry (Art. 16(11a)).
- Scope: ships of 5,000 GT and above carrying cargo or passengers. Offshore ships of 5,000 GT and above join in 2027; cargo ships of 400–5,000 GT and offshore ships below 5,000 GT report under EU MRV but are outside the ETS.
- Only CO₂ is counted for 2024 and 2025; CH₄ and N₂O from 1 January 2026 (Annex I).
- A container ship's stop at a listed neighbouring transhipment port is not a port of call (Art. 3(z)); this is already in the verifier's figure, which is why the register path uses k.
- Certified sustainable biofuel (RED) can be zero-rated; uncertified biofuel uses the fossil factor.
- The shipping company may recover the cost from the charterer or operator (Art. 3gc); see sections 12 and 13.
Worked example: 3,000 t HFO, all between EU ports, 2026
| CO₂ (4.1) | 3,000 × 3.114 = 9,342.0 t |
| CH₄ as CO₂e | 3,000 × 0.00005 × 28 = 4.2 t |
| N₂O as CO₂e | 3,000 × 0.00018 × 265 = 143.1 t |
| Escope (4.3), σ = 1 | 9,489.3 t CO₂e |
| Allowances (4.5), φ = 100% | 9,489.3 |
| Cost at €85 | €806,590 |
9,489.3 EUAs, €806,590
Worked example: PETER OLDENDORFF, register 2025
| EETS (4.4), k = 1.0000 | 7,409.0 t CO₂ (2025: CO₂ only) |
| Allowances, φ2025 = 70% | 7,409.0 × 0.70 = 5,186.3 |
| Cost at €85 | €440,834 |
| Same activity on 2026 rules | 100%, with CH₄ and N₂O: 7,525.3 EUAs, €639,654 |
€440,834 for 2025; €639,654 if the same year were sailed under 2026 rules.
5UK Emissions Trading Scheme (shipping) and your own fuel by scope
The Greenhouse Gas Emissions Trading Scheme (Amendment) (Extension to Maritime Activities) Order 2026, SI 2026/392, Schedule 2A. Same gases, factors, GWPs and monitoring formula as (4.1)–(4.2).
UK allowances
$$ A_{UK} = \sum_{legs} u_{leg}\,\mathrm{CO_2e}_{leg}, \qquad u = \begin{cases} 1.0 & \text{UK domestic voyages, UK berths} \\ 0.5 & \text{Great Britain} \leftrightarrow \text{Northern Ireland} \\ 0 & \text{otherwise} \end{cases}, \qquad \text{Cost}_{\pounds} = A_{UK}\,P_{UKA} \tag{5.1} $$
| where |
|---|
| \(u\) | UK share | – | Order para 15(1) |
| \(P_{UKA}\) | UK allowance price | £ | input, default 40 (indicative) |
EU and UK together
$$ \text{Bill}_{\text{€}} = \text{Cost}_{EU} + \text{Cost}_{\pounds} \times FX \tag{5.2} $$
| where |
|---|
| \(FX\) | euros per pound | €/£ | input, default 1.15 |
Your own fuel split by scope
$$ M_{EU} = M\,(s_{between} + 0.5\,s_{in/out} + s_{berth}), \qquad M_{UK} = M\,(s_{UK} + 0.5\,s_{GB\text{-}NI}) \tag{5.3} $$
| where |
|---|
| \(M\) | the year's fuel of one type | t | customer data |
| \(s\) | share of the year's fuel burned on each kind of voyage, stated by the operator | – | |
Rules and nuances
- Ships of 5,000 GT and above; excluded: armed services, law enforcement, fishing, research and rescue, wooden and non-mechanical ships, ships operating a Scottish ferry service, offshore ships until 31 Dec 2026 (para 5).
- A voyage starts at the last berth in a UK port and ends at the first berth in a UK port without calling outside the UK (para 7): a voyage between the EU and the UK is EU ETS at 50% and not UK ETS. Northern Ireland ports are UK ports here and not EU ports. A leg is never counted in both schemes; the engine refuses one that would be.
- No phase-in. The first scheme year runs 1 July–31 December 2026 and is not pro-rated. Surrender 30 April of the following year, except 2026 emissions: 30 April 2028. Verified report by 31 March.
- The EU register cannot show UK voyages, so on public data the UK figure is reported as not observable rather than zero.
Worked example: 4,300 t HFO in 2026: 40% between EU ports, 30% into or out of the EU, 10% at EU berths, 5% UK domestic
| EU fuel (5.3) | 4,300 × (0.40 + 0.5 × 0.30 + 0.10) = 2,795 t |
| EU CO₂e | 2,795 × (3.114 + 0.00005 × 28 + 0.00018 × 265) = 8,840.86 t |
| EU cost at €85 | €751,473 |
| UK fuel and CO₂e | 4,300 × 0.05 = 215 t; × 3.1631 = 680.07 t |
| UK cost at £40 | £27,203, or €31,283 at 1.15 |
€782,756 for both schemes together
6FuelEU Maritime
Regulation (EU) 2023/1805: Art. 4 (limit), Annex I (intensity), Annex IV (compliance balance and penalty), Art. 20–21 (banking, borrowing, pooling), Art. 23 (penalties). From reporting period 2025.
Energy in scope
$$ E_{MJ} = \sum_{legs}\sigma_{leg} \sum_f M_f\,LCV_f \tag{6.1} $$
| where |
|---|
| \(\sigma\) | scope share, as (4.3): 1, 0.5 or 0 | – | Art. 2 |
| \(LCV_f\) | lower calorific value | MJ/t | Annex II, section 2 |
GHG intensity
$$ I = \frac{\sum_{legs}\sigma \sum_f M_f\,LCV_f\,WtW_f}{E_{MJ}} \tag{6.2} $$
| where |
|---|
| \(I\) | GHG intensity of the energy used on board, well to wake | g CO₂e/MJ | |
| \(WtW_f\) | Annex II default, or the certified value (Art. 10), LNG by engine class | g CO₂e/MJ | section 2 |
Limit
$$ I_{target}(y) = 91.16\,\big(1 - r_y\big) \tag{6.3} $$
| where |
|---|
| \(91.16\) | 2020 reference value | g CO₂e/MJ | Art. 4(2) |
| \(r_y\) | 2025: 2%, 2030: 6%, 2035: 14.5%, 2040: 31%, 2045: 62%, 2050: 80% (each holds until the next) | – | Art. 4(2) |
Compliance balance
$$ CB = (I_{target} - I)\,E_{MJ}\;\;[\mathrm{g\,CO_2e}], \qquad CB_t = CB / 10^6 \tag{6.4} $$
| where |
|---|
| \(CB\) | compliance balance: positive surplus, negative deficit | g CO₂e | Annex IV Part A |
Penalty
$$ \text{Penalty} = \frac{|CB|}{I \times 41\,000} \times 2\,400 \times \Big(1 + \frac{n - 1}{10}\Big) \quad (CB \lt 0) \tag{6.5} $$
| where |
|---|
| \(41,000\) | energy of one tonne of VLSFO | MJ/t | Annex IV Part B |
| \(2,400\) | penalty per tonne of VLSFO-equivalent | €/t | Annex IV Part B |
| \(n\) | consecutive reporting periods with a FuelEU penalty, this one included | – | Art. 23(2); stated by the user |
Penalty per tonne, and pooling instead
$$ p_{t} = \frac{10^6}{I \times 41\,000} \times 2\,400, \qquad \text{Pooled} = |CB_t| \times P_{pool} \tag{6.6} $$
| where |
|---|
| \(p_t\) | statutory cost of one tonne of deficit at this intensity (about €638 at HFO's 91.74) | €/t CO₂e | |
| \(P_{pool}\) | price of surplus bought from a pool | €/t CO₂e | input, default 110 |
Rules and nuances
- Applies to ships above 5,000 GT carrying cargo or passengers (Art. 2), the same ships as the ETS. On public data a ship whose verifier reported no ETS-scope emissions (k = 0) is shown as outside FuelEU, so no phantom penalty appears.
- A surplus can be banked (Art. 20) or pooled (Art. 21); a deficit can be pooled, part-borrowed from the next year with 10% added (Art. 20), or paid. Pooled ships cannot borrow (Art. 21(7)); a ship can be in only one pool per year; pools are recorded by the verifier by 30 April.
- Surplus value: negotiated, and never above the penalty the other party avoids. The scorecard values it at half that ceiling (section 10).
- Not modelled: the RFNBO reward factor (2 until 2033), wind-assisted propulsion reward, on-shore power obligations from 2030, and the 2034 RFNBO sub-target. They need customer data the register does not have.
Worked example: 3,000 t HFO between EU ports, 2026
| Energy (6.1) | 3,000 × 40,500 = 121,500,000 MJ |
| Intensity (6.2) | 91.74 g CO₂e/MJ |
| Limit (6.3), 2026 | 91.16 × 0.98 = 89.34 |
| Compliance balance (6.4) | (89.3368 − 91.74) × 121.5 × 10⁶ = -292.0 t CO₂e |
| Penalty (6.5), n = 1 | 292 × 10⁶ ÷ (91.74 × 41,000) × 2,400 = €186,309 |
| Third consecutive deficit, n = 3 | × 1.2 = €223,571 |
| Pooled at €110 (6.6) | 291.99 × 110 = €32,119 |
€186,309 as a penalty, or €32,119 bought from a pool
Worked example: PETER OLDENDORFF, register 2025
| Energy in scope | 96,671,549 MJ (each scope with its own mix, section 3) |
| Intensity against the 2025 limit | 91.61 against 89.34 |
| Compliance balance | -219.4 t CO₂e |
€140,221 penalty, or €24,138 pooled at €110
7Carbon Intensity Indicator (CII)
MARPOL Annex VI Regulation 28 and the guidelines G1 MEPC.352(78), G2 MEPC.353(78), G3 MEPC.338(76) as amended by MEPC.400(83), G4 MEPC.354(78), G5 MEPC.355(78).
Attained (G1)
$$ \mathrm{CII}_{attained} = \frac{\sum_j M_j\,C_{F,j} \times 10^6}{\text{Capacity} \times D} \tag{7.1} $$
| where |
|---|
| \(M_j\) | fuel of type j in the calendar year (IMO DCS, all voyages) | t | |
| \(\text{Capacity}\) | DWT; GT for ro-ro, ro-pax, cruise and vehicle carriers; bulk capped at 279,000 DWT | t or GT | G1 |
| \(D\) | distance sailed | nm | |
Reference line (G2)
$$ \mathrm{CII}_{ref} = a \times \text{Capacity}_{ref}^{\,-c} \tag{7.2} $$
| where |
|---|
| \(a, c\) | per ship type and size, Appendix table A1 | – | G2 |
| \(\text{Capacity}_{ref}\) | as (7.1), except vehicle carriers capped at 57,700 GT and LNG carriers below 65,000 DWT taken at 65,000 | | G2 |
Required (G3)
$$ \mathrm{CII}_{required} = \Big(1 - \frac{Z_y}{100}\Big)\,\mathrm{CII}_{ref} \tag{7.3} $$
| where |
|---|
| \(Z_y\) | 2023: 5%, 2024: 7%, 2025: 9%, 2026: 11%, 2027: 13.625%, 2028: 16.25%, 2029: 18.875%, 2030: 21.5% | % | G3, MEPC.400(83) |
Rating (G4)
$$ \text{rating} = \begin{cases} A & R \le d_1 \\ B & d_1 \lt R \le d_2 \\ C & d_2 \lt R \le d_3 \\ D & d_3 \lt R \le d_4 \\ E & R \gt d_4 \end{cases}, \qquad R = \frac{\mathrm{CII}_{attained}}{\mathrm{CII}_{required}} \tag{7.4} $$
| where |
|---|
| \(d_1 \ldots d_4\) | dd vector per ship type, Appendix table A1 | – | G4 |
With G5 corrections
$$ \mathrm{CII}_{G5} = \frac{\sum_j C_{F,j}\,\big\{M_j - \big(M_{voy,j} + TF_j + (0.75 - 0.03\,y')(M_{el,j} + M_{boil,j} + M_{oth,j})\big)\big\}}{f_i\,f_m\,f_c\,f_{iVSE}\;\text{Capacity}\;(D - D_x)} \times 10^6 \tag{7.5} $$
| where |
|---|
| \(M_{voy}, D_x\) | fuel and distance of voyages endangering safe navigation (reg. 3.1) or within the ice edge | t, nm | G5 4.1 |
| \(M_{el}\) | reefers (2.75 kW × 24 h × SFOC × reefer-days without a meter), cargo cooling on gas/LNG carriers, electric discharge pumps on tankers | t | G5 4.3, App. 1 |
| \(M_{boil}, M_{oth}\) | cargo heating and steam pumps; standalone engine-driven cargo pumps (tankers) | t | G5 4.4–4.5 |
| \(y'\) | years from 2023 (0.75 in 2023, 0.66 in 2026, 0.54 in 2030) | – | G5 4 |
| \(TF_j\) | STS tankers: (1 − 6.1742·DWT−0.246) × fuel on STS voyages; shuttle tankers with DP: (1 − 5.6805·DWT−0.208) × all fuel | t | G5 2.8–2.9 |
| \(f_i, f_m, f_c, f_{iVSE}\) | only if in the ship's EEDI/EEXI Technical File | – | G5 4.6 |
Fuel from speed (when fuel is not known)
$$ M_{ME} = M_{ref}\Big(\frac{V}{V_{ref}}\Big)^{n} t_{sea}, \qquad D = 24\,V\,t_{sea} \tag{7.6} $$
| where |
|---|
| \(M_{ref}\) | main-engine fuel per day at the reference speed | t/day | sea trial or charter party |
| \(n\) | speed exponent, 3 (cube law) by default, 2.6–3.5 typical | – | user |
| \(t_{sea}\) | days at sea; auxiliary and port fuel are added flat per day | days | |
Worked example: Bulk carrier, 50,000 DWT, 3,000 t HFO, 50,000 nm, 2026
| Attained (7.1) | 9,342 × 10⁶ ÷ (50,000 × 50,000) = 3.737 |
| Reference (7.2) | 4,745 × 50,000−0.622 = 5.669 |
| Required (7.3), Z = 11% | 5.669 × 0.89 = 5.045 |
| Ratio | 3.737 ÷ 5.045 = 0.741 |
| Boundaries (dd × required) | A ≤ 4.339, B ≤ 4.742, C ≤ 5.348, D ≤ 5.953 |
Rating A
Rules and nuances
- The CII covers the ship's whole IMO DCS year. From the EU register only EU-related voyages are visible, so a CII from public data is an estimate, not offered below 1,000 nm in the year.
- Z rises every year to 2030, so the same ship drifts down a band without any change; the trajectory view recomputes every year, including the G5 deduction share.
- Rated D three years in a row, or E once: a corrective action plan in SEEMP Part III (section 18).
- G5 deductions are applied only from documented values; any deduction the guideline does not allow for the ship type, or larger than the fuel reported, is refused.
8Energy Efficiency Existing Ship Index (EEXI)
MARPOL Annex VI Regulations 23 and 25 as revised by MEPC.328(76); calculation guidelines MEPC.350(78); survey and certification MEPC.351(78); capacity MEPC.364(79).
Required
$$ \mathrm{EEXI}_{required} = \Big(1 - \frac{Y}{100}\Big)\,a\,b^{-c} \tag{8.1} $$
| where |
|---|
| \(a, b, c\) | EEDI reference line, Appendix table A2; b = DWT (GT for cruise) | | Reg. 24.3 Table 2 |
| \(Y\) | reduction factor by type and size, linear inside the starred bands | % | Reg. 25 Table 3 |
Y inside a band
$$ Y = Y_{lo} + (Y_{hi} - Y_{lo})\,\frac{b - b_{lo}}{b_{hi} - b_{lo}} \tag{8.2} $$
| where |
|---|
| \(b_{lo}, b_{hi}\) | edges of the band the ship falls in | DWT or GT | Reg. 25 Table 3 |
Attained (Technical File)
$$ \mathrm{EEXI}_{attained} = \frac{f_j\,P_{ME}\,C_{F,ME}\,SFC_{ME} + P_{AE}\,C_{F,AE}\,SFC_{AE}}{f_i\,f_c\,f_l\;\text{Capacity}\;f_w\,V_{ref}\,f_m} \tag{8.3} $$
| where |
|---|
| \(P_{ME}\) | 75% of MCR per engine; with a power limitation min(0.83 × MCRlim, 0.75 × MCR) | kW | MEPC.350(78) 2.2.1 |
| \(P_{AE}\) | 0.025 × ΣMCR + 250 where ΣMCR ≥ 10,000 kW, else 0.05 × ΣMCR | kW | EEDI guidelines 2.2.5.6 |
| \(SFC\) | from the NOx Technical File; otherwise SFCapp 190 (ME) and 215 (AE) g/kWh with CF 3.114 | g/kWh | MEPC.350(78) 2.2.4–2.2.5 |
| \(\text{Capacity}\) | DWT; 70% of DWT for container ships; GT for cruise | | MEPC.364(79) 2.2.3 |
| \(V_{ref}\) | speed at PME on the reference draught, deep water | kn | speed-power curve |
| \(f_j, f_i, f_c, f_l, f_w, f_m\) | correction factors from the Technical File; 1 when not applicable | – | MEPC.350(78) |
Rules and nuances
- Container ships: the attained index uses 70% of DWT, but the required value uses full DWT, because a = 174.22 and c = 0.201 were fitted on 100% DWT (MEPC.364(79) 2.2.3.3.3–4). Using 70% in both understates the requirement.
- Bulk carriers: b capped at 279,000 DWT. Ro-ro cargo and ro-pax use the phase-2 lines (Reg. 25.2): a = 1,686.17 with b capped at 17,000 DWT, and a = 902.59 with b capped at 10,000 DWT.
- Vehicle carriers: a = (DWT/GT)−0.7 × 780.36 where DWT/GT < 0.3, and 1,812.63 where DWT/GT ≥ 0.3; both DWT and GT are needed.
- The register may report EEXI, EEDI or EIV. EEDI and EIV are design or estimated indices: the verdict is then labelled INDICATIVE.
- Not included: power take-off/take-in, shaft generators and innovative technologies (their terms are zero). The usual remedy above the requirement is an engine or shaft power limitation documented in the Onboard Management Manual.
Worked example: Bulk carrier, 93,000 DWT, filed EEXI 2.97
| Reference | 961.79 × 93,000−0.477 = 4.10 |
| Y | 20% (20,000–200,000 DWT band) |
| Required (8.1) | 0.80 × 4.10 = 3.28 |
| Margin | (3.28 − 2.97) ÷ 3.28 = 9.5% |
COMPLIANT
Worked example: Vehicle carrier, 22,500 DWT and 60,868 GT, filed EEXI 13.69
| DWT/GT | 22,500 ÷ 60,868 = 0.370 ≥ 0.3, so a = 1,812.63 |
| Reference | 1,812.63 × 22,500−0.471 = 16.16 |
| Required, Y = 15% | 13.74 |
COMPLIANT (13.69 ≤ 13.74)
Worked example: Technical File, 150,000 DWT bulk carrier with a power limitation (MEPC.351(78) sample)
| PME | min(0.83 × 9,940, 0.75 × 15,000) = 8,250.2 kW |
| PAE | 0.025 × 15,000 + 250 = 625.0 kW |
| SFC and CF | ME 166.5 g/kWh, AE 220 g/kWh, CF 3.206 (diesel oil) |
| Attained (8.3) | (8,250.2 × 3.206 × 166.5 + 625 × 3.206 × 220) ÷ (150,000 × 13.2) = 2.45 |
| Required | 2.61 |
2.45 against 2.61: COMPLIANT
Screening estimate on the EEXI page, when only MCR and Vref are known: (8.3) with every f = 1, SFC 175 (ME) and 215 (AE) g/kWh and CF of the main fuel. Example: 93,000 DWT, MCR 12,000 kW, 14 kn → 4.05. Always labelled INDICATIVE.
9IMO Net-Zero Framework (scenario until adopted)
Draft MARPOL Annex VI Chapter 5, approved in principle at MEPC 83; adoption postponed in October 2025 and not adopted when this guide was built. Every output carries that note; all parameters are configurable.
GHG fuel intensity
$$ GFI = \frac{\sum_{all\ legs}\sum_f M_f\,LCV_f\,WtW_f}{\sum_{all\ legs}\sum_f M_f\,LCV_f} \tag{9.1} $$
| where |
|---|
| \(GFI\) | GHG fuel intensity of all the ship's energy, international voyages and berths (not only EU) | g CO₂e/MJ | |
Targets
$$ T_{base} = 93.3\,(1 - b_y), \qquad T_{direct} = 93.3\,(1 - d_y) \tag{9.2} $$
| where |
|---|
| \(93.3\) | 2008 reference | g CO₂e/MJ | MEPC 83 |
| \(b_y\) | 2028: 4%, 2029: 6%, 2030: 8%, 2031: 12.4%, 2032: 16.8%, 2033: 21.2%, 2034: 25.6%, 2035: 30% | % | base target |
| \(d_y\) | 2028: 17%, 2029: 19%, 2030: 21%, 2031: 25.4%, 2032: 29.8%, 2033: 34.2%, 2034: 38.6%, 2035: 43% | % | direct compliance target |
Remedial and surplus units
$$ \begin{aligned} GFI \gt T_{base}: &\quad U_2 = (GFI - T_{base})E,\; U_1 = (T_{base} - T_{direct})E \\ T_{direct} \lt GFI \le T_{base}: &\quad U_1 = (GFI - T_{direct})E \\ GFI \le T_{direct}: &\quad SU = (T_{direct} - GFI)E \end{aligned} \qquad \text{Cost} = 100\,U_1 + 380\,U_2 \tag{9.3} $$
| where |
|---|
| \(E\) | energy, in MJ; U and SU in t CO₂e (÷ 10⁶) | MJ | |
| \(100, 380\) | Tier 1 and Tier 2 remedial unit prices | US$/t | MEPC 83 draft |
Worked example: 3,000 t HFO, scenario year 2028
| GFI | 91.74 (FuelEU WtW values as provisional defaults) |
| Targets | base 89.57, direct 77.44 |
| Tier 2 units | (91.74 − 89.57) × 121.5 = 263.9 t |
| Tier 1 units | (89.57 − 77.44) × 121.5 = 1,473.7 t |
US$247,649 in remedial units (scenario)
10The four-score ship card
Regulatory health
$$ H = \min\big(100,\max(0,\;P_{rating} - 15\,[CB \lt 0])\big) \tag{10.1} $$
| where |
|---|
| \(P_{rating}\) | A 100, B 85, C 65, D 35, E 10 | points | |
| \([CB < 0]\) | 1 when the FuelEU balance is a deficit | – | |
Cost exposure
$$ \text{Exposure} = \text{Cost}_{EU} + \text{Penalty}_{FuelEU} + \text{Cost}_{\pounds}\,FX, \qquad \text{Exposure}_{pooled} = \min(\text{Exposure},\; \text{Exposure} - \text{Penalty} + \text{Pooled}) \tag{10.2} $$
Compliance asset
$$ \text{Asset} = 0.5 \times \frac{CB}{I \times 41\,000} \times 2\,400 \quad (CB \gt 0) \tag{10.3} $$
| where |
|---|
| \(0.5\) | a negotiated midpoint: half the penalty the counterparty avoids | – | planning proxy |
Worked example: 3,000 t HFO example, 2026
| Health | A = 100, deficit −15 → 85 |
| Exposure | €806,590 + €186,309 = €992,899 |
| Pooled exposure | €838,709 |
Future readiness is the NZF scenario of section 9.
11What-if levers and scenario comparison
Fuel at sea
$$ \frac{M'_{sea}}{M_{sea}} = (1 - a)\,(1 + \Delta v)^{\,n-1}(1 - e) + \frac{a}{1 + \Delta v}, \qquad \frac{t'_{sea}}{t_{sea}} = \frac{1}{1 + \Delta v} \tag{11.1} $$
| where |
|---|
| \(\Delta v\) | speed change on the same distance (−0.10 = 10% slower) | – | user |
| \(n\) | speed–power exponent, 3 by default (2 to 4.5) | – | user |
| \(a\) | auxiliary and boiler share of fuel at sea, default 10% | – | user |
| \(e\) | main-engine fuel saved by hull, propeller and trim | – | user or section 19 |
Biofuel, same energy
$$ M_{B100} = \beta\,\sum_{f\,fossil} M_f\,\frac{LCV_f}{LCV_{B100}}, \qquad M'_f = (1 - \beta)\,M_f \tag{11.2} $$
| where |
|---|
| \(\beta\) | share of fossil energy switched to certified B100 | – | user |
Biofuel break-even
$$ \text{Break-even premium} = \frac{-\Delta\text{Carbon} - \Delta M_{fossil}\,P_{fuel}}{M_{B100}} - P_{fuel} \tag{11.3} $$
Worked example: 10% slower, n = 3
| Main engine only (a = 0) | 0.9² = 0.8100 |
| With a = 10% | 0.9 × 0.81 + 0.1 ÷ 0.9 = 0.8401 |
Fuel at sea falls by about 16% (not 10%); berth fuel is unchanged, and each scheme then applies only its own scope.
12Owner and time-charterer split
Pro-rata share
$$ s_{ch} = \frac{\text{charter days in the year}}{\text{days in the year}} \;\text{(or the stated emissions share)}, \qquad \text{Charterer} = s_{ch} \times \text{Cost} \tag{12.1} $$
Worked example: 1 March–31 August 2025 on a €100,000 EU ETS cost
| Days | 184 of 365 |
| Share | 50.41% |
Charterer €50,411, owner €49,589
Basis: BIMCO ETS Allowances Clause for Time Charter Parties 2022 and FuelEU Maritime Clause 2024. The clauses allocate the emissions reported for the charter period; days are a proxy when voyage data is missing.
13EU ETS statement to charterers (document)
Allowances to transfer
$$ A_v = \Big[\mathrm{CO_2}_v + \delta_{y_v}(28\,\mathrm{CH_4}_v + 265\,\mathrm{N_2O}_v)\Big]\,\sigma_v\,\phi_{y_v}\,(1 - 0.05\,\iota), \qquad A = \Big\lceil \sum_v A_v \Big\rceil \tag{13.1} $$
| where |
|---|
| \(v\) | a voyage in the charter period, counted in the year it starts (Reg. 2015/757 Art. 3(m)) | | |
| \(\lceil\cdot\rceil\) | allowances are whole units: rounded up | | |
Example (release-gate check): 40 t MDO between EU ports in 2026 = 40 × (3.206 + 0.00005 × 28 + 0.00018 × 265) = 130.3 → 131 allowances. With cash settlement, × the agreed price.
14FuelEU pooling: allocation, settlement and the optimiser
Allocation in proportion to surplus
$$ \text{valid} \iff \sum_{i \in pool} CB_i \ge 0, \qquad CB'_i = \begin{cases} 0 & CB_i \lt 0 \\ CB_i\,(1 - \theta) & CB_i \gt 0 \end{cases}, \qquad \theta = \frac{\sum_{def}|CB|}{\sum_{sur} CB} \tag{14.1} $$
| where |
|---|
| \(\theta\) | share of each surplus used; the rest stays with its ship and may be banked (Art. 21(6)) | – | |
Transfers and money
$$ T_{s \to d} = |CB_d|\,\frac{CB_s}{\sum_{sur} CB}, \qquad \text{Pays}_d = P\,|CB_d|, \qquad \text{Receives}_s = P\,\sum_d T_{s\to d}\,(1 - \text{fee}) \tag{14.2} $$
| where |
|---|
| \(P\) | agreed price per t CO₂e | € | |
| \(\text{fee}\) | platform share of the gross, from the surplus side | % | |
Optimiser (0/1 knapsack)
$$ \max_{S \subseteq \text{deficits}} \sum_{d \in S} \text{Penalty}_d \quad \text{s.t.} \quad \sum_{d\in S}|CB_d| \le \sum_{sur} CB \tag{14.3} $$
Solved exactly by dynamic programming at 1-tonne granularity below 500,000 t of capacity, by penalty density above. Each deficit ship's saving = its penalty (6.5) − what it pays.
15Allowance planner
Need
$$ N_{ship} = \big\lceil A_{2026}\big\rceil, \qquad N_{co} = \sum_{ships} N_{ship} \tag{15.1} $$
| where |
|---|
| \(A_{2026}\) | (4.5) on the ship's last reported year under 2026 rules (100%, CO₂ + CH₄ + N₂O) | EUA | |
| \(co\) | the filing company, grouped by its IMO company number | | |
Lots per month
$$ L = \Big\lceil \frac{N_{co}}{500} \Big\rceil, \qquad \ell_m = \Big\lfloor \sum_{k\le m} s_k L \Big\rfloor - \sum_{k\lt m}\ell_k \tag{15.2} $$
| where |
|---|
| \(500\) | EUAs per lot at EEX primary auctions | | |
| \(s_m\) | share of the need in month m by pattern: steady 1/M; early ⅔ by March 2027; as emitted | – | |
| \(\ell_m\) | whole lots bought in month m; any remainder in the last buying month | lots | |
Budget and peers
$$ \text{Budget}_m = 500\,\ell_m\,P, \qquad \text{Percentile} = 100\,\frac{\#\{c : x_c \lt x_{me}\}}{\#\text{peers}} \tag{15.3} $$
| where |
|---|
| \(P\) | price: latest EEX auction clearing price, or the year's low and high as scenarios | € | data/eua_market.json |
| \(x\) | allowances per ship in scope; peers run mainly the same type with a similar number of ships (≥ 5 companies) | EUA | |
Worked example: Oldendorff Carriers GmbH & Co. KG, 52 ships in scope, planned on 31 October 2026
| Need | 205,461 EUAs |
| Lots | ⌈205,461 ÷ 500⌉ = 411 (spare 39) |
| Price | latest EEX auction €84.7 |
| Auctions to August 2027 | 180, 0.056% of the supply |
About €17,405,850 at €84.7
16MOHA workspace: obligations, reconciliation, funding, penalty watch
Required per company
$$ R_c = \Big\lceil \phi_y \sum_{i \in c} E_{ETS,i} \Big\rceil \tag{16.1} $$
| where |
|---|
| \(c\) | the responsible shipping company (registered owner, or the ISM company with a mandate); ships below 5,000 GT left out | | Directive Art. 3(w) |
Outstanding and funding call
$$ O_c = \max\big(0,\; R_c - H_c - S_c\big), \qquad O'_c = \max\big(0,\; O_c - T_c\big), \qquad \text{Call}_c = O'_c\,P_{EUA} \tag{16.2} $$
| where |
|---|
| \(H_c, S_c\) | in the company's own MOHA, and already surrendered | EUA | Registry statement |
| \(T_c\) | pending transfers into that company's own MOHA only | EUA | |
Penalty watch
$$ \text{Penalty}_{watch} = 100 \times \text{short}, \qquad \text{still owed} = \text{short} \times P_{EUA} \tag{16.3} $$
Rules
- Each company has one MOHA; a surplus in one never offsets a shortfall in another; a transfer to the wrong company's MOHA does not count (Delegated Reg. 2019/1122 Art. 15a).
- States: early, watch (from 120 days before 30 September), at risk (30 days), missed; expulsion risk after a previous miss.
- Example: required 9,490, covered 9,000, on 10 September 2027 → short 490, penalty €49,000, still owed €41,650, state “at risk”.
17Poseidon Principles climate alignment
Attained (Equation 2)
$$ AER_{WtW} = \frac{\sum_f M_f\,WtW^{PP}_f \times 10^6}{\text{DWT} \times D} \tag{17.1} $$
| where |
|---|
| \(WtW^{PP}\) | Table 8 factors, section 2 | g CO₂e/g | Technical Guidance v5.2 |
| \(\text{DWT}\) | GT for cruise, ferries and vehicle carriers (cgDIST) | | |
Trajectory
$$ r_s = (a\,Y^3 + b\,Y^2 + c\,Y + d)\;\text{Size}^{\,e} \tag{17.2} $$
| where |
|---|
| \(a…e\) | Table 6 (minimum) and Table 7 (striving), Appendix table A4 | | |
| \(\text{Size}\) | DWT, GT, TEU or m³ by type; bulk from 279,000 DWT uses its own line | | |
Alignment delta (Equation 3)
$$ \Delta = \frac{AER_{WtW} - r_s}{r_s} \times 100 \tag{17.3} $$
Check against the guidance's worked example, 80,000 DWT bulk carrier, 2024: minimum 3.88, striving 3.66 g CO₂e/dwt-nm (the guidance prints 3.9 and 3.7).
18SEEMP Part III plan
Combined effect
$$ \mathrm{CII}_{target}(y) = \mathrm{CII}_{attained}\prod_{m\ \in\ \text{force}(y)} \varphi_m, \qquad \varphi_{speed} = (1 + \Delta v)^{n-1}, \quad \varphi_m = 1 - \frac{s_m}{100} \tag{18.1} $$
| where |
|---|
| \(s_m\) | routing 2.5%, jit 2%, hull_clean 4%, trim 1.5%, aux 1%, coating 4%, esd 3% | % | planning defaults (VERIFY per ship) |
Interactions
- With a speed reduction in force, weather routing and just-in-time arrival count at half their effect.
- Hull cleaning and a low-friction coating address the same loss: only the larger counts.
- Target: at least C in the first plan year and at or below the required CII in later years; the automatic plan keeps a 2% margin (MEPC.395(82) Appendix 3 layout).
19Hull and propeller performance (ISO 19030 approach)
Reference curve
$$ P = a\,V^{n}\;\;(\text{fit } \ln P = \ln a + n \ln V), \qquad P_{T} = P_{T_{ref}}\Big(\frac{T}{T_{ref}}\Big)^{2/3} \tag{19.1} $$
| where |
|---|
| \(T\) | mean draught; between laden and ballast curves ln a and n are interpolated | m | |
Performance values
$$ \Delta P = \frac{P_{meas}}{P_{exp}(V_{meas},T)} - 1, \qquad \text{speed loss} = 1 - \frac{V_{meas}}{V_{exp}(P_{meas},T)} \tag{19.2} $$
Cost of fouling
$$ M_{excess} = M_{ME}\,\frac{\Delta P}{1 + \Delta P}, \qquad c_t = C_F P_{EUA} s_{EU} + (WtW - I_{target})\,LCV\,P_{pool}\,s_{EU} \times 10^{-6} \tag{19.3} $$
| where |
|---|
| \(s_{EU}\) | share of fuel in EU scope | – | |
| \(c_t\) | carbon cost of one tonne of fuel | €/t | |
Only steady, fair-weather days: ≥ 20 h under way, Beaufort ≤ 4 when reported, speed within 10% and draught within 1 m of the reference. Records are split at cleanings, polishes and dry-dockings; an event's effect is the mean speed loss in the 30 days before minus the 30 days after. A cleaning pays back when its cost (default €25,000) ÷ the daily cost of the excess.
20Part-year data: annualising
Linear scaling
$$ k_{year} = \frac{365}{\text{days observed}}, \qquad M' = k_{year}\,M, \quad D' = k_{year}\,D \tag{20.1} $$
The CII is unchanged by scaling (a ratio); costs grow with it. Confidence: ≥ 270 days HIGH, ≥ 90 MEDIUM, ≥ 30 LOW, otherwise INDICATIVE. Seasonality, dry-dock and idle time are not modelled.
21Appendix: parameter tables
A1. CII reference lines (G2) and rating vectors (G4)
| Ship type | a | c | d₁ / d₂ / d₃ / d₄ |
|---|
| Bulk carrier | 4745 | 0.622 | 0.86 / 0.94 / 1.06 / 1.18 |
| Tanker | 5247 | 0.61 | 0.82 / 0.93 / 1.08 / 1.28 |
| Container | 1984 | 0.489 | 0.83 / 0.94 / 1.07 / 1.19 |
| General cargo | 31948 | 0.792 | 0.83 / 0.94 / 1.06 / 1.19 |
| Gas carrier | 8104 | 0.639 | 0.85 / 0.95 / 1.06 / 1.25 |
| Refrigerated cargo | 4600 | 0.557 | 0.78 / 0.91 / 1.07 / 1.2 |
| Combination carrier | 5119 | 0.622 | 0.87 / 0.96 / 1.06 / 1.14 |
| Ro ro | 1967 | 0.485 | 0.76 / 0.89 / 1.08 / 1.27 |
| Ro pax | 2023 | 0.46 | 0.76 / 0.92 / 1.14 / 1.3 |
| Cruise | 930 | 0.383 | 0.87 / 0.95 / 1.06 / 1.16 |
| General cargo below 20,000 DWT | 588 | 0.3885 | as general cargo |
| Gas carrier 65,000 DWT and above | 14405×10⁷ | 2.071 | 0.81 / 0.91 / 1.12 / 1.44 |
| LNG carrier 100,000 DWT and above | 9.827 | 0 | 0.89 / 0.98 / 1.06 / 1.13 |
| LNG carrier 65,000–100,000 DWT | 14479×10¹⁰ | 2.673 | 0.78 / 0.92 / 1.1 / 1.37 |
| LNG carrier below 65,000 DWT (at 65,000) | 14779×10¹⁰ | 2.673 | 0.78 / 0.92 / 1.1 / 1.37 |
| Vehicle carrier 30,000 GT and above (cap 57,700 GT) | 3627 | 0.590 | 0.86 / 0.94 / 1.06 / 1.16 |
| Vehicle carrier below 30,000 GT | 330 | 0.329 | 0.86 / 0.94 / 1.06 / 1.16 |
A2. EEXI reference lines (Reg. 24.3 Table 2) and reduction factors (Reg. 25 Table 3)
| Ship type | a | c | Y by size band (DWT; GT for cruise) |
|---|
| Bulk carrier | 961.79 | 0.477 | 10,000–20,000: 0→20%; 20,000–200,000: 20%; 200,000–∞: 15% |
| Gas carrier | 1120 | 0.456 | 2,000–10,000: 0→20%; 10,000–15,000: 20%; 15,000–∞: 30% |
| Tanker | 1218.8 | 0.488 | 4,000–20,000: 0→20%; 20,000–200,000: 20%; 200,000–∞: 15% |
| Container | 174.22 | 0.201 | 10,000–15,000: 0→20%; 15,000–40,000: 20%; 40,000–80,000: 30%; 80,000–120,000: 35%; 120,000–200,000: 45%; 200,000–∞: 50% |
| General cargo | 107.48 | 0.216 | 3,000–15,000: 0→30%; 15,000–∞: 30% |
| Refrigerated cargo | 227.01 | 0.244 | 3,000–5,000: 0→15%; 5,000–∞: 15% |
| Combination carrier | 1219 | 0.488 | 4,000–20,000: 0→20%; 20,000–∞: 20% |
| Lng carrier | 2253.7 | 0.474 | 10,000–∞: 30% |
| Vehicle carrier | 780.36 | 0.471 | 10,000–∞: 15% |
| Ro ro | 1686.17 | 0.498 | 1,000–2,000: 0→5%; 2,000–∞: 5% |
| Ro pax | 902.59 | 0.381 | 250–1,000: 0→5%; 1,000–∞: 5% |
| Cruise | 170.84 | 0.214 | 25,000–85,000: 0→30%; 85,000–∞: 30% |
A3. FuelEU and NZF targets
| From | FuelEU reduction | FuelEU limit, g CO₂e/MJ |
|---|
| 2025 | 2% | 89.34 |
| 2030 | 6% | 85.69 |
| 2035 | 14.5% | 77.94 |
| 2040 | 31% | 62.90 |
| 2045 | 62% | 34.64 |
| 2050 | 80% | 18.23 |
| Year | NZF base % | NZF direct % | Base, g CO₂e/MJ | Direct, g CO₂e/MJ |
|---|
| 2028 | 4 | 17 | 89.57 | 77.44 |
| 2029 | 6 | 19 | 87.70 | 75.57 |
| 2030 | 8 | 21 | 85.84 | 73.71 |
| 2031 | 12.4 | 25.4 | 81.73 | 69.60 |
| 2032 | 16.8 | 29.8 | 77.63 | 65.50 |
| 2033 | 21.2 | 34.2 | 73.52 | 61.39 |
| 2034 | 25.6 | 38.6 | 69.42 | 57.29 |
| 2035 | 30 | 43 | 65.31 | 53.18 |
A4. Poseidon Principles trajectory coefficients
| Trajectory | Type | Size | a | b | c | d | e |
|---|
| minimum | Bulk carrier | DWT | 0.209808 | -1278.76 | 2.59776e+06 | -1.75894e+09 | -0.621796 |
| minimum | Bulk carrier (279k DWT and above) | DWT | 8.62515e-05 | -0.525695 | 1067.93 | -723097 | 0 |
| minimum | Chemical tanker | DWT | 0.764174 | -4657.57 | 9.46172e+06 | -6.40652e+09 | -0.708012 |
| minimum | Container | TEU | 0.0170465 | -103.897 | 211064 | -1.42911e+08 | -0.428275 |
| minimum | Cruise | GT | 3.40417 | -20734.6 | 4.20938e+07 | -2.84824e+10 | -0.781306 |
| minimum | Ferry-RoPax | GT | 0.33488 | -2044.33 | 4.15975e+06 | -2.8212e+09 | -0.533656 |
| minimum | General cargo | DWT | 0.039377 | -240 | 487552 | -3.30121e+08 | -0.434669 |
| minimum | Liquefied gas tanker (100k CBM and above) | CBM | 0.000507847 | -3.09529 | 6287.98 | -4.25758e+06 | -0.00798691 |
| minimum | Liquefied gas tanker (below 100k CBM) | DWT | 0.12737 | -776.312 | 1.57705e+06 | -1.06782e+09 | -0.50641 |
| minimum | Oil tanker | DWT | 0.911577 | -5555.99 | 1.12868e+07 | -7.64229e+09 | -0.710709 |
| minimum | Refrigerated bulk | DWT | 1.05901 | -6454.59 | 1.31123e+07 | -8.87832e+09 | -0.689616 |
| minimum | Ro-Ro | DWT | 1.66276 | -10134.4 | 2.05877e+07 | -1.39399e+10 | -0.736571 |
| minimum | Vehicle | GT | 1.61483 | -9843.08 | 1.99977e+07 | -1.35416e+10 | -0.798599 |
| striving | Bulk carrier | DWT | 0.182599 | -1111.05 | 2.25324e+06 | -1.52305e+09 | -0.621796 |
| striving | Bulk carrier (279k DWT and above) | DWT | 7.50661e-05 | -0.456752 | 926.303 | -626123 | 0 |
| striving | Chemical tanker | DWT | 0.665073 | -4046.75 | 8.20689e+06 | -5.54734e+09 | -0.708012 |
| striving | Container | TEU | 0.0148359 | -90.2713 | 183072 | -1.23745e+08 | -0.428275 |
| striving | Cruise | GT | 2.86535 | -17417.1 | 3.52856e+07 | -2.38256e+10 | -0.781306 |
| striving | Ferry-RoPax | GT | 0.318318 | -1941.05 | 3.94515e+06 | -2.67265e+09 | -0.533656 |
| striving | General cargo | DWT | 0.0342705 | -208.524 | 422892 | -2.85848e+08 | -0.434669 |
| striving | Liquefied gas tanker (100k CBM and above) | CBM | 0.000441988 | -2.68935 | 5454.06 | -3.6866e+06 | -0.00798691 |
| striving | Liquefied gas tanker (below 100k CBM) | DWT | 0.110853 | -674.501 | 1.3679e+06 | -9.24616e+08 | -0.50641 |
| striving | Oil tanker | DWT | 0.793361 | -4827.34 | 9.78994e+06 | -6.61739e+09 | -0.710709 |
| striving | Refrigerated bulk | DWT | 0.921676 | -5608.09 | 1.13733e+07 | -7.68765e+09 | -0.689616 |
| striving | Ro-Ro | DWT | 1.44713 | -8805.3 | 1.78573e+07 | -1.20704e+10 | -0.736571 |
| striving | Vehicle | GT | 1.41164 | -8590.43 | 1.74238e+07 | -1.1779e+10 | -0.798599 |
A5. Open items (marked VERIFY in the code)
Checked before relying on them for a customer
- Load shares λ for the deadweight estimate (3.6): container 0.68 checked on six ships; the others are physical defaults.
- Biofuel treatment: MEPC.1/Circ.905 (CII) and RED certification (ETS, FuelEU); B100 WtW per the actual certificate.
- SEEMP measure savings and interaction rules are planning defaults, to check against the ship's own data.
- NZF targets and unit prices against the final adopted text.
- The excess emissions penalty: €100 indexed since 2013, shown as “at least” until the year's indexed figure is published.
A6. Primary sources
Directive 2003/87/EC (consolidated) and Directive (EU) 2023/959; Regulation (EU) 2015/757 and Delegated Regulation (EU) 2023/2776; Delegated Regulation (EU) 2020/1044; Regulation (EU) 2023/1805 (FuelEU Maritime); Delegated Regulation (EU) 2019/1122 as amended by 2023/2904 (Union Registry); SI 2026/392 (UK ETS maritime); MARPOL Annex VI as revised by MEPC.328(76), MEPC.338(76), MEPC.350(78), MEPC.351(78), MEPC.352(78)–355(78), MEPC.364(79), MEPC.395(82), MEPC.400(83); Poseidon Principles Technical Guidance v5.2 (July 2025); ISO 19030; BIMCO ETS Allowances Clause 2022 and FuelEU Clause 2024; EMSA THETIS-MRV public emission reports; EEX primary auction results.