Emissions Assessment of Container Ships Sailing under Off-Design Conditions

: Maritime transportation is the prevalent mode of transport for overseas freight, and it is frequently recognised as a relatively environmentally sustainable means of transport. However, shipping is still a substantial source of greenhouse gas emissions. We investigate the effect on fuel consumption and emissions when container ships are sailing below the design speed (i


Introduction
The greenhouse gas (GHG) emissions of total shipping have increased from 977 million tonnes in 2012 to 1076 million tonnes in 2018 (a 9.6% increase).In 2012, there were 962 million tonnes of CO 2 emissions, while in 2018, this amount grew by 9.3% to 1056 million tonnes [1].Moreover, a growth in global seaborne trade is forecasted in the near future because of the world's growing population, which will translate into an increase in air pollution from maritime transport.As a result, the International Maritime Organisation (IMO) has developed and adopted over the years more stringent regulations aimed at dramatically abating emissions from vessels [2].These air pollution regulations focus on the reduction in CO 2 , NO x , SO x and PM since these are the main emissions from vessel engines.Shipping companies have addressed several solutions for meeting the new standards of cost efficiency, such as the use of ultralow sulphur fuels, scheduling, route optimisation or the installation of scrubbers inter alia.However, the costs for technically adapting their fleets to new fuels or affording the installation of abatement techniques are not feasible for all ship owners.For a number of shipping companies, slow steaming (SS), understood as a process of deliberately reducing speed in order to minimise fuel consumption (the largest cost), has seemed to be the main strategy to reduce fuel consumption while preserving the viability of a service route [3].For instance, a reduction of 13% in a vessel's speed could lead to CO 2 emission abatement around 30% [4].SS led to a significant reduction in shipping emissions as a consequence of the need to reduce costs after the world financial crisis in 2008 [5].Consequently, the IMO adopted SS as an important procedure to reduce emissions [6].Nonetheless, in some cases, either more vessels were used or larger vessels were deployed in order to prevent an increase in transit times or cargo demurrage [7].
There are extensive and multiperspective ways to assess ship emissions based on methodologies that either combine fuel sales data with emissions (top-down methods) or are based on vessels' technical and operating conditions (bottom-up methods) [8,9].In this sense, bottom-up approaches are widely used because they are ship specific.In that respect, [10,11] suggest a methodology for the evaluation of the exhaust emissions of marine traffic by using the Automatic Identification System (AIS).The emissions are computed based on the relationship between the instantaneous speed and the design speed and take into account the detailed technical information of the engines installed on board.
This study goes on to analyse the cubic speed-power relation in the slow steaming condition and to shed some light on the discussion of the suitability of the cubic value of the exponent as a "universal" for fuel consumption assessments and its influence on ship emission mitigation.The investigation is underpinned by using real data of the fuel consumption on a set of container ship voyages in the Mediterranean Sea and then comparing the results with those obtained when applying the cubic relation.Methodologically, the engine power assessment is based on [11], through the assumption that hull-specific parameters are ship-specific constants.The emissions factors used to assess the emissions derived from the fuel consumption are taken from [12], as will be detailed in the methods section.
This paper is structured as follows: After the Introduction (Section 1), the Methods and Tools section (Section 2) presents the methodology followed to assess the revision of the speed-power relation exponent together with a description of the vessels and routes used in the analysis.Section 3 shows the Results from the case study, including the percentages of the overestimation of fuel consumption and emissions reduction by using real data in comparison to the previously mentioned methodologies.Additionally, the results of applying a weather ship routing to slow steaming routes are also presented in this section.The Discussion section (Section 4) describes the feasibility and the limitations of the assumptions made, including a simplified comparison of the result obtained with the average data reported from vessels under annual regulation requirements.Finally, the conclusions and future developments are underlined in the last section (Section 5).

Methodology 2.1. Literature Review
Several studies have analysed slow steaming in terms of CO 2 emission reduction while minimizing operation costs.For instance, [13] studied the impact of slow steaming in the container ship sector depending on bunker prices and concluded that SS reduces emissions without the adoption of any new technology in a short-term time period despite the fact that it remains frail in the long term.Additionally, [14] used a large dataset of noon reports for 16 crude tankers to estimate the fuel consumption-speed curve when sailing in SS conditions, and they concluded that the classical cubic law is valid only near the design speed.
Furthermore, [7] warned that even though slow steaming seemed to be the solution for cutting CO 2 emissions, this statement required a careful analysis.The aforementioned study recalls the proportionality between the propulsion power and the speed raised to a power of n, pointing out that in some specific cases, this exponent can be up to a maximum of 6 or 7, values far from the design conditions parametrised by the cubic speed-power law.
Other studies such as [15] used a model based on econometric and naval architectural data to ascertain that the n exponent diverges from 3 at speed intervals below the design speed, focusing attention to speed optimisation rather than a systematic reduction in speed to mitigate emissions.From another point of view, [4] analysed the fuel consumption reduction in container ships using slow steaming based on the numerical simulations of resistance and open water and self-propulsion tests using computational fluid dynamics.This study concluded that the chosen approach was more reliable than using the assumption that fuel consumption and the required power are proportional to the cubed value of the ship speed.
All the studies mentioned above show that the tendency has turned to questions about the adequacy of the application of the cubic speed-power relation, widely applied for design conditions [16,17], to analyse the real impact of SS.Considering the cubic relation (i.e., P = k•v 3 ), the first conclusion would be that reducing speed would mean a straightforward reduction in power and thus fuel consumption.However, the aforementioned studies suggest that maintaining the value of the exponent equal to 3 when the vessel is not sailing at design speed could lead to inaccuracies when assessing the global benefits of this operational technique.

Analysis and Strategic Objectives
The strategy of analysis is underpinned by real fuel consumption data (see Figure 1) jointly with AIS information for the route and ship characteristics [18].Firstly, the theoretical fuel consumption for the routes analysed is calculated following the methodology explained by Jalkanen [10,11].As stated in former studies, the formula used to predict the engine instantaneous power has been the speed-power relation proposed by the International Maritime Organisation [1,17], using 3 as the exponent value (n).The methodology followed to estimate emissions based [10,19] is detailed in the authors' former study [20].Afterwards, the speed-power relation exponent is adjusted to the particularities of the operational characteristics of the container ships under study (adj), thanks to the real fuel consumption data provided (the names of the vessels have not been revealed following ship-owner requirements).Finally, the results obtained from applying the cubic rule and the newly adjusted one are compared with the real fuel consumption data.This comparison is used to certify that the consumption calculated with the cubic relation (n = 3) underestimates the quantity of fuel consumed while the ship is sailing in the SS condition.Furthermore, this investigation also includes an estimation of the effect of applying weather ship routing (WSR) for slow steaming voyages in order to assess the savings in fuel consumption derived from a combination of both operational techniques (i.e., SS plus WSR).

AIS and Ships Technical Data
The initial data used to adjust the n exponent are taken from real Automatic Iden cation System (AIS) data.The AIS is an automated, autonomous tracking system for sh identification operating in the VHF maritime band.AIS data reports, with static and namic vessel information, were obtained from the marine traffic website (m Figure 1 shows the strategy of analysis followed in this study according to the methods and the strategic objectives described as follows: (i) Impact of the cubic speed-power relation: Firstly, fuel consumption and emissions are theoretically calculated by using 3 as an exponent value; secondly, real emissions are assessed thanks to the availability of real fuel consumption data.The results are compared in order to assess the impact of the cubic relation.(ii) Accurate estimation of the power relation by using real fuel consumption data (i.e., the new n exponent adjusted): By using real fuel consumption data, the n exponent derived from these real data is calculated (n adj ), and it is used afterwards for the theoretic assessment of fuel consumption.The real data are compared with the theoretical data obtained with the newly adjusted exponent.(iii) Added enhancement of WSR for SS cases in terms of ship emissions reduction: the potential additional reduction in emissions by using WSR on the routes analysed is assessed.

AIS and Ships Technical Data
The initial data used to adjust the n exponent are taken from real Automatic Identification System (AIS) data.The AIS is an automated, autonomous tracking system for ships' identification operating in the VHF maritime band.AIS data reports, with static and dynamic vessel information, were obtained from the marine traffic website (marinetraffic.com)from July 2021 to December 2021.In this study, the required AIS data are the time, position (latitude and longitude) and Speed Over Ground (SOG) for each of the particular voyages analysed.
The ship's technical data are required to estimate fuel consumption and emissions, and they are obtained from the IHS Markit Sea-web database (installed engine power, P installed , and design speed, V design ).Also, real voyage data are obtained from the ship owner (maximum continuous rating, MCR; engine load, EL real ; engine revolutions, rpm; and real fuel consumption, FC real ) and from the engine manufacturer (specific fuel consumption, SFOC man , and engine load, EL man ).
2.4.Formulation for Fuel Assumptions and Emissions Assessment 2.4.1.Theoretical Fuel Consumption through the Cubic Relation (n = 3) First, the consumption for the routes analysed is calculated following the STEAM2 emissions methodology explained by Jalkanen [11,12] (see Appendix A) by using 3 as the exponent value (n) for the speed-power relation proposed by the International Maritime Organisation: where k is a ship-specific parameter [11]: where EL man is the engine load from the manufacturer data, P Installed is the installed power per engine (in kW) and V design is the design speed (in knots).
With the SOG data assessed in 5 min intervals, the average power needed to maintain the speed of the vessel over a voyage is calculated: where P AIS is the average power from the AIS data (in kW), v AIS is the average speed from the AIS intervallic data (in knots) and n is an exponent that is equal to 3.
At this point, the theoretical fuel consumed through the route when considering the cubic relation can be calculated by where FC theo is the theoretical fuel consumption (in g), SFOC mod is the Specific Fuel Oil Consumption (in g/kWh) assessed from P AIS [9] and t is the total time of the voyage from the AIS data (in hours).
2.4.2.Assessment of the Speed-Power Relation Exponent Based on n Adjusted (n adj ) The availability of real fuel consumption data provides the possibility to determine an adjusted n exponent applicable per voyage.Firstly, the average power delivered from engines (P real ) can be assessed as the real fuel consumption (FC real ), SFOC mod data and the total time of the voyage are already known.
P real would be the average power for the route with the condition of slow steaming: where P real is the average power for the route (in kW), FC real is the fuel consumption provided by the ship owner (in g), SFOC mod is the Specific Fuel Oil Consumption (in g/kWh) and t is the time of the voyage from the AIS data (in hours).
Taking into account the following expression, which also assesses the real average engine power, the new speed-power relation exponent n adj can be isolated given the following expression: Note that Equation ( 6) is equivalent to Equation (3), but instead of the cubic relation, the n to be adjusted is considered.
In favour of accuracy, the modified Specific Fuel Oil Consumption (SFOC mod ) was assessed rather than using the design condition values, which are not maintained when the engine runs out of its design conditions.Two different methodologies were considered to estimate the Specific Fuel Oil Consumption.On the one hand, the formula used to assess SFOC mod is the one proposed by Jalkanen [12], who state that the assumption of a constant linear relation between the fuel consumption, EL and SFOC is not certain, as derived from the engine manufacturer's data.Instead, there is an approximately parabolic dependency between them.Using regression analysis from the engine manufacturer's data [10] leads to the following equation for a relative SFOC (α): where EL real is the real engine load average per trip obtained from the ship-owner data.Equation ( 8) is also used by the IMO in its 3rd Greenhouse Gas Study to assess the SFOC [17]: On the other hand, the proposal of [12] has also been used.The author stated that SFOC mod is not constant over the whole operation range as it depends on the engine load in percent of the maximum continuous service rating (% MCR).According to Kristensen [17], the variation in the SFOC in % for two-stroke diesel engines can be approximated by giving the MCR in % from the ship-owner data.As per the above formulation, it has to be highlighted that besides taking into account the Speed Over Ground, this approach also accounts for weather and oceanographic conditions as the engine load used to obtain the results is the real value provided from ships.
Once the value of n adj is obtained from both methodologies (SFOC mod obtained alternatively from Equations ( 9) and ( 11)), an averaged value is used to estimate the fuel consumption.

Theoretical Fuel Consumption through Adjusted Speed-Power Relation Exponent
At this stage, the fuel consumed per trip can be assessed through the application of Equations ( 3) and ( 4) recalled below, but taking into account the newly assessed exponent (n adj ): where P adj is the average power considering (n adj ), n adj is the newly adjusted exponent, FC adj is the fuel consumption considering n adj ∧ SFOC adj is the Specific Fuel Oil Consumption considering the adjusted power.Obviously, discrepancies between FC adj and FC real emerge due to the fact that the former is theoretically assessed, meaning that some assumptions are made, such as an average engine load over the whole trip.Other factors could be critical, for instance, the influence of the fuel temperature over the engine performance inter alia.

Emissions Assessment
The total emissions for each pollutant (E T p ) per ship and per route can be obtained by multiplying the fuel consumption by the emission factor for each pollutant analysed [12].The formula shown in Equation ( 14) was applied, changing the emissions factor related to one pollutant or another: where FC is the fuel consumption (in g) and EF p is the emission factor of each pollutant (units according to Table 1).

Weather Ship Routing (WSR) Software
In order to investigate the enhancement of operational characteristics such as SS, a weather ship routing software (SIMROUTE, Version 1; see Appendix B) was used and applied to the routes described in the next subsection.SIMROUTE [21] is an open-source software that uses an A* pathfinding algorithm and ship velocity penalisation due to the waves and has been applied previously in different cases and scenarios [22][23][24].The wave information was obtained from MedSea Copernicus products (see specific procedures in [20]).The open-source software (GPL Licence), jointly with support manuals, is available in GitHub.com/ManelGrifoll/SIMROUTE.
The methodology used in the software requires the inclusion of several initial parameters such as (i) the route characteristics (the port of departure and port of arrival) and the period of study (day/month/year); (ii) the vessel characteristics (the length, deadweight (DWT) and cruising speed); and (iii) the wave field for the sailing days, planned by the EU Copernicus Marine Environmental Monitoring Service (CMEMS).Second, the minimum and optimal routes are obtained for the selected period.Then, technical data from the IHS Markit Sea-web database (the engine power, design speed, lowest possible Specific Fuel Oil Consumption and the engine load) are used to estimate the emissions.Finally, the percentage of fuel savings and emission mitigation are obtained.Daily wave information is obtained from the Copernicus Marine Service (CMEMS).As the cases selected are routes in the Mediterranean Sea, the MEDSEA product is used to provide wave information.SIMROUTE also includes three different parametrisations of the wave effect on navigation: Aertssen [25], Khokhlov (suggested by Lubkovsky) [26] and Bowditch [27].As can be seen in [20], these formulations consider different wave parameters (i.e., a significant wave height and wave direction) and different ship characteristics, penalising ship speed as the significant wave height increases.

Ship Dataset and Route Description
The dataset used in the present study consists of 19 voyages sailed by three Panamaxtype container ships during the second semester of 2021.These ships have similar characteristics, and they follow routes that cover the whole Mediterranean.
Table 2 shows the ships' main particulars.The selected routes are described in Figure 2A-C, each representing the trips of the container ships M/V "First" (F), M/V "Second" (S) and M/V "Third" (T), respectively.Figure 2 shows the routes followed by the aforementioned vessels and analys this case study.These routes were plotted thanks to the AIS data obtained for each vo Table 3 shows a summary of the main characteristics of the routes studied.Note the route IDs include information about the vessels shown in Table 2. Figure 2 shows the routes followed by the aforementioned vessels and analysed in this case study.These routes were plotted thanks to the AIS data obtained for each voyage.
Table 3 shows a summary of the main characteristics of the routes studied.Note that the route IDs include information about the vessels shown in Table 2.

Results
The results obtained with the new exponent value (n adj ) compared to the ones obtained by using the cubic exponent (n = 3) and with the real fuel consumption data are shown in Table 4 for each case studied (i.e., vessels and voyages).These results reveal an underestimation of the fuel consumed of 33.6% (the averaged value weighted according to the sailing speed), reaching values of more than 60% in cases where the vessel is under very slow steaming sailing conditions.
Consistent with the strategic objectives drawn in Figure 1, the results section is structured with three different subsections.Firstly, the values related to fuel consumption are presented.Secondly, a quantitative summary of the emissions assessment is included.Finally, the benefit in terms of fuel consumption when weather ship routing is applied to the case study routes is also evaluated.

Fuel Consumption Assessment
Table 4 reveals significant differences in the quantity of fuel consumption assessed when applying the cubic speed-power relation with regard to the real figures compared to the values obtained with the newly adjusted speed-power relation.The analysis considers the over-and underestimation from the real values (i.e., FC theo − FC real and FC adj − FC real ).
This table shows that when the vessels are under very slow steaming conditions (i.e., sailing speeds of 10-11 knots), the percentages of value discrepancies when applying the cubic exponent are in the range of 50-60%.A particular example of this assertion can be seen in route "S.2", which represents a trip between the Ashdod and Haifa ports that the vessel nicknamed "Second" undertook in December 2021 (as per Table 3).In this particular case, the reported fuel consumption was 6.20 tonnes.When theoretically assessing the fuel consumed under the aforementioned sailing conditions, the values attained with the cubic relation and the newly adjusted relation (FC adj ) were 3.09 t and 7.05 t, respectively.Even though the newly adjusted relation overestimated the quantity of fuel consumed by 12%, the results are almost 40% more accurate than applying the cubic speed-power relation (FC theo ).In very slow steaming conditions, when the newly adjusted relation is applied, the discrepancies are limited to 6-15%.
However, the disparities also appear when the vessels are slow steaming closer to their design speed, as can be deduced from the route T.2 data.This route represents a case where vessel "T" sailed from the port of Tarragona to the port of Haifa between 7 and 11 November 2021 (see Table 3).In this specific case, the vessel was slow steaming only 4 to 5 knots below its design speed, and the reported real fuel consumption for that trip was 431.68 t.When assessing the fuel consumption with the cubic speed-power relation, however, the quantity of the fuel obtained was 258.30 t, meaning an underestimation of 40%.This difference was reduced to a 3.68% overestimation when applying the newly adjusted exponent for the speed-power relation.
In brief, the fuel consumption values obtained by using the adjusted speed-power relation (n adj ) show an average difference from the real fuel consumption data of 3-15%.When comparing the real values with the fuel consumption obtained by applying the cubic speed-power relation, the discrepancies range from 20% up to 60% of fuel consumption underestimation.

Emissions Assessment
As the emission of pollutants is dependent on the quantity of the fuel consumed, it can be stated that emissions are underestimated in all the cases analysed when the cubic speedpower relation is used, whereas the results are more accurate when the newly adjusted relation is applied.According to Equation ( 12), the disparities in under-or overestimation percentages are the same as for the fuel consumption due to the proportionality between fuel consumption and emissions.Table 5 summarises the results for the quantity of pollutants derived from the real fuel consumption and the theoretical assessment of pollutants when the fuel consumption was calculated by using the cubic (exponent n = 3) and the adjusted (n adj ) speed-power relation.The emissions assessment shown in Table 5 reveals a substantial variability in the quantity of the pollutants assessed, depending on whether the cubic or the adjusted speed-power relation was used to assess the fuel consumption.In order to investigate the emissions' under-or overestimation pattern, Table 5 shows the amount of pollutants theoretically generated through the routes under study, including the assessment of carbon mono-and dioxide, sulphur dioxide, particulate matter, hydrocarbons and a threshold for the nitrogen oxides.
A qualitative examination of the Table 5 data reveals, for instance, that the carbon dioxide (CO 2 ) for all voyages is equal to 4158.50 t.On the other hand, the total amount of CO 2 when applying the cubic exponent and the newly adjusted one is 2654.05t and 4451.59t, respectively.Consequently, it can be ascertained that the cubic speed-power relation underestimates the total amount of CO 2 emitted to the atmosphere by 36%, while the adjusted formulation overestimates the quantity of CO 2 by 7%, thus being five times more accurate than the theoretical formulation.
Furthermore, when looking at the other pollutants, as the case of sulphur dioxide, the percentage of underestimation rises to 41% when using the cubic relation, while there is only a 2% discrepancy when the adjusted formulation is used.Finally, regarding particulate matter, the figures are in the same order, with an almost 37% underestimation of emissions when n = 3 and a 6% overestimation when using n adj .
In consequence, as derived from the data shown in Table 5, the quantification of the amount of pollutants is substantially underestimated when applying the cubic speed-power relation, suggesting the significance of the application of a more accurate formulation for fuel consumption.

Benefits of Combined Weather Ship Routing and Slow Steaming
The resolution MEPC.213(63) adopted the 2012 guidelines for the development of a Ship Energy Efficiency Management Plan (SEEMP).A SEEMP provides a possible approach to monitoring the ship and fleet efficiency performance over time, and some different options could be considered when seeking to optimise the performance of the ship.Among the best practices proposed by the guidelines for the fuel-efficient operation of ships, we can find weather routing, among others [28].Therefore, in terms of complying with the actual and the upcoming emissions regulations, the combination of weather routing optimisation in addition to slow steaming could be considered.The present study analyses all the routes and vessels presented in Section 2.6 by using the weather ship routing (WSR) software SIMROUTE briefly described in Section 2.5.
Figure 3 shows the percentage of time saved and the consequent fuel consumption reduction when applying weather ship routing in parallel to slow steaming on the case study vessels and AIS routes plotted in Figure 2. Figure 3 reveals that 15 out of the 19 routes would have saved time if a weather routing software had been used while sailing.Furthermore, it has to be pointed out that more than 50% of the routes analysed showed values of time saving above 5%, even though none of the vessels faced bad weather conditions over the routes covered (only 3 out of the 19 routes occasionally showed waves above 2 m high).As follows from Figure 3, the range of the time saved oscillates from 0.6% up to 11.2%, and so does the fuel consumption reduction.
In consequence, as stated above, the simultaneous use of slow steaming and weather ship routing could provide the targeted emissions reduction, becoming an option that should not be neglected by stakeholders.
above 2 m high).As follows from Figure 3, the range of the time saved oscillates from 0.6% up to 11.2%, and so does the fuel consumption reduction.
In consequence, as stated above, the simultaneous use of slow steaming and weather ship routing could provide the targeted emissions reduction, becoming an option that should not be neglected by stakeholders.3. Blue colour' bars are for M/V "F", green colour for M/V "S" and red colour for M/V "T".

Discussion
Slow steaming is a well-known practice widely applied in the container ship sector as a consequence of the need to reduce costs after the world financial crisis in 2008 [17,29].In slow steaming, the ship speed is deliberately reduced in order to minimise fuel consumption (the largest cost), leading to a significant reduction in shipping emissions [30][31][32].Consequently, the International Maritime Organisation (IMO) adopted this speed reduction practice as an important procedure to reduce emissions [17].However, some studies reveal that sailing at a reduced speed does not mean that consumption will be reduced according to the well-known cubic relation [13,14,16,33].In fact, it can be stated that sailing at less than the design speed will consume more fuel than expected [13,16,34].Our results agree with previous studies discussing the appropriateness of applying the widespread use of the cubic speed-power relation to evaluate the benefits of the application of slow steaming.For instance, Ref. [14] reviewed the speed-power relation through the analysis of empirical data from the examination of a fleet of 16 oil tanker ships to determine the fuel consumption versus ship speed elasticity under real sea conditions.Their study concluded that the cubic relation holds true near design conditions but can be substantially lower in smaller speed ranges.Furthermore, Ref. [15] stated that when vessels sail below the design speed, slow steaming will not be as beneficial as is often asserted.Their approach is based on a data-driven model that combines economic analysis with naval architecture and is supplied with operational data from 88 tankers.Additionally, references  3. Blue colour' bars are for M/V "F", green colour for M/V "S" and red colour for M/V "T".

Discussion
Slow steaming is a well-known practice widely applied in the container ship sector as a consequence of the need to reduce costs after the world financial crisis in 2008 [17,29].In slow steaming, the ship speed is deliberately reduced in order to minimise fuel consumption (the largest cost), leading to a significant reduction in shipping emissions [30][31][32].Consequently, the International Maritime Organisation (IMO) adopted this speed reduction practice as an important procedure to reduce emissions [17].However, some studies reveal that sailing at a reduced speed does not mean that consumption will be reduced according to the well-known cubic relation [13,14,16,33].In fact, it can be stated that sailing at less than the design speed will consume more fuel than expected [13,16,34].Our results agree with previous studies discussing the appropriateness of applying the widespread use of the cubic speed-power relation to evaluate the benefits of the application of slow steaming.For instance, Ref. [14] reviewed the speed-power relation through the analysis of empirical data from the examination of a fleet of 16 oil tanker ships to determine the fuel consumption versus ship speed elasticity under real sea conditions.Their study concluded that the cubic relation holds true near design conditions but can be substantially lower in smaller speed ranges.Furthermore, Ref. [15] stated that when vessels sail below the design speed, slow steaming will not be as beneficial as is often asserted.Their approach is based on a data-driven model that combines economic analysis with naval architecture and is supplied with operational data from 88 tankers.Additionally, references stating a value of the speed-power exponent above five for container ships can be found in the literature [7,35].Aligned with these studies, our analysis of container ships in the Mediterranean Sea also suggests differences when the cubic relation is applied.
In order to further emphasise the correlation of the above literature with the results of our research, Figure 4 shows the n exponent value in terms of the navigational speed.This figure ascertains that the value of the exponent increases when the speed of the vessels is reduced for the container ship voyages analysed.This assertion cannot be generalised to any type of container ship and route as the quantity of data is critical to make more categorical statements.However, regarding the case study vessels, the data analysed show a correlation coefficient of 0.51, which means a moderate relationship between the variables n and speed of navigation.As can be deduced from Figure 4, the value of the n exponent tends to three as the vessel's speed approaches the design speed (23.5 knots).Nevertheless, when the vessel is sailing in the slow steaming condition, the assumption based on a cubic exponent for assessing fuel consumption clearly leads to an overestimation of the positive effect of this operational technique.From the data used in this investigation, a new relation of n as a function of ship velocity (v cruising ∈ knots) may be found: sels is reduced for the container ship voyages analysed.This assertion cannot be generalised to any type of container ship and route as the quantity of data is critical to make more categorical statements.However, regarding the case study vessels, the data analysed show a correlation coefficient of 0.51, which means a moderate relationship between the variables n and speed of navigation.As can be deduced from Figure 4, the value of the n exponent tends to three as the vessel's speed approaches the design speed (23.5 knots).Nevertheless, when the vessel is sailing in the slow steaming condition, the assumption based on a cubic exponent for assessing fuel consumption clearly leads to an overestimation of the positive effect of this operational technique.From the data used in this investigation, a new relation of n as a function of ship velocity ( ∈ ) may be found:  0.016  3.45 Through the application of Equation ( 15), the parameter n can be approximated, enabling the measurement of the sensitivity of fuel consumption to changes in speed.In order to come up with the above expression, several sources were used, as stated in the Methods section with specific limitations.In this sense, some points are highlighted below: (i) A reliable data source is a cornerstone to investigating the reliability of ship emission assessments.We draw attention to the fact that vessels' performance data are normally regarded as sensitive and either are not currently offered by stakeholders or are not quantitatively significant enough.Therefore, empirical researchers may be forced to focus on small samplings, and usually the source is from one ship owner only [14].
(ii) Several studies use vessels' data from the AIS to estimate emissions in the same manner as the present research [11,17].However, there are limitations in that sense, as occasionally the data have to be discarded due to excessively large blanks or due Through the application of Equation ( 15), the parameter n can be approximated, enabling the measurement of the sensitivity of fuel consumption to changes in speed.In order to come up with the above expression, several sources were used, as stated in the Methods section with specific limitations.In this sense, some points are highlighted below: (i) A reliable data source is a cornerstone to investigating the reliability of ship emission assessments.We draw attention to the fact that vessels' performance data are normally regarded as sensitive and either are not currently offered by stakeholders or are not quantitatively significant enough.Therefore, empirical researchers may be forced to focus on small samplings, and usually the source is from one ship owner only [14].(ii) Several studies use vessels' data from the AIS to estimate emissions in the same manner as the present research [11,17].However, there are limitations in that sense, as occasionally the data have to be discarded due to excessively large blanks or due to limitations related to human error that occurred during the data-input process [9,36].(iii) Additional observations have to be highlighted when taking into account operative considerations.For instance, considering the cubic speed-power relation, the instantaneous speed applied plays a very important role since it is a cubed factor, so the variation in the power obtained by using this approximation is highly dependent on the ship velocity.However, since the speed obtained through the AIS data is the Speed Over Ground (SOG) of the ship, it does not manifest the influence of the weather on the ship and, in turn, on the engine load.This consideration is relevant due to the fact that most models in the literature assume a constant speed-consumption elasticity across the expected range of the sailing velocity and for a specific vessel and contour conditions [14].However, in the present study, this potential limitation is overcome thanks to the data provided from the vessels, which include the real engine load per trip.
In order to emphasise the relevance of using an accurate formulation for fuel consumption and emissions assessments, Table 6 shows the comparison between the averaged values, in kg fuel/nmile units, of the real amount of fuel consumed and the fuel consumption as estimated by using both the cubic relation and the adjusted speed-power rule formulation.These values are also compared to the data reported in the annual European Union report for Monitoring, Reporting and Verification (MRV) (https://mrv.emsa.europa.eu/#public/emission-report(accessed on 20 july 2022)).The MRV report considers the annual average values provided by the ship owner under the requirements of the European Union [37].However, this report contains yearly averaged data, and it also includes the consumption for auxiliary engines and boilers.In spite of this, the values obtained when using the cubic relation underestimate the fuel consumption by an order of 50%, while the nadj-based assessment overestimates consumption by an average value of 8.5%.The values of the n adj also indicate less divergence with the MRV report, being more reliable container-ship fuel-consumption assessments.As per [17] the fuel consumed in auxiliary engines is in the range of 5 to 15% of the main engine consumption.Therefore, deducting an average 7% from the MRV figures, i.e., for vessel M/V "T", the difference between the reported consumption on MRV and the one assessed with the adjusted n exponent is only 9%, a value that would be further reduced if data on fuel consumption during manoeuvres were available and taken into account.Several assumptions were made to obtain the adjusted exponent for the speed-power relation.In our analysis, only fuel consumption from the navigation period was considered, and average values of the power delivered by the engines over the route were used.Consequently, a deeper analysis on the adjustment of the well-known cubic speed-power relation should be carried out to set an n exponent threshold, thus making it possible to set a classification of the ranges of n to apply when assessing fuel consumption on a particular container ship sailing at a determined slow steaming speed.In order to set these ranges for the n exponent, the collaboration of the stakeholders by means of providing real data is crucial.In some cases, they are reluctant to provide large amounts of data for a scientific analysis, which may introduce uncertainties to the analysis.Intercomparisons with the literature provide consistency to our research.In our case, despite the scarce quantity of data available, the values of the n exponent obtained range between 3.1 and 3.5, similar to several studies, confirming that the outcomes are of the same order.For instance, ref. [38] establishes an exponent value of 3.3 for container ships under the SS condition, ref. [16] provides a range from 2.7 to 3.3 and ref. [7] sets a tier from 1.9 to 4.4 depending on the container ship size and degree of slow steaming.Furthermore, values of the speed-power law exponent between 3 to 4.2 are found in [17,39] for container ships with a DWT similar to the case study ones.
Besides pursuing an accurate formulation for the speed-power relation in SS sailing conditions, we also introduced an analysis of the combined benefits of adding weather ship routing.The outcomes of these combined techniques (i.e., SS plus WSR) have pointed to an optimisation of between 0.6% and 11.2% in terms of time over 78% of the cases anal-ysed.These percentages increase when high energetic wave events are considered, according to previous investigations (e.g., [21,40]).
The effect of applying weather ship routing in the SS routes analysed is particularly observed in route S.4.In this particular route, the vessel sailed about 180 nautical miles, maintaining an average speed close to 15 knots.If the route followed was the optimised route proposed by the WSR software, the time saved would mean a 3.3 t (i.e., 11%) reduction in fuel consumption in comparison to the real route.
Among other operational measures, slow steaming is noticeable due to its straightforward and obvious benefits to reduce energy usage, but its potentiality to further reduce emissions is limited once a slow speed is already in practice.For the greatest emission reduction potential, other operational solutions must be implemented into the energymanagement strategies of shipping businesses [41].
As noted by [42], research on WSR in world navigation will be a topic deserving ever more attention in the coming years, in particular with the gradual introduction of autonomous ships.In this sense, the simultaneous use of different operational techniques could mean a step forward towards emission abatement and sustainable development in the maritime industry.
According to [21,40], the savings in fuel consumption may increase when high energetic wave events are considered.In that sense and as stated by Zis, Psaraftis and Ding (2020), weather ship routing models could also be used in autonomous shipping to avoid potential damages by avoiding bad weather.The aforementioned study also states that autonomous vessels will sail at lower speeds, thus increasing the sailing time as there will not be consequences for seafarers during board periods.As time will not be a constriction, the optimum route can be optimised be searching for favouring currents to reduce fuel consumption.Furthermore, ship operators can also utilise weather ship routing to establish a time frame for a vessel's arrival based on weather forecasts, particularly when anticipating potential delays.
However, autonomous vessels will not allow high speeds or will adopt a changing speed pattern to take time advantage at the beginning of the trip and to be able to adjust its speed to meet a certain ETA later on.In that sense, engines will work in design conditions partially as speed may be reduced in high-traffic areas or when having to meet a specific time window.This fact could mean a reduction in emissions while sailing below the design speed, but it should be properly analysed, as proved in the present study.Slowing down the speed is a multicriteria decision as it can be a consequence of overcapacity in depressed market periods, a response to high bunker prices or it can also depend on decisionmaking stakeholders.

Conclusions and Future Work
Our investigation focuses on the importance of using suitable factors when assessing the benefits of using slow steaming as an operational technique.Furthermore, this study includes the assessment of the theoretical fuel consumption abatement when combining weather ship routing and slow steaming.
Based on 19 study cases of container ship voyages undertaken in the Mediterranean Sea over the second semester of 2021, the assessed speed-power relation proved to be higher than the cubic one in all the cases when the vessel sailed below the design speed.Our results show that the application of this universal relation to assess the fuel consumption (and emissions) for slow steaming led to underestimation by up to 60%.In consequence, the validity of this relation when sailing far from design conditions is revised, and the results show that the value of the exponent increases when the speed of the vessel is reduced for these particular vessels and sailing conditions.
Additionally, an enhancement towards sustainability is highlighted through the presentation of the results of combining two operational techniques at the hands of ship owners such as WSR and SS.The results show an abatement on emissions above 11% in some cases and an emissions reduction in the 78% of the cases analysed, even though none of the vessels faced highly energetic wave events as the waves' maximum height was below 2 m in all the routes.
To conclude, and as suggestions for future research, an assessment to evaluate the advantages of maintaining a certain speed and a recommended engine load for low consumption is considered as further work.That means focusing on the reduction in fuel consumption, emphasizing the use of an optimum speed instead of a persistent use of slow steaming in order to fulfil the cargo delivery on time.
Furthermore, for a broader perspective of the influence of the n exponent on fuel consumption assessments, deeper and wider research on container ships is recommended, as well as on other types of vessels such as tankers or Ro-Pax in order to provide an n exponent calibrated with real data.In this sense, the collaboration of stakeholders providing factual on-board fuel consumption figures is a key element in the future developments of sustainable actions in the maritime industry.
to the nearest node.The heuristic function used in weather ship routing is the sailing time associated with the minimum distance between the origin and destination.
SIMROUTE may be applied worldwide in order to estimate the emissions mitigation through weather ship routing.As an illustrative example, Figure A1 shows an illustrative case for coastal shipping in Japan between the ports of Hakodate and Kagoshima (route HAK-KAG).This case test shows how the optimum route follows a path in the opposite coast of the Honshu Island in comparison to the minimum distance route.In this case, the time saving is equal to 6.36%.
to expand into one or more longer paths.It does so based on an estimate of the cost (in our case, the travel time) to go to the goal node.Specifically, A* selects the path that minimises the total cost function f(n): ℎ  (A7) where n is the last node on the path, g(n) is the cost of the path from the start node to n and h(n) is a heuristic that estimates the cost of the cheapest path from n to the goal.The heuristic is problem specific.For the algorithm, to find the actual shortest path, the heuristic function must be admissible, meaning that it never overestimates the actual cost to obtain to the nearest goal node.The heuristic function used in weather ship routing is the sailing time associated with the minimum distance between the origin and destination.SIMROUTE may be applied worldwide in order to estimate the emissions mitigation through weather ship routing.As an illustrative example, Figure A1 shows an illustrative case for coastal shipping in Japan between the ports of Hakodate and Kagoshima (route HAK-KAG).This case test shows how the optimum route follows a path in the opposite coast of the Honshu Island in comparison to the minimum distance route.In this case, the time saving is equal to 6.36%.The period analysed, the distance sailed and the sailing time are shown in Table A3, including the saving provided by the optimal route in comparison to the minimum distance route.The emissions reduction percentage is also shown.The period analysed, the distance sailed and the sailing time are shown in Table A3, including the saving provided by the optimal route in comparison to the minimum distance route.The emissions reduction percentage is also shown.

Figure 1 .
Figure 1.Diagram of analysis including the data sources, the methods based on fuel and emiss assessment and the strategic objectives.

Figure 1 .
Figure 1.Diagram of analysis including the data sources, the methods based on fuel and emissions assessment and the strategic objectives.

Figure 2 .
Figure 2. Routes considered in the analysis for vessels (A) M/V "F", (B) M/V "S" and (C) M/V The red points correspond to the different ports.

Figure 2 .
Figure 2. Routes considered in the analysis for vessels (A) M/V "F", (B) M/V "S" and (C) M/V "T".The red points correspond to the different ports.

Figure 3 .
Figure 3. Percentage of time saved (histogram) and fuel consumption reduction (orange line) when applying weather ship routing for the study cases shown in Table3.Blue colour' bars are for M/V "F", green colour for M/V "S" and red colour for M/V "T".

Figure 3 .
Figure 3. Percentage of time saved (histogram) and fuel consumption reduction (orange line) when applying weather ship routing for the study cases shown in Table3.Blue colour' bars are for M/V "F", green colour for M/V "S" and red colour for M/V "T".

Figure 4 .
Figure 4. Value of assessed n exponent (i.e., nadj) in reference to average navigational speed.

Figure 4 .
Figure 4. Value of assessed n exponent (i.e., n adj ) in reference to average navigational speed.

Figure A1 .
Figure A1.Case test showing optimised and minimum distance routes from the port of Hakodate to Kagoshima by using CMEMS products.

Figure A1 .
Figure A1.Case test showing optimised and minimum distance routes from the port of Hakodate to Kagoshima by using CMEMS products.

Table 4 .
Comparison between real fuel consumption (FC real ) and the fuel consumption obtained by using the cubic relation (FC theo ) and the same relation with the adjusted exponent n (FC adj ) (per route).

Table 5 .
Summary of emissions assessment per route.

Table 6 .
Comparison among real quantity of fuel consumed and assessed values (i.e., fuel consumption considering n = 3 and the n adj exponent).

Table A3 .
Test case results.Time (in h) and distance (in nm) for the case test route Hakodate-Kagoshima.