Last modified on Jan 16, 2024 17:31
Contributors: S. Dokken (Offshore Monitoring Ltd), J. Gruszka (Offshore Monitoring Ltd), Capt. J. Grindevoll (Offshore Monitoring Ltd),

C. Panteli (Offshore Monitoring Ltd), W.Qazi (Offshore Monitoring Ltd), K. Xu (Offshore Monitoring Ltd), G. Radhakrishnan (Offshore Monitoring Ltd), K. Lemmens (Offshore Navigation Ltd), Capt. R. Maalen, Cruise vessels, Mega-yachts (Global Maritime Services), W. Mao (Chalmers University), L. Eriksson (Chalmers University), L. Jonasson (Chalmers University), X. Lang (Chalmers University), Capt. P. Brandholm (Team Tankers International)

Issued by: OSM / Sverre Dokken

Issued Date: 01/12/2018

Ref: C3S_D422Lot1.OSM.2.6(3)_201809_Operational_Indicators_Technical_Note_v2

Official reference number service contract: 2018/C3S_D422_Lot1_OSM/SC2

Introduction

This document forms the final update and extension to previous versions of deliverable D2.6 for the C3S for Global Shipping project and describes the further and final development of the operational indicators as achieved at the end of November 2018 (Previous update of this document gave the situation up to September 2018). A detailed introduction to the indicators is available in the first version of this deliverable with document title "C3S_D422Lot1.OSM.2.6(1)_201805_Operational_Indicators_Technical_Note_v1"
Within the document presented here, updates and extended information is given to the "Route Cost ETA" operational indicator and to the "Fuel Consumption Model" while new sections have been added on "Route Cost Performance Speed", "Route ETA Variation" and "Artic Sailing Cost". A separate section has been specifically added to discuss the use of seasonal forecast data in the Route/Fuel Consumption related indicators.
With this document, together with the previous versions, the technical description of all the operational indicators included in the scope of the project is completed. The list below gives the names of the indicators and the version(s) of the technical description document in which their respective definitions can be found:

1. Fuel consumption model (D2.6 versions 1, 2 and 3)
2. Route cost ETA (Estimated Time of Arrival) (D2.6 versions 1, 2 and 3)
3. Route cost performance speed / STW (Speed Through Water) (D2.6 version 3)
4. Route ETA variation (D2.6 version 3)
5. Ice limits for different ship ice classes (D2.6 version 2)
6. Availability of new Arctic routes / Route availability index (D2.6 version 2)
7. Cost of new Arctic routes / Arctic sailing cost (D2.6 version 3)

Fuel Consumption Model

The fuel consumption model is developed to calculate the power needs and fuel consumption of a ship when it sails in the ocean. The model has been developed for several standard ship categories
w.r.t. maritime operation and dimensions. Further details, background, and input data requirements are already defined in: C3S_D422Lot1.OSM.2.6(1)_201805_Operational_Indicators_Technical_Note_v1 and C3S_D422Lot1.OSM.2.6(2)_201808_Operational_Indicators_Technical_Note_v1. Here we describe the specification of the shaft power ranges for different ship types, validation of the directional wave resistance code, and validation of the full FCM through comparison with ship-logged data.

Shaft power ranges for different ship types

In practice, the shaft power can be measured using torsion meter to determine the power delivered to a propeller shaft before it is converted into thrust by the propeller. Alternatively, the approximate power prediction method of Holtrop & Mennen (1982) can be adopted to estimate the shaft power of the various vessels. A total of 14 different standard ship types and categories are used in the calculations of the fuel consumption model, and these are already specified in C3S_D422Lot1.OSM.2.6(1)_201805_Operational_Indicators_Technical_Note_v1.

In order to validation the shaft range, a data collection of many existing operating vessels is carried out as shown in Table 1. The shaft power is predicated based on the approximate power prediction method and the values with minimum and maximum shaft power are given in relation to the minimum and maximum speed. A few assumptions have to be made to estimate the shaft power results, and discrepancies of 3-5 % are expected. A benchmarking using existing operational vessels has been established to validate the data in Table 1, and results are within the acceptable and reasonable range.

Table 1: Derived data of the shaft power range for existing operational vessels relevant to the defined ship types and size categories used for C3S for Global Shipping service.

Validation for directional wave resistance / mean added resistance

This work mainly involves the validation of the directional wave resistance code developed by Chern Fong Lee from GMS. The algorithm for the wave added resistance had been created using MATLAB. This resistance component is an integral component of the fuel consumption model, as it is essential to compute the total resistance, which is then used for the evaluation of shaft power and total fuel consumption. As part of this validation study, look up files had been provided which comprise the transfer functions of wave added resistance, computed as the summation of diffraction and wave motion resistance components divided with the square of wave amplitude. These values are generated for different ship types using Chern Fong's code.

Mean added resistance is the final value that represents the directional wave resistance and will be included in the fuel consumption model. This mean added resistance is evaluated using the following formula in Eqn. (1)

where  \( \frac{R_{aw}(w)}{\zeta_a^2} \) is the Transfer function of wave added resistance and  \( S_{\zeta}(w) \) is the Wave Spectrum.
Since the transfer functions were already available, the wave spectrums are constructed for range of wave heights using Bretschneider function inside WAFO tool box in MATLAB. Based on the above formulae, the transfer functions are integrated (Trapezoidal integration) across the spectrum and mean added resistance values are derived. The obtained directional wave resistance results are compared against the values from the deployed code by BOPEN and it is found that the two results matched closely with a negligible discrepancy of less than 0.5%. The validation results of VLCC325 ship are shown using illustrative plots in Fig. 1 below.

Figure 1: Wave added resistance validation results 

Validation of the full FCM

This section summarizes the study followed for validating the fuel consumption model implemented in the C3S for Global Shipping service. The concerned algorithms have been developed by Alexis and Chern Fong from GMS and have been implemented in Python code into the service by project partner BOPEN. In order to verify if the function for computing the fuel consumption is functioning correctly and results in output are within acceptable error margins, the function has been used on historical routes for which both metocean conditions as well as the actual recorded ship's shaft power and fuel consumption were available. The input CDS netcdf files concerning the metocean conditions (wind, waves, currents) were accessed from BOPEN FTP. The metocean data corresponding to daily measurements with a resolution of 1x1 have been used for wind and waves. For currents, mean measurements taken between 1958-2017 have been considered. The ship data against which the outputs of the fuel consumption model have been compared belong to two from the fleet of project partner Team Tankers International, which falls under the "Product Tanker" ship type.

For this validation, separate netcdf route files have been created based on the latitudes and longitudes of different route waypoints along which the ships had been travelling. This has resulted in a series of so-called "historical routes". To initiate the python code for calculating the shaft power on these historical routes, an input value corresponding to speed over ground (SOG) is needed. For every case, the code has been run twice, using two different speeds. One is the constant SOG which is computed by estimating the distance between the starting and ending points of a route and dividing the same with the overall transit time taken in that route. The other is the varying SOG which contains an array of velocities wherein each value represents the distance over time calculated on each and every leg along the route. The shaft powers obtained from constant and variable velocity, in turn have been used to evaluate fuel consumption.

The shaft power and fuel consumption results of the two velocity cases and their comparison with ship logs are performed for seven different routes and reported. In addition, the effect of currents on the shaft power results have also been assessed for two routes. The validation results of one such case on the route between Singapore and Suez are presented below in Fig. 2, 3, 4.

Figure 2: Historical route with waypoints between Singapore and Suez 

Figure 3: Bar plot depicting the shaft power results from ship-based measurements and implemented model 

Figure 4: Total fuel consumption from ship-based measurements and implemented model 

Moreover, the attained shaft power corresponding to variable velocity is then used to predict the speed profile using an inversion function. Three different SOG profiles are plotted, one is the SOG computed using the python function historical_power_to_vel python code, the other is the SOG determined by taking distance over time on each leg along the route and the third one being the GPS Speed of the actual ship extracted from ship logs.

Figure 5: Comparison of Speed Over Ground (SOG) profiles 

In comparison with the actual ship measurements, the simulated measurements showed discrepancies less than 10% for most of the cases, except two routes which exhibited variations above 15%. These two routes happened to be the longest routes, trans-Pacific and trans-Atlantic. To summarize, the error margin is quite acceptable on account of some uncertainties within the numerical model. These are errors due to ship shape and dimensions, limitations related with strip theory on calculation of RAOs and subsequent added resistance values, uncertainties associated with the measurement of metocean conditions etc. Especially, the daily 1° x 1° metocean measurements are relatively smoother when compared with the conditions encountered at sea, and furthermore the speed inputs from actual ships are more noisier. This is evident in the figure on SOG comparisons where the SOG computed from python code is more uniform whereas the speed graph from ship has many peaks and troughs.

Route Cost ETA

The process of sail planning or route optimization is to calculate a constant shaft power (i.e. constant energy provided to the propeller for the ships propulsion to move her forward) for the full duration of the journey, to arrive at a given ETA (Estimated Time of Arrival). The Route Cost ETA operational indicator aims to take the fixed great circle routes as reference, and then calculate an optimized route for a fixed ETA, which use minimal constant shaft power, taking into account the met-ocean conditions.
The detailed description of the Route Cost ETA operational indicator has earlier been given in the first version of this document C3S_D422Lot1.OSM.2.6(1)_201805_Operational_Indicators_Technical_Note_v1. In the second version of this document,

C3S_D422Lot1.OSM.2.6(2)_201808_Operational_Indicators_Technical_Note_v1, the functional basic system has been presentedthe initial test cases and their results have been presented.
The DIRECT (Dividing RECTangles) optimization method is used, and reference is made to D2.6(1) and D2.6(2) for details regarding input data and method description.
Below are described the primary updates and developments in the reporting period of this document D2.6(3).

Improving ship bearing calculation

The ship bearing calculation between successive waypoints was being done using the assumption that the route is on a 2-D planar surface. This has now been updated by using the rhumb line heading (fixed bearing) taking into account the curved surface of the Earth over which the ship moves.

Implementing wave and wind direction contributions in the simple fuel consumption model

There was uncertainty about ingestion of the wave & wind direction contribution into the basic fuel consumption model and the calculation of the ship headings relative to the wave and wind directions. This uncertainty arised from the different definition conventions for the ship heading direction and wave/wind directions. It is now confirmed that the ship heading angle is defined with reference to the latitude axis increasing clockwise; i.e. it is 0° / 360° for north-ward motion, 90° for east-ward motion, 180° for south-ward motion, and 270° for west-ward motion. The wave / wind direction are defined according to the standard Cartesian convention with reference to the longitude axis increasing anti-clockwise; i.e. it is 0° / 360° for east-ward motion, 90° for north-ward motion, 180° for west-ward motion, and 270° for south-ward motion. The given basic fuel consumption model follows the convention of 0° relative wind / wave direction for head sea and 180° relative wind / wave direction for following sea; this is shown below in Fig. 6.

Figure 6: Head sea and following sea convention for the basic fuel consumption model being used for teasting and prototyping the DIRECT route optimization system; taken from Lu et al. (2015). 

Taking into account the definition of ship heading, wave/wind directions, and the head/following sea conventions for the ship, the following equation is used for determining the ship heading relative to wave direction at each waypoint:

where \( \theta_{wa} \) is the wave direction, \( \theta_{COG} \)  is the ship heading / COG (Course Over Ground), and  \( \theta_{COG\_rel\_wa} \) is the ship heading relative to the wave direction.

In Eqn. 2 above, the term \( (90- \theta_{COG}) \)  transforms the coordinates of the ship COG from north- reference clockwise system to regular Cartesian grid east-reference anti-clockwise system. The factor of 180 is subtracted to conform to the head/following sea definition for the basic fuel consumption model.

Similar equation is used for wind direction as well.

Indicator definition

A first version of the detailed Product Definition Document (Implementation) has been delivered to BOPEN earlier, while an updated / revised version of the same document with further refinements is being delivered to BOPEN with this delivery. The document details the step-by-step procedure for algorithm procedure and implementation. Important variables and their interaction with each other is explained. A concise indicator implementation plan has been included in this document, whose summarized version is given in the sections below. The full detailed Product Definition Document (Implementation) is included in the Appendix for reference.

While some of the test results were shown in the previous version of this document D2.6(2), the detailed testing and validation results are also being delivered to BOPEN with this delivery as the Product Definition Document (Validation); this document is included in the Appendix for reference. An example result using CDS metocean data is shown below in Fig. 7, where the CDS ERA-Interim mean monthly climatology wave and wind data for the month of February is used to perform route optimization on a sample great circle route in the Arabian Sea. The expected ETA specified is 40 hours, with an ETA relaxation of 5 hours. The optimized route arrives at the destination in 44.9 hours, and delivers a fuel consumption saving of 12.5% by adjusting the route waypoints and speed profiles according to the metocean condition impact.

Both of these documents follow up on and include the extensive technical discussions between the partners regarding debugging, algorithm improvements, implementation strategies, and indicator output specifications. Both of these documents also form the basis for the implementation, whose demonstration can be seen in D2.11(2).

Figure 7: DIRECT route optimization for a custom-defined great circle route in the Arabian Sea, going from west to east. The CDS mean monthly climatology is used for the month of Feb. for waves and winds information. With an expected ETA of 40 hours, and an ETA tolerance of 5 hours, the optimized route follows an ETA of 44.9 hours and reports fuel consumption savings of 12.5 %. The first three panels show the input great circle route and the optimized route on the same map with no background, SWH / wave direction background, and wind magnitude / wind direction, respectively. The last panel the speed profiles for the optimized route.

Indicator implementation and visualization plan

The route optimization works with fixed ETA constraint, i.e. the ship has to arrive at some pre- determined ETA. Some small ETA margin may be assigned according to user choice (described below).
Discussions with end-users have made it clear that the end-user interaction with the route optimizer will not be on a basis of daily values, rather they will almost always want to interact with the system based on the monthly time scale. The end-users would like to see and interact with how the optimized route changes in different months. Also they would like to see comparison between route optimization in different months and / or different years. Since nearly all the fixed routes are less than

30 days in terms of ETA, and the end-users do not want to interact with the system on a time scale less than a month as well, we do not want to add extra complexity to the system, and monthly mean reanalysis data from CDS will be the most suitable data to be used for the optimizer implementation.

The DIRECT optimization does not give a global minima, so it is important to specify optimization termination criteria. The maxevals parameter is used for termination, i.e. optimization terminates when this threshold is reached.
The parameters, requirements, and procedures for the indicator implementation and visualization plan are detailed below.

Input parameters

• Metocean data:
  • Month and year
  • Resolution
  • size_timedim
  • Latitude coordinate grid definition parameter (f1) / Latitude grid
  • Longitude coordinate grid definition parameter (f2) / Longitude grid
• DIRECT optimization parameters:
  • Max no. of iterations (maxits)
  • Max no. of functions evaluations (maxevals)
  • Max rectangle divisions (maxdeep)
  • Time resolution (time points of metocean data – monthly data is replicated)
  • Number of sampling points during TimeStep (npoints)
• Fuel Consumption Model
  • Fuel consumption model needs to be integrated within the DIRECT algorithm
  • SFOC values for each ship type
• Route parameters
  • Route with waypoints and start / end points (chosen from list of fixed routes)
  • Expected ETA (to be calculated using average ship speed)
  • ETA margin; there should be two options:
    • Optimize without any ETA margin (strict ETA)
    • Optimize with ETA margin defined according to ship type and shipping practice
  • No. of waypoints or waypoints specification according to a pre-specified distance
• Ship parameters
  • Ship type (to be selected from given list)
  • Max ship speed (kts) (depending on ship)
  • Min ship speed (kts) (depending on ship)
  • Average ship speed (kts) (calculated as: (min_speed + max_speed) / 2).

Implementation plan

1. Select great circle fixed route
   1. The route is recommended to be resampled to have a waypoint at every 600 km.
   2. There are some routes which are in the region of a channel which is not very wid (such as Suez / Panama canal, Persian Gulf, or the Red Sea). For these routes, it is recommended to pick only part of the route for optimization, while the route part in the channel should not be optimized because of low resolution of input CDS data, channel traffic restrictions and separation zones etc. An example of this shown for the Bombay to Port Said route in Fig. 8 below.

Figure 8: Recommendation for route segment selection for optimization in case part of the route sails too close to land or sails in a channel which is not very wide; example shown of Bombay to Port Said route.

1. Select sailing month and year. Here the assumption is that the expected ETA is not more than 30 days; if it is slightly more than 30 days (may happen in rare cases), then still assume that sailing time is within the same month.
   1. This choice from the user will let the system pick the relevant monthly mean reanalysis CDS data to be used: waves and winds from ERA5 and currents from ORAS4 (or ORAS5 if available).
   2. The mean monthly currents data is given as the u- and v-component values for each month, therefore the mean current direction derived from these values will be valid as the monthly mean direction.
   3. For algorithm prototyping, the mean monthly wind u- and v-component values are being used from ERA-Interim, and mean wind direction can be derived in the same way as for currents. In case the ERA5 data to be used for operationalization does not contain monthly averages, but rather hourly or 6 hourly data of u- and v-components of wind, then the u- and v-components will be averaged separately over the month; subsequently these single values of u- and v-component for the month will be used to calculate mean wind speed and mean wind direction through the trigonometry functions.
   4. For algorithm prototyping, the mean monthly wave direction values are being used from ERA-Interim. In case the ERA5 data to be used for operationalization does not contain monthly averages, but rather hourly or 6 hourly data of mean wave direction, then a new strategy has to be devised. The prevailing wave direction can be used by finding the median value from all the wave direction measurements in each month.
2. Select ship type
   1. The min and max speed of ship will be picked from the pre-defined speed profile; average speed will be calculated from these values
   2. The average speed will determine the expected ETA
3. ETA margin; there should be two options for the user:
   1. Optimize without any ETA margin (strict ETA)
   2. Optimize with ETA margin:
      • For ferry/cruise ships:fixed margin of 2 hours
      • For all other ship types:fixed margin of 10 % of expected ETA
4. DIRECT optimization parameters:
   1. Max no. of iterations (maxits) should be set as 8000
   2. Max no. of functions evaluations (maxevals) should be set as 60000
   3. Max rectangle divisions (maxdeep) should be set as 10000
   4. Time resolution (time points of metocean data); monthly mean data to be replicated at every point in 3D matrix or to be used as fixed data in 2D matrix. If the sub- waypoints are defined by distance, then the time resolution is immaterial, as the metocean data would be used for each sub-waypoint, whatever the time interval is between them.
   5. The no. of sampling points during TimeStep (npoints) should be set in such a manner that there is an optimization sub-waypoint at every 100 km. This can also be set simply as allocating distance-based sub-waypoints to the optimizer system.

Output parameters

• Waypoints of the optimized route: Latitude and longitude values
• Speed profiles for the optimized route: Ship speed in knots, entrance speed at each waypoint
• ETA profiles for the optimized route: ETA values in hours at each waypoint
• Minimized shaft power for the optimized route
• Optimized fuel consumption: Total fuel consumption (kg / tons) for the optimized route
• Fuel savings percentage

Visualization (essential)

• The reference fixed route should always be displayed on the map, before and after optimization
• After optimization is successful, the optimized route should be displayed on the map as well (color
• / legend will differentiate the original and optimized routes).
• Shaft power: Since the optimizer is based on fixed shaft power, therefore shaft power values for original and optimized routes should be displayed as well.
• Total fuel consumption: Show numbers of total fuel consumption for fixed route, total fuel consumption for optimized route, and % of fuel savings
• Show as a graph peed profiles for the optimized route: Ship speed in knots, entrance speed at each waypoint
• ETA profiles for the optimized route: ETA values in hours at each waypoint (and also the achieved ETA for optimized route)
• CDS data: For monthly mean data usage, we should give the user the option to turn on/off layers displaying the various metocean datasets like SWH, wind, currents. There should be one map, with various layer options. This display can also be done in carousel form
• Optimizer result comparisons: The user should be given some options to do comparative analysis of optimization depending on CDS data. This comparison should be of different optimizations of the same route, and not between different routes. The user should be able to take a fixed route, then analyze and compare what would be optimized route for let's say Jan. 1999, and Jan. 2010, or Jan. 1999 and June 1999, or analyze how the optimized route changes from June 2001 consecutively to June 2005, etc. This should be effectively just plotting multiple optimized route on the same map with legend labels (color / line type) specifying them (adding more optimized routes from different months to a plot like Fig. 2), and displaying the respective parameters specified above for each route. The comparative analysis option can be given for up to 5 choices.

Visualization (optional)

• We can also display the same features of visualization like used for FCM operational indicator, i.e. display contribution of met-ocean conditions to ship resistance for both fixed and optimized routes. This will help the interacting user also understand a bit which metocean parameter is contributing more towards the optimization.
• Aggregates by month for a fixed route: Take the mean over all the years for each month, and display a bar / line graph with months on x-axis and % of fuel savings on y-axis. This will show the user which month gives the most % fuel savings for optimization.

Implementation support

Extensive technical correspondence with implementing partners BOPEN to support them in implementation of the route optimization system, answering technical queries, providing diagnostic datasets, etc. Some bugs / issues were identified with the product definition, which have been largely corrected.

Ongoing / future tasks

• Implementation support to BOPEN
• Testing & validation of the implemented code
• Provide wind / wave monthly mean direction definition / ingestion
• Provide fix for velocity jumps issue
• Provide more information regarding maxf (function evaluations) threshold
• Implement land constraint if needed and feasible

Route Cost Performance Speed

Slow steaming practices

Slow steaming is a practice mostly employed by transoceanic cargo ships, bulk carriers, tankers and in particular container ships, to sail at a reduced speed compared to the ship and engine design speed. This practice has arisen in the past due to the rapid increase of fuel costs: reducing the cruise speed of a vessel results in a significant reduction in the required engine power due to the non-linear relation between speed and power needs. Slow steaming is a strategy that could potentially be implemented during certain seasons of strongly adverse weather where historically the waves/winds are particularly "rough". In these circumstances of heavy metocean conditions, reducing the ship's speed will have an even larger impact on the power needs. A rough general estimate is that with 10% reduction in vessel speed, there is a 15% to 20% reduction in fuel consumption and emissions. In addition to fuel savings, slow steaming practice also significantly reduces the emissions of Greenhouse Gasses and other pollutants such as NOx, SOx and fine Particle Matters (PM10, PM5, PM2.5).

In most cases when a ship is not operated in slow steaming mode for an entire voyage, slow steaming is nonetheless used towards the end of a ship's route. The idea is to first sail full speed and cover a large portion of the journey in the shortest time possible for creating an arrival time buffer. After this, greatly slowing down is considered acceptable and "safe" for the remaining distance and estimated time of arrival.

Route cost performance speed indicator

Given that the shipping industry is not optimally using the savings potential of slow steaming, providing it with more insight into voyage duration and potential fuel savings due to slow steaming, as well as when and where such potential savings are higher and lower, it is anticipated that the slow steaming practice will become more widely adopted with increased use frequency and better implementation along an entire voyage.

Therefore, the "Route Cost Performance Speed" operational indicator has been defined for the C3S for Global Shipping Service. This indicator will provide the users of the service insight into the effects on fuel savings and voyage duration when practicing slow steaming (instead of full steaming) along any of the service's pre-defined 80+ routes and this during different times of the year with associated metocean conditions, and for different engine load profiles. The indicator will be available for containership, bulk carrier and tanker ship types, as these are the types of vessels that are most likely to use slow steaming.

Specific Fuel Oil Consumption Model (SFOC)

According to a web survey conducted within the shipping industry relevant to the slow steaming practice, the use of engine loads between 30 – 50 % was most prevalent (Man Diesel, 2012). However, an assessment on specific fuel consumption in relation to engine load by Jalkanen et al. (2012) found that the typical two-stroke engines achieve their highest fuel efficiency for engine loads within the range of 70% to 80% of their maximum capacity.

Most of the available literature shows the use of a constant SFOC and instantaneous engine power for calculation of fuel consumption, resulting in a linear relationship between fuel consumption and engine power. The same study by Jalkanen et al., (2012), done on the engines from Caterpillar, MAN and Wartsila, concluded that the SFOC is a non-linear function of engine load and, with minimum fuel oil consumption at a specific engine load from 70% to 80%.

Using regression analysis of the comprehensive SFOC-measurement data from Wartsila, Jalkanen et al. (2012) derived a second-degree polynomial equation for the relative SFOC w.r.t. engine load, which will be used in the indicator calculations. With minimal differences between engine types, a single parabolic function is applied to all engine types potentially installed per different ship types.

Calculations by the SFOC model are as follows:

• First, the engine load (EL) is determined based on one main engine: 

  \[ EL = \frac{P}{P_{MCR}} \quad (3) \]

  where

EL = Engine Load (Range from 0.1 to 1.0)

P = Ship power (unit: kW)

PMCR = Max Continuous Rating of one installed engine (unit: kW). The PMCR value depends on the chosen ship type and associated engine, and can be obtained from major engine manufacturers' datasheets such as MAN-Diesel and Wartsila.

• Then the second-degree polynomial equation is used to calculate the relative SFOC: 

  \[ SFOC_{Relative}=0.445EL^2-0.71EL+1.28 \quad (4) \]

  where  \( SFOC_{Relative} = Relative SFOC (g.kW/hr) \)

• Finally, for calculating fuel consumption, the Fuel Consumption Model (FCM) is used with the SFOC set equal to: 

where

SFOC = Specific Fuel Oil Consumption (g.kW/hr)

SFCO_base = Base value for SFOC that is a constant for each engine (g.kW/hr)

With the correct SFOC for each ship type, a more accurate estimation of fuel consumption is achieved together with a better understanding of the relationship between Engine Load, Shaft Power and change in fuel consumption with a change in these parameters. The SFOC model also clearly shows for which Engine Load engine operations is most efficient or in other words provides optimal fuel consumption. Table 2 illustrates these parameters for the Panama container ship type.

Indicator implementation

The purpose of the Route Cost Performance Speed Indicator is to help the user determine their optimal Slow Steaming regime for their specific vessel type. With reduced engine load the ship will not only consume less fuel, but will also sail slower and thus need more time to make the same crossing; the user therefore needs to balance desired fuel savings with increased sailing time. Further complexity is added by the effect of the metocean conditions on the slow steaming operations on different route and during different months of the year. The Route Cost Performance Speed Indicator will help the users to make informed decisions on desired sailing mode and associated expected outcome with regards to sail time and fuel consumption.

Table 2: An example of Panama container ship of how slow steaming is defined.

Input parameters

• Route parameters
  • Route with waypoints and start / end points (chosen from list of fixed routes)
  • No. of waypoints
  • Year of sailing
• Ship parameters
  • Ship type (to be selected from list of ship types)
  • Max ship speed (kts) (depending on chosen ship type)
  • Min ship speed (kts) (depending on chosen ship type)
  • Average ship speed (kts) (depending on chosen ship type as it is calculated as: (min_speed + max_speed) / 2).
• SFOC model
  • Engine Load factor selected from a range between 0.1 to 1.0 with 0.05 interval.
• Fuel Consumption Model (FCM)
  • Given that the indicator needs the fuel consumption model to generate the outputs relevant to slow steaming practices, the CDS metocean parameters needed as input are given below in Table 3.
  • The FCM obtains the correct SFOC value from SFOC model

Table 3: CDS metocean parameters and their data sources

Algorithm implementation

A step-wise description is given below to facilitate implementation into the CDS service:

1. Initial inputs needed to start the algorithm are a choice of ship type, an engine load, a specific route and a year in which the route is sailed. All these parameters will come from user inputs chosen from a drop-down list.
2. The user choice of ship type will allow for the system to automatically extract the correct SFOCBase and PMCR values per ship type that are available in the system database
3. Using the inputs from step 1 and 2, the shaft Power is computed by using eqn. 3.
4. Simultaneously and using the same Engine Load input from step 1, eqn. 4 is used to calculate SFOCRelative.
5. Then, the output from step 4 is used together with SFOCBase from step 2 in eq. 5 to calculate actual SFOC.
6. The chosen route from step 1 comes from a list of 80+ predefined routes which in combination with the chosen year of sailing (step 1) allows for the selection of corresponding metocean conditions. These data are obtained from the CDS according to the parameters given in Error! Reference source not found..
7. Outputs from step 3 and step 4 together with the metocean conditions from step 6 are used in the FCM to calculate fuel consumption, speed profiles and ETA for each one of the twelve months of the chosen year.
8. In parallel, the algorithm will make the same exact run as described above for an additional standard engine load of 1.0 (maximum) and of 0.8 (optimal).
9. Based on the outputs generated by the calculations for the three engine loads (1.0, 0.8, user chosen) three graphs are generated, plotting ETA, fuel consumption and average speed against all months of the chosen year for the three engine loads.

Output parameters    

• • • • Monthly Voyage duration profiles: average voyage time duration in hours per month.
      • Monthly Total Fuel cost profiles: average total fuel consumption (kg / tons) per month.
      • Monthly Speed profiles: average speed in (m/s) per month.

Output visualization

The user should have an overview of the average fuel cost, average voyage duration and average speeds of a route for different months of a specific year at three different engine loads. The best way of visualizing this data is to plot it in a line graph. Examples are given below in Fig. 9, 10, and 11 for all three parameters for a panama container ship type, for the route Bimini Island to Bishop Rock, with the year selected to be 2015 and a chosen engine load of 0.65.
From the plots below, it can be seen that the different engine loads are not always equally affected by the different metocean conditions for the different months of the year. Error! Reference source not found. for example shows the most prominent differences, where ETA at an EL of 1.0 is hardly affected throughout the year while for an EL of 0.65 the impact is more pronounced. A similar observation can be made for fuel consumption in Error! Reference source not found. but not for average speed in Error! Reference source not found..

Figure 9: Comparison of average speed vs months for EL factor of 0.6, 0.8, and 1.0. 

Figure 10: Comparison of voyage duration vs months for EL factor of 0.65, 0.8, and 1.0. 

Figure 11: Comparison of fuel consumption vs months for EL factor of 0.65, 0.8, and 1.0. 

Route ETA Variation

This indicator is intended to show to the end-users the difference in average sailing time they will experience when sailing certain pre-defined routes at different months of the year, both according to the climatological average and the seasonal forecast of metocean conditions. It will show which parts of the routes cause delay and which cause a speed-up by linking route sections to their metocean conditions and generating a speed profile. Average sail times will be calculated for several standard ship types sailing with a predefined shaft power that is equal to the shaft power needed for sailing at its maximum design speed in calm water. This way it will also be possible to display the speed variations of the ship along different route sections as it encounters different metocean conditions.

The presence of wind, current and waves play a major role in governing the ship's speed variation and transit time on different routes. Especially, depending upon the direction of the waves, the sailing time may increase or decrease on a particular route. For example, if a ship encounters head on waves (waves that strike the vessel at its bow section) along its route, the additional resistance caused due to such waves may inhibit the ship's speed, thus the estimated time of arrival (ETA) to the desired port may be delayed. Head waves render maximum loss of speed to a ship, the beam and quartering seas also cause speed loss but with lesser intensities than head waves. On the other hand, if a ship travels in a route where there are following waves (waves aligned along the ship's transit direction), the speed of the ship may increase due to the contribution from waves, thereby the sailing time may decrease. Thus, the degree of variation of speed and consequent ETA of a ship varies greatly on a route depending on the direction of waves in different seasons of a year. Similarly, the windward direction and influence of currents also affect the ship's speed to a considerable extent.
The core idea behind the route ETA variation indicator is to assess the difference in the ship's sailing time and speed variations owing to metocean conditions in different route sections. In the first place, using ship's design speed, the shaft power in calm water is determined, which is then used to estimate ship's speed in presence of wind, wave and currents. Based on the results, the ship's speed and ETA variations in a route can be predicted.

Finally, the results obtained from the calm water and metocean conditions can be compared, using which the speed and ETA variation on different routes can be studied. For example, if the speed of ship inclusive of metocean conditions is lesser than its speed in calm water. it can be deduced that the metocean conditions restrains the ship's speed and as a result the time of arrival will be prolonged. The magnitude of difference between the two speeds varies with respect to wind, current and wave directionality and it will be maximum for head on wind and waves. Suppose if the speed of the ship in presence of metocean conditions are higher than the calm water speed, it is inferred that the metocean parameters aid in the speedy travel of the ship, consequently the transit time is shortened. Also, the speed and ETA variations on a route in different time periods, can also be predicted using this indicator.

Indicator implementation plan

A flowchart depicting the implementation plan is shown below in Fig. 12. The full detail of the implementation is given in the Product Definition Document for this indicator, which is included in Appendix C for reference.

Figure 12: Flowchart showing Route ETA Variation implementation procedure 

Indicator visualization plan

Visualization (essential)

• Speed profiles in calm water and metocean conditions should be represented in line plots for any desired month with speed on Y-axis and waypoints on X-axis: Entrance ship speed at each waypoint in knots.
• Sailing Time: The total sailing time in calm water and metocean conditions can be depicted using a bar plot with time in hours along the X-axis.
• ETA profiles: ETA values in hours at each waypoint. For this, route with way points must be shown on a map, and the ETA values can be displayed above each way point. Two such maps can be presented one for ETA in calm water conditions and another for ETA including metocean conditions.
• Route ETA variations in different time periods due to metocean conditions: Since, the direction and intensity of metocean parameters changes with respect to months and years. The users should be given some options to do comparative analysis on changes in ETA in various seasons depending on CDS data. This comparison should be of different runs on the same route, and not between different routes. The user should be able to take a fixed route, then analyze and compare what would be the ETA variation for let's say Jan. 1999, and Jan. 2010, or Jan. 1999 and June 1999, or analyze how the route ETA changes from June 2001 consecutively to June 2005, etc. This should be effectively performed just by plotting multiple maps with ETA profiles for different time periods on the same route, displaying the parameters (month and year) for each map. Usually, this is done only for the ship's ETA in presence of waves, winds & currents and not for the calm water conditions, as the metocean conditions changes with respect to different time periods. In this way, the ETA variations along the same route in different months or years can be analysed. The comparative analysis option can be given for up to 5 choices.

Sample runs have been run and the first two plots proposed in the essential visualisation section are shown below as example plots. These trial runs have been conducted for product tankers on the route between Bimini islands and Bishop rock points. Figure 13 depicts the ship's speed variations in calm water and metocean conditions for four different months in a year. The calm water speed will be the same irrespective of the month, but the speed in metocean conditions will vary. The second plot in Figure 14 presents the variations in ETA comparing the ship's transit duration in calm water and in presence of metocean conditions. These two plots can be generated for any desired months.

Figure 13: Ship speed variations due to metocean conditions in different months 

Figure 14: ETA variation due to metocean conditions in the month of June

Visualization (optional)

• The variation of ETA profiles on different months can also be shown using bar charts with time in hours on X-axis and month, year along Y-axis.
• The ETA on destination point can be represented using a bubble chart with time axis along X- direction. The dimensions along X-axis can be in hours. Two bubbles signifying ETA in calm water and metocean conditions so that the ETA variation can be pictorially displayed from the location of bubbles above the time axis

An example plot is shown in Fig. 15 below, representing the first visualization option proposed here. Fig. 15 compares the ETA changes for different months in presence of metocean conditions. Same test conditions are chosen as for Sec. 5.2.1. In this plot, ETA variations for four different months are shown, however this limit on the number of months can be extended based on user's choice.

Figure 15: ETA variations in different months due to metocean conditions

Arctic Sailing Cost

Due to the global warming and the continuous shrinking of Arctic sea ice, maritime transport in the Arctic region has been increased dramatically since early 2000s. For the Arctic shipping, the so-called Northeast Passage (NEP) from Pacific to the Northern Atlantic, along the Norwegian and Russian Arctic coasts is considered as the most practicable routes in the future shipping (Farre et al., 2014). For shipping between Europe and Northeast Asia, the NEP has the potential to shorten the distance up to approximately 40% compared to Suez Canal (Schøyen & Bråthen, 2011). While the safety and economic benefits are the two important factors to affect the popularity of the Arctic shipping. Owing to the reduced sailing distance, the NEP could potentially help to lower fuel consumption and overall operational cost, leading to more frequent shipping operations and reshape maritime transport geography (Theocharis et al., 2018). Hence, a reasonable economic/cost assessment regarding the actual benefits for the Arctic shipping could be an important factor to affect the NEP exploration for commercial transits. Driven by the potentiality, this study presents a systematic approach of cost evaluation to study the economic feasibility for Arctic NEP shipping till the end of this century using sea ice conditions, which obtained by an innovative method to integrate both historical and long- term projected ice conditions. In this method, the most skilful Coupled Model Intercomparison Project Phase 5 (CMIP5) climate projection models are selected to construct prediction data for ice concentration and thickness. Since the direct interpolation of model data to geographical points along routes has the drawback of using very limited information from the climate models, the evaluation routes are divided into several sections where average sea ice conditions are calculated from a larger geographic region. The hindcast data from e.g., ECMWF is used to develop the correlation between regional sea ice area and local ice concentration, to determine the ice concentration in each section based on CMIP5 models using reanalysis data. Due to the limited amount of observations for the sea ice thickness, the data from CMIP5 models are directly interpolated and thickness statistic is

calculated in the same route section as the concentration estimation. The sea ice concentration, thickness is validated by history data from ERA-Interim, Envisat and CryoSat-2 missions in the Climate Data Store (CDS), respectively. The obtained sea ice conditions are used to estimate the actual cost and sailing strategies for practical shipping navigation. In the economic assessment of Arctic shipping routes, the requisite for icebreaker, sailing speed, etc., are more specifically rest on the sea ice conditions and ship ice-class. The total cost indictor is eventually evaluated with some recommendations for future ship construction and navigation guideline.

Input data

The CDS input data, and associated ship parameters data for the cost analysis, and ship operational cost data, which are needed for the arctic cost indictor, are described below.

Raw metocean data

The CDS data being used for this indicator is listed in Table 4. No external data is being used at this time.

Table 4: CDS raw input data

Ship parameter data

For this indicator, we only take into account a handysize bulk carrier as an example for the cost analysis. It means that the ship parameters and the corresponding operational cost listed in the following Sec 6.1.3 are specially for this specific ship size.

Ship operational cost

The following operational cost will be included in the operational cost:

• • • • Insurance cost: 500 usd/day
      • Ship renting cost: 40kusd/day
      • Crew cost (including wages, social benefits, entertainments,…) 6kusd/day
      • Fuel cost will be the propulsion fuel cost that overtake the resistance from calm water, wind, wave, and in particular, ice. It should be noted that since in the climate projection data does not contain the wave and wind information, the resistance caused by wind and wave will be neglected in the calculation. This is reasonable in the sense that the ice induced resistance should be much higher than waves. It leads to the fact that the wave

resistance can be neglected. Normally, the wind resistance is only around 10% of wave induced resistance. Hence, it is reasonable to be neglected as well.

Detailed algorithm implementation

Input parameters

• Load Ice (MetOcean) data from CMIP-5 model data, since the whole NSR is divided into 6 sections, in this code, the following parameters are need (note that the section id is based on the arctic route availability indicator):
  • NSR Section id
  • Decade (10, 20, 30 years unit)
  • Month
• Ice class limit parameters (For each ice condition, which types of ice class ship can be navigated in the ice condition independently):
  • Ice thickness
  • Ice concentration factor
  • Ice year: ice age is not available in the CMIP5 data, we will relate the ice age data with ice thickness, i.e., the thicker of ice thickness, the old of the ice age. In this case, if the ice thickness is thicker than 1.8 meters, it will be regarded as the second or multi-year ice.
• Icebreaker_support_need (this function is to check if the ship can navigation independently or she should be navigated/escorted under the help an ice-breaker)
  • Ice class: A ship's ice class type. The definition of ice class is based on the Russian ice class code, which can be seen from a separate document.
  • Ice class limit: This is computed based on the ice conditions, which types of ice class ships can be navigated independently.
  • Speed_max: For the inputted ice condition and the ship class, what is the maximumly allowed ship speed.
• Get fuel consumption parameters: In this part, it contains 5 sub-functions, where 3 of them are considered in the previous calm water and added resistance analysis, i.e., within the code ship_behaviour_validation.py. In this case, all inputs related to the calm water, wind and wave resistance are the same as in the ship_behaviour_validation.py function. In the following, we only list the parameters for the propulsion efficiency and ice resistance calculation. (It should be noted that in the ship_behaviour_validation.py code, you are using the xarray as input; while in the ice resistance and propulsion efficiency calculation, we are using the simple list or np.array):
  • ship_behaviour_validation inputs from previous implementation.
  • Propulsion coefficient: ship propulsion parameters, ship speed
  • Ice resistance: ship parameters (in addition to those similar as the calm water and wave resistance calculation, some additional parameters for the ice resistance calculation are: ice friction factor against hull platin, stem angle, waterline entrance angle and flare angle that are given as constant in the code ), ship speed, ice thickness, ice concentration, ship draft
• Get the total sailing cost
  • Sailing time at specific sections
  • Fuel cost

Output parameters

• Arctic sailing cost at various sections
• The costs are estimated in terms of various projected decades and various months
• Further, the cost can be also categorized into fuel costs and other operational cost, which may allow for assessment of various business models for Arctic shipping

Description of major Python code files

• Main.py: Main driver code file, which runs the whole algorithm.
• Ship_behaviour_validation.py: This is the simple repeated code for the previous calm water, wind and wave resistance part
• load_ice_data: In this section, we need to load the MetOcean data, including ice thickness, ice concentration, ice age, wind and wave conditions from the CMIP5 product
• ice_class_limit: With the ice conditions as input, this function will compute for certain ice conditions, which ice classed ships can be navigated independently in the provided ice conditions, as well as the maximumly allowed ship sailing speed.
• prop_coeff.py: It compute various propulsion efficiency that determine the shaft power from the effective power, that are directly obtained from the total ship resistance.

Description of important variables

The main work is to estimate a ship’s ice resistance at various ice conditions, i.e., level ice condition with ice concentration of 100%; clashed ice conditions of ice concentration among [0.5, 0.95], which are caused by either ice breaking or not serious ice freezing seasons;  and less severe ice conditions of ice concentration less than 0.5, which is treated as open sea navigation but with limited sailing speed. It should be noted that for the second scenarios of clashed ice navigation, there is no existing theoretical models to get reliable and validated results. Hence, after consulting some ice research experts and open literature, we have made the following assumptions: 

• R_ICE: added resistance due to ice o
  • Lindqvist: A straightforward method for calculation of ice resistance of ships (Lindqvist, 1989). The formula has its limitation due to that it works for the level ice resistance for independent ship navigation (ice breaking). A ship’s ice resistance is composed of three components:
  • R_b: ice breaking component
  • R_c: ice crushing component
  • R_s: ice submergence component 

For case, an ice class needed ice breaker assistance, i.e., escorted ship sailing with 100% concentration (the Channel ice resistance proposed by Riska et al. (1997) is used). For case with ice concentration less than 75%, only R_s is considered in ice resistance calculation. The ice thickness is estimated using equivalent ice thickness proposed by Kenneth Eik (2011).

Algorithm implementation

The overall conceptual framework of the system is shown in Fig. 16.

Figure 16: Conceptual framework of the arctic cost analysis 

The step-wise pseudo-code description is given below. The Python code itself is extensively commented, and will serve as support as well.

1. Generate the NSR and discrete into various waypoints (available from C3S added resistance analysis)
2. For each waypoint, get the necessary Ice and sea conditions (available from CMIP5 model for the arctic sailing availability indicator)
3. For the generated route with provided sea/ice conditions, estimate the fuel cost (see right figure)
   • Based on the sea/ice conditions of each waypoint, check if ice breaker is needed
   • Based on a ship's service speed and ice condition, select suitable sailing speed
   • Based on the weather conditions, estimate the total resistance, which includes, calm water and ice resistance
   • Estimate the sailing time, and the total effective power consumption
   • Estimate the ship's propulsion coefficient to get the consumed power during the selected NSR

Use of Seasonal Forecast

There is no seasonal forecast data available for currents, while there is only test data for waves seasonal forecast. The only seasonal forecast data available is for winds. Wind is the least important factor in naval architecture and ship operations, especially for the defined operational indicators which utilize the metocean conditions of wind, waves, and currents. Therefore, due to the lack of availability of seasonal forecast data for operationalization, we present here only a prototype implementation plan for utilization of wind and wave seasonal forecast data for the Fuel Consumption Model (FCM) operational indicator.

The seasonal forecast is delivered as an "anomaly" w.r.t. to the past forecasts. These forecast anomalies need to be calibrated by adding them to the reanalysis measurements; this is especially relevant as often the forecast anomaly can be similar in scale to the forecast model bias. The choice of hindcast calibration period will affect the absolute calibration of forecast anomalies, and the calibration period will be selected in consultation with CNR. Once the seasonal forecast data is calibrated, then for ingestion and use into an operational indicator, it can be used in the same manner as reanalysis data.
It is to be noted there that the FCM model itself has already been validated as a correct model with reanalysis data (see Sec. 2 of this document).

However, since climate modeling on the monthly and longer time scales cannot be deterministic and is only probabilistic, it is important to perform the skill quantification of the operational indicator when seasonal forecast data is used. We follow the recommendation from CNR in the deliverable C3S_D422_Lot1.OSM.2.4(2)Scientific_Indicators(MetOcean)_Technical_Note_v1 to utilize the multi-category Ranked Probability Score (RPS) and Ranked Probability Skill Score (RPSS) parameters for calculation of the skill. These skill parameters will assess the operational indicator skill for seasonal forecast data, against the operational indicator calculations performed using reanalysis data. The step-by-step procedure is outlined in D2.4(2).
After skill calculation, some regions and / or time periods may be identified where the skill is too low. These areas or time frames will either be then excluded from analysis, or a specified warning / info note will be displayed with these results of the FCM.

Summary

This document presents an overview of the status of the operational indicators for the C3S for Global Shipping project and developments done in the last 3 months since delivery of C3S_D422Lot1.OSM.2.6(2)_201808_Operational_Indicators_Technical_Note_v1 (Period 31 August - 01 November). This document describes the final phases of operational indicator definition and validation, while the definition and description of three new indicators has also been added.

The mean added resistance in the fuel consumption model has now been validated, and also the shaft power calculations of the full FCM have been validated against ship-log measurements. The detailed implementation and visualization plan for Route Cost ETA has been presented. A brief prototype workplan for calculation of the FCM with seasonal forecast data has been given.
Three new operational indicators of Route Cost Performance Speed, Route ETA Variation, and Arctic Sailing Cost have been defined in this document, and are ready for transition into the implementation phase of the service.

Appendices (Not available)

Appendix A – Route Cost ETA Product Definition Document (Implementation)

The Product Definition Document (Implementation) for Route Cost ETA is given as Appendix A.

Appendix B – Route Cost ETA Product Definition Document (Validation)

The Product Definition Document (Validation) for Route Cost ETA is given as Appendix B.

Appendix C – Route Cost Performance Speed Product Definition Document

The Product Definition Document for Route Cost Performance Speed is given as Appendix C.

Appendix D – Route ETA Variation Product Definition Document

The Product Definition Document for Route ETA Variation is given as Appendix C.

Appendix E – Code for Mean Added Resistance

The Python code files for Arctic Sailing Cost ETA are delivered in the form of a zip archive datafile together with this document. Filename "AppendixD_Code_MeanAddedResistance"

Appendix F – Code for Fuel Consumption Model Validation

The MATLAB and Python code files used for the FCM shaft power validation with historical ship-log data are delivered in the form of a zip archive datafile together with this document. Filename "AppendixE_Code_FCMValidation"

Appendix G – Code for Route Cost ETA

The updated MATLAB code files for Route cost ETA are delivered in the form of a zip archive datafile together with this document. Filename "AppendixF_Code_RouteCostETA"

Appendix H – Code for Arctic Sailing Cost

The Python code files for Arctic Sailing Cost ETA are delivered in the form of a zip archive datafile together with this document. Filename "AppendixG_Code_ArcticSailingCost"

References

Farré, A.B., Stephenson, S.R., Chen, L., Czub, M., Dai, Y., Demchev, D., Efimov, Y., Graczyk, P., Grythe,
H., Keil, K., Kivekäs, N., Kumar, N., Liu, N., Matelenok, I., Myksvoll, M., O'Leary, D., Olsen, J., Pavithran.A.P, S., Petersen, E., Raspotnik, A., Ryzhov, I., Solski, J., Suo, L., Troein, C., Valeeva, V., Rijckevorsel, J. van, & Wighting, J. (2014). Commercial Arctic shipping through the Northeast Passage: routes, resources, governance, technology, and infrastructure. Polar Geography, 37, 298–324.

Holtrop, J. & Mennen, G. G. J. (1982). An approximate power prediction method. International Shipbuilding Progress, 29(335): 166-171.
Jalkanen, J.-P., Johansson, L., Kukkonen, J., Brink, A., Kalli, J., & Stipa, T. (2012). Extension of an assessment model of ship traffic exhaust emissions for particulate matter and carbon monoxide. Atmospheric Chemistry and Physics, 12, pp. 2641-2659.

Lindqvist, G. (1989). A straightforward method for calculation of ice resistance of ships. Proceedings of 10h International Conference on Port and Ocean Engineering under Arctic Conditions (POAC), Lulea, Sweden, 12-16 June 1989, pp. 722-735.

Lu, R., Turan, O., Boulougouris, E., Banks, C., & Incecik, A. (2015). A semi-empirical ship operational performance prediction model for voyage optimization towards energy efficient shipping. Ocean Engineering, 110, 18-28.

Man Diesel (2012). Slow Streaming Practises in Global Shipping Industry, Copenhagen: Man Diesel & Turbo.

Kim, M., Hizir, O., Turan, O., Day, S., & Incecik, A. (2017). Estimation of added resistance and ship speed loss in a seaway. Ocean Engineering, 141(1), 465-476.

Pascoe, David. July. Dockside Reports. 2001 14. Accessed November 22, 2018. http://www.docksidereports.com/rough_water_seamanship_2.htm.

Riska, K., Wilhelmson, M., Englund, K., & Leiviska, T. (1997). Performance of merchant vessels in the Baltic. Research report no 52. Espoo: Helsinki University of Technology, Ship Laboratory, Winter Navigation Research Board.

Schøyen, H. & Bråthen, S. (2011). The Northern Sea Route versus the Suez Canal: cases from bulk shipping. Journal of Transport Geography, 19, 977–983.

Theocharis, D., Pettit, S., Rodrigues, V.S., & Haider, J. (2018). Arctic shipping: A systematic literature review of comparative studies. Journal of Transport Geography, 69, 112–128.
Copernicus Climate Change Service

Related articles

• Page:
  NEMO-ERSEM and POLCOMS-ERSEM: User Guides for Products (v1.21)
• Page:
  NEMO-ERSEM and POLCOMS-ERSEM: User Guides for Products (v1.1)
• Page:
  Summary indicators (Tier 1): Product User Guide
• Page:
  Risk indicators (Tier 3): Product User Guide
• Page:
  Loss indicators (Tier 3): Product User Guide

climate.copernicus.eu copernicus.eu ecmwf.int