## 1 Introduction  
Despite worldwide efforts to contain greenhouse gas emissions (GHGs) as a key measure to prevent excessive temperature rise, they are increasing at an alarming pace. In 2019, CO\({}_{2}\) emissions from fossil fuel combustion reached 36.7 Gt with total GHG emissions approaching 50 Gt CO\({}_{2}\)e--an almost 40% increase compared to 1990 [1] (GHG emissions--from carbon dioxide, methane, nitrous oxide, and fluorinated hydrocarbons--are expressed as carbon dioxide equivalents (CO\({}_{2}\)e), where \"equivalent\" means \"having the same warming effect as CO\({}_{2}\) over a period of 100 years\"). Although there is some annual variation and a clear decrease in 2020 due to COVID-19, GHG emissions are on the rise and an intensification of reduction strategies in all sectors is tantamount. Power generation and transport sectors together account for more than two-thirds of the total GHG emissions [2] (2019 data) and have been responsible for almost all global growth since 2010. The transport sector alone produces roughly 25% of the total global emissions with the shipping industry being responsible for generating 12% of the transport emissions amounting to almost a billion metric tons per year [3]. As world trade is expected to rise by almost 40% by 2050 [4], future projections for maritime GHG emissions inevitably show similar trends. Estimates for 2050 vary significantly depending on the assumptions used in the calculations as well as on the projected global economic growth and assumed climate management strategy. For example, the most recent report of IMO [3] predicts significant emissions growth for maritime-attributed CO\({}_{2}\) emissions, ranging from 1100 to 1700 Mt/y. Depending on the scenario and assumptions used, the upper range can be shifted to even higher values approaching even 2350 Mt/y. There is thus an increasing pressure from international and intra-national organizations and regulatory bodies on the maritime industry to reduce GHG emissions. This has resulted in the definition and implementation of several energy efficiency measures by the International Maritime Organization (IMO) designed to have a direct impact on GHG emissions from shipping. These include the energy efficiency design index (EEDI), implemented in 2013, expressed as gCO\({}_{2}\)/tonne-mile, which targets the design phase of _new ships_ through measures that affect hull hydrodynamics, propulsion and power systems, machinery technology integration, and the use of alternative fuels and renewable energy sources [4; 5]. Compliance with the EEDI is mandatory. In 2018, IMO adopted the initial strategy for the reduction in GHG emissions from shipping, a policy framework which sets key ambitions, mainly to reduce GHG from international shipping by at least 50% by 2050 compared with their level in 2008, with the aim of phasing them out completely within this century, and to reduce the carbon intensity of international shipping by 40% by 2030 and by 70% by 2050 [6]. More recently, in June 2021, IMO adopted key short-term measures aimed at cutting the carbon intensity of all ships by at least 40% by 2030 [4]. In a marked change from the previous EEDI-based measures, the new initiative targets existing ships through the definition of metrics that reflect not only design but also operational strategies for energy efficiency and carbon reduction. The energy efficiency existing ship index (EEXI), equivalent to EEDI and also expressed as gCO\({}_{2}\)/tonne-mile, will quantify the effects of energy efficiency improvements in existing ships compared to the original design. The carbon intensity indicator (CII) will be introduced for all large ships (with a gross tonnage of over 5000). CII is expressed in gCO\({}_{2}\)/dwt-m and will provide the basis for a vessel energy efficiency rating system on a yearly basis, thus assessing primarily operational efficiency.