Issued by: OSM / Sverre Dokken

Date: 31/05/2018 Ref:


Official reference number service contract: 2017/C3S_D422_Lot1_OSM/SC2

Table of Contents


This document forms deliverable D2.6 for the C3S for Global Shipping project and describes the development and progress of the operational indicators up to and including May 2018. The "operational indicators" are offered to the end-users via the C3S Global Shipping service that itself is being provided on ECMWF's CDS platform. They are data products delivering information relevant to the operational activities of the end-users. These products differentiate themselves from the other type of information products provided via the C3S Service, the so called "scientific indicators", in the sense they are a higher/second level product/derivation that is based either on the "scientific indicators" or directly on the CDS's available met-ocean data. These indicators were envisioned to be of direct interest to the end-users, allowing them to assess possible variations in cost/timing/routing/safety factors of their operations, whereas the "scientific indicators" form background information, indirectly used as the context within which end-users plan their operations.
Initial choices for the development and implementation of certain specific operational indicators and their envisioned operational use, were made following a three-day project meeting in Rome at the beginning of January 2018. During this meeting, the findings of the scope refinement process that had taken place during the initial three months of the project together with the feedback from ECMWF on the scope document and its presentation at Reading, were further analysed and discussed among the project members, emphasizing the inputs, comments and needs of the end-users. This resulted in a list of indicators that at the time of discussion were deemed meaningful, technically feasible and reachable within the allotted time-frame. However, since not all information on temporal, spatial and dynamic resolution of the input data nor the full availability of input data as well as envisioned validation data was known at the time of consolidating the indicators list, some priority shifts have taken place within the development strategy of the operational indicators. The following list of operational indicators are in order of development priority which is relative to the level of validity and meaningfulness of the indicator reachable with currently available data and algorithms:

  1. Fuel consumption model
  2. Route cost ETA (Estimated Time of Arrival)
  3. Route cost performance speed / STW (Speed Through Water)
  4. Route ETA variation
  5. Ice limits for different ship ice classes
  6. Availability of new Arctic routes
  7. Cost of new Arctic routes
  8. Risk of hull damage due to Structural Fatigue
  9. Risk of cargo loss
  10. Biofouling

From the list, the first seven indicators are expected to deliver high quality products for the C3S for Global Shipping service, with relatively high accuracy giving a high usability of these indicators to the shipping operations. The remaining three indicators have been found to be more difficult to produce and/or validate as a result of limited (or no) validation data and likely a too coarse spatial resolution of the input data leading to a coarsely gridded output that is likely less effective for shipping operations. Also, the algorithms that have been under investigation for their production are currently still in their basic stages, as these sub-fields of ship related research are still strongly experimental.
In this regard, we see the appearance of Biofouling at number 10, which was not part of the initial proposed list of operational indicators as was put forth in the 'Description of the Scope' document. We initially had not intended to commit to this indicator, however, as end-user interest grew in the past months and we managed to get into contact with Florida Institute of Technology, which are investigating this matter, we have increased hopes that we might be able to deliver a basic model for bio-fouling predictions. Therefore, we added it here to the list but it has to be kept in mind that we have less certainty as to the usability and actual feasibility of this indicator. Things are developing fast however and we foresee an incremental improvement of the accuracy and precision of the outputs of all basic algorithms as they will surely improve as their complexity increases in the coming years. Such improvements will likely come in parallel with an increased interest in these types of information by the end-users as they gradually discover the (limited but potential) benefits they can already gain from the currently coarse information outputs.
Another addition that has been made to the list that was not already mentioned in the 'Description of the Scope' document, is 'Route ETA Variations', for which we have good hopes that we will be able to deliver high quality and highly usable outputs, hence its position at number four. This indicator came up while developing certain other indicators for which we were in constant communication with the end-users, which in turn led to the realization that knowledge on the variation in route ETA for standard routes over the course of a year is very much appreciated by the end-users.
Project members OSM, ONL and GMS are primarily responsible for the first 4 of the non-experimental indicators, while the following two indicators, related to arctic sea ice, are under primary responsibility of project partner Chalmers. OSM, ONL and GMS are again responsible for the last three 'experimental' indicators. Some more information about the indicators and how they fit into the C3S for Global Shipping service is available in project deliverables "D1.1.1 Description of the Scope of the Service" (and its addendum, the 'vision document') and "D1.1.2 User Champions and Business Cases".
As a side note to the general evolution of the operational deliverables as described above, the distinction between scientific and operational indicators has also been influenced by their perceived foreseen use within the context of operational shipping, i.e. as important background info (scientific indicator) or as directly usable parameters (operational indicator). As the project continues, we have grown aware that different shipping operations and more importantly different types of end-users use different types of information in a different way. As such the distinction between the two is not as clear-cut as it initially seemed and therefore, some indicators that were identified as scientific indicators can in fact also be seen as operational indicators. Due to the initial division between the two, these scientific but operationally useable indicators are not described in this deliverable (or in any of the following versions of this deliverable) but they are described in deliverable "D2.4 Scientific Indicators (MetOcean) Technical Note" and its follow-ups.

Short description of indicators and their development

This document describes the development state of the two first listed operational indicators. The results shown here are preliminary and have not yet been validated. The other indicators are to be described in detail in the next iteration of this deliverable, foreseen in three months from the time of this delivery. Here we will describe in short what each indicator stands for and what their current state of development is and how we see their further development in the coming months. Later iterations of this deliverable will include detailed description of the remaining indicators and possibly updates on the currently described indicator.

  1. Fuel consumption model: This indicator is explained in further detail in section 2. Note that work on this indicator experienced some time lag due to its key developer having been lost from the project due to an unforeseen private matter. A replacement is being sought for and interviews have already been done as well as offers have been sent out to two candidates. One of those has already accepted and will become available already on the 11th of June. We are positive this delay can be minimised over the rest of the project
  2. Route cost ETA (Estimated Time of Arrival): This indicator is explained in further detail in section 3.
  3. Route cost performance speed / STW (Speed Through Water): This indicator will inform the end-user on the fuel and emission savings they will be able to obtain by having their ship sail at a reduced speed over a pre-defined route during different times of the year (note that we have pre-defined over 80 routes, coinciding with the world's most sailed trade routes). The indicator directly relates to the so-called "slow-steaming" practice, i.e. sailing at lower than maximum design speed, that is used in the shipping industry to save fuel costs. The end-user will be able to choose from a number of several discrete values and several standard ship types, the combination of which will determine the route cost as a function of metocean conditions with respect to the ship's normal/design speed. Development of this indicator will be based on the relation between a ship's speed through water and its power needs. For its further development we can heavily rely on the fuel consumption model and, with the latter well underway, it is foreseen that that this indicator will be the next in line to be developed and implemented.
  4. 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. It will show which parts of the routes cause delay and which cause a speed-up by linking route sections to the metocean conditions. Average sail times will be calculated for several standard ship types sailing with a 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. As such, like with route cost performance speed, also this indicator will be based on the relation between a ships speed through water and the effect of metocean conditions while keeping a constant shaft power. Therefore, we expect that this indicator will be further developed in parallel to the route cost performance speed.
  5. Ice limits for different ship ice classes: This indicator will display the geographical extend of different ice conditions that in effect create the boundaries which different ships with different ice classes may or may not sail within. Development of this indicator has started and it is clear that the input data that is needed, sea-ice thickness and sea-ice concentration, will be available. Good progress is expected over the next three months.
  6. Availability of new Arctic routes: This indicator is related to the previous one, but instead of looking at geographical boundaries, this indicator will provide information on the possibility of sailing along the NE and/or NW passage for ships with different ice class certification. For its current development state, several NE and NW passage routes have been defined. Further steps, linking these routes to the ice conditions, will be taken in the coming months.
  7. Cost of new Arctic routes: This indicator will determine the cost of sailing along the ice infested NE and NW passages for ships of different ice classes. Similarly as the previous indicator, we will use the concentration and thickness of sea-ice as input data for this indicator. In this case the ice conditions will be linked to the impact they will have on ship performance (speed, power need) which in turn will be linked to the fuel consumption via the fuel consumption model. In addition, we will investigate other costs that are associated with arctic voyages such as the cost of an ice-breaker or other escort vessels. This indicator is still in its initial stage of development. The largest issue for this indicator at the moment is to find data for linking the influence of ice conditions (i.e. sea ice resistance) to a ship's performance. Because of this, progress is momentarily slow but expected to pick up pace once the data is found since it is expected to benefit heavily from the development of the related operational indicators.
  8. Risk of hull damage due to structural fatigue: This indicator will give the probability of experiencing or accumulating significant hull stress for a ship in different areas of the world at different months throughout the year. As described in "D1.1.1 Description of the scope of the service - Operational Indicators", the development of this indicator will be based on linking certain metocean conditions to the occurrence of so called springing and/or whipping vibrational effects in ships, and this for several standard ship types with different dimensions and hull specifications. Development of this indicator is still in an early stage. This is due to the fact that until now we have been unsuccessful in obtaining the needed data for testing and validating the proposed method. A method in itself has been found to be available from literature, however, it is important to obtain ship load and stress measurements time-series for any testing and validation of the method (the needed metocean data is available from the CDS). At this stage we are in contact with DNV-GL (top world ranking classification society), since we know they have a working group executing related work on owners with hull stress devices in place. DNV-GL sees a lot of potential in providing structural fatigue risks (as well as cargo loss risk information, see next indicator) as they know there is nothing of the sorts available currently and they anticipate that exposure of end-users to even a basic implementation of this indicator will help develop the industry's interest and speed-up development in this area beyond its current experimental stage. Therefore, DNV-GL is open to provide contributions to the project where time permits. When it comes to providing the data we need, it is so that this data does not belong to DNV-GL themselves, but are the property of the individual shipping companies. These companies are not immediately keen on sharing their data if they do not see any value for them in doing so. As such, we are now investigating how to convince the shipping companies to share their data with us within the context of this project and for developing the indicator.
  9. Risk of cargo loss: This indicator will give the probability of experiencing cargo loss for container ships in different areas of the world at different months throughout the year. As described in "D1.1.1 Description of the scope of the service - Operational Indicators", the development of this indicator will be based on the 6-degrees of motion of a ship in relation to average and extreme metocean conditions for a few standard container ship types. Development of this indicator is still in an early stage due to the same reasons as described above for Damage risk due to structural hull fatigue. Also here we are looking for assistance from DNV-GL related to data sets they have indirect access to.
  10. Biofouling: This indicator will give the probability of experiencing increased bio-accumulation on the hull of a ship (resulting in fuel penalties and increased emissions) in different parts of the world for different months of the year. Development of this indicator is in an early stage as we are looking for a method that has predictive value and only needs a limited number of input parameters. Discussions have been ongoing with the Center for Corrosion and Biofouling Control, Florida Institute of Technology, Melbourne, FL, USA ( to deploy a simple method for biofouling risk calculation using the primary parameters of sea surface temperature, sea surface salinity, ocean colour and ocean currents (Dürr & Thomason, 2010). Discussions are advancing but some issues have recently arisen regarding IPR related concerns on the side of Florida Tech, complicated due to the fact that their research up to now has been done for the navy and thus is not easily/freely available. A common agreement is sought for and the issues will hopefully be resolved in the coming weeks. We expect to implement this indicator only at an experimental/basic level, primarily because the scale and resolution of the input datasets are not very well suited for defining a regional/local phenomenon such as biofouling. Also, it should be noted that biofouling was not promised as an indicator at the end of SC1, but is being taken up again due to a lot of interest from the end-users.

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 is developed for a few standard ship categories w.r.t. maritime operation and dimensions; these ship categories were selected after discussions with/input from the end-users.
Using known and well-established ship models from the literature and knowledge domain of naval architecture, the fuel consumption model was developed to calculate fuel/power consumption for each ship type. The model comprises two major modules: resistance due to calm water, and resistance due to met-ocean parameters.
The fuel consumption model is a self-standing model as well as an integral module as it forms the basis of many other operational indicators; such as Route cost ETA, Route cost performance speed, Route ETA variation, and Cost of new Arctic routes.

Input data

A total of 14 different standard ship types and categories are used in the calculations of the fuel consumption model; these are detailed in Table 1. The CDS data being used for development of this indicator is 6-hourly ocean waves and winds from ERA-Interim reanalysis, and monthly mean ocean currents reanalysis data from ORAS4.

Table 1: Standard Ship types used for the fuel consumption model

Ship Type

Size Category

L (Length) (m)

B (Breadth) (m)

T (Draught) (m)

Typical speed profiles (kts)


Product tanker




10 - 16





10 - 16





10 - 16

VLCC (Very Large Crude Carrier)




10 - 16


Small conventional prismatic deck




16 - 20

Small conventional spherical deck




16 - 20

Large conventional prismatic deck




16 - 20

Large conventional spherical deck




16 - 20

Bulk Carries

Handymax (same full as product tanker)




10 - 16

Container Ships


(10000 - 14500 TEU capacity)




20 - 25


(3001 - 5100 TEU capacity)




20 - 25


(1001 - 3001 TEU capacity)




18 - 23

Ferry/Cruise Ship

Ferry/Cruise ship




17 - 23

Car Carrier

Same hull as ferry, different wind coefficients




17 - 23

Method / algorithm description

The methods used are established and recommended methods in the field of naval architecture. The specifications from the ITTC (International Towing Tank Conference) and the Holtrop-Mennen method (Holtrop & Mennen, 1982; Holtrop, 1984) are used. ITTC is a voluntary association of international organizations that model the hydrodynamic performance of ships and marine installations. For wave-added resistance, the method of Liu et al. (2016) is used, and the WAFO toolbox is used for wave spectrum information during the development & testing phase. The model is implemented with the assumption of a ship sailing on fixed speed. As an intermediate step, the effective power requirement is calculated which is then converted to shaft power. The effect of currents is included as an additive/subtractive factor to maintain a constant SOG (speed over ground) for the ship. Only the effect of the tangential to ship current component is used, while the perpendicular component is ignored. To account for different fuel types that may be used on ships, the specific fuel oil consumption (SFOC) parameter is used. Specific fuel oil consumption is the measure of the mass of fuel consumed per unit of time to produce a KW; the marine engine efficiency is usually determined using the SFOC. The fuel consumption can then be calculated from the shaft power by simply a multiplication of the shaft power with the SFOC.

Results & discussion

An example of the calculation of intermediate quantities is shown in Figure 1, which depicts the wind coefficient behaviour for two categories of different sizes of the LNG ship type.
In its current form, the fuel consumption model results calculate the power requirement for a ship sailing at different fixed speeds. Examples of such calculations are shown below in Figure 2 and Figure 3, for container ships and tankers, respectively.
A demonstration of the fuel consumption model over a fixed route is given further down. The route selected for demonstration here is the fixed great circle route from Bimini Island (near East Coast of USA) to Bishop Rock (entrance to the English Channel), cf. Figure 4. The shaft power contributions for calm water and metocean parameters is shown in Figure 5 (for mean climatologies of January and July). The plots in Figure 5 are produced by BOPEN as part of the operational service. These types of calculations and visualizations will be performed for all fixed routes being used in the service, for different ship types. It should be noted that the results shown in this section are preliminary and have not yet been validated.

Figure 1: Wind coefficient of two categories of LNG ships of different size, varying with the angle of attack (i.e. the angle between a ship's true heading and the wind direction). Results shown are preliminary and not yet validated.    

Figure 2: Fuel consumption model calculations of power requirements for container ships. Results shown are preliminary and not yet validated. 

Figure 3: Fuel consumption model calculations of power requirements for tankers. Results shown are preliminary and not yet validated. 

Figure 4: Bimini Island to Bishop Rock great circle fixed route used for fuel consumption model example. Map plot produced from fixed routes created by BOPEN using Robinson projection. 

Figure 5: Shaft power requirements for calm water resistance and met-ocean parameter resistance for the Bimini Island to Bishop Rock great circle fixed route. The top figure is for January mean climatology values, and the bottom figure is for July mean climatology values. Notice the large difference in contribution of waves from January to July. The ship model used here is a product tanker sailing at a fixed speed of 16 knots. Both plots are produced by BOPEN as part of the operational service strategy. Results shown are preliminary and not yet validated. 

Further developments

The effect of wave directionality is not yet included in the fuel consumption model (only head waves are considered). It is a target for future upgrades to the system. Discussions are already underway on implementation (Lin et al., 2013).
The present implementation is with fixed ship speed, while in the next upgrades of the model, fixed shaft power will be considered.
The model will be integrated with seasonal forecast data in the future.

Route Cost ETA

A common requirement of most shipping operations is that the vessel has to arrive at a fixed ETA (Estimated Time of Arrival) at its destination port. 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. Thus, the goal of a sail planning system is to calculate the minimal constant shaft power required by the ship to arrive to its destination at a given ETA. To be able to do so, predictions about the sea states during the course of the journey are necessary (in addition to many other parameters and calculations). If we keep shaft power fixed, then ship speed will automatically vary due to the sea state and metocean parameters. The Route Cost ETA operational indicator aims to take the fixed great circle routes as reference, and then calculate an optimized route for the same departure and destination ports (holding the ETA time fixed), which use minimal constant shaft power, according to different met-ocean conditions (climatology / season forecast) at different times (monthly scale).
It should be noted that due to the low spatial (~50 km) and temporal (~monthly means for currents) resolutions of the CDS products of interest (waves, winds, currents), and due to the use of generic ship types, this indicator will NOT be a "route optimizing service" in terms of giving optimized route to a ship. Instead, it should be considered as a generic "representation" or "depiction" of the usefulness when sail planning takes into account the sea state. On the user end, the indicator will show the fuel/power cost of the fixed great circle route, and the fuel/power cost of the calculated optimal route for the specified time-frame and associated CDS metocean parameters.

Input data

Generally, currents, waves and winds are the important metocean parameters for sail planning and ship routing operations. The first version(s) of the indicator is (are) being developed using climatology data, which in a later phase will be expanded to involve seasonal forecast as well. Table 2 below describes the required and available metocean data from CDS for this indicator.

Table 2: CDS climatology metocean data to be used for Route Cost ETA indicator

MetOcean Parameter

Information available

Temporal resolution

Spatial resolution



Significant wave height (wind and waves combined)

6 hours

1° x 1°


Peak wave period

Directional wave spectrum


Eastward           wind speed

6 hours

1° x 1°


Northward wind speed

Currents (ORAS4)


Monthly mean

1° x 1°

The fixed monthly mean values will be replicated every 6 hours within the month to bring the data in synchronization with wave / wind data time steps

There is a limitation with the availability of currents data in the CDS climatology: only monthly mean currents are available. In the first stage of indicator development, these monthly means will be replicated every 6-hours to synchronize with the 6-hourly waves and winds data. Subsequently, we may use other sources of suitable currents data, as outlined in Table 3.

Table 3: Other sources of currents climatology data

Product name


Information available

Temporal range

Temporal resolution

Spatial resolution

Mercator Ocean GLORYS2V4 ocean reanalysis currents


Surface currents

1993 to 2015

Daily mean / Monthly mean

1/4° x 1/4°

AVISO gridded L4 reprocessed


Geostrophic surface currents

1993 to mid-2017


1/4° x 1/4°


Globcurent (soon available on

Geostrophic surface currents

1993 to now

Daily mean

1/4° x 1/4°

Ekman surface

3 hours

Total surface

3 hours

Both waves and wind parameters are available in the seasonal forecast, however currents information is not available. When using seasonal forecast in the indicator, we plan to replicate and use fixed climatology values as seasonal forecast. It should be noted that raw seasonal forecast data cannot be directly used, and should be used after analysis and validation through scientific indicators developed by project partners CNR and Chalmers.

Method / algorithm description

The DIRECT (DIviding RECTangles) optimization method will be used for route optimization. The algorithm is based on Lipschitzian optimization and the algorithm name reveals it is used to find an optimum solution (Jones et al., 1993; Liuzzi et al., 2010; Custódio & Madeira, 2015). The DIRECT optimization is a popular algorithm for aircraft route optimization (Bartholomew-Biggs et al., 2002; Wilson et al., 2009) and has recently been successfully adopted for ship route optimization (Larsson
& Simonsen, 2014; Larsson et al., 2015, Walther et al., 2016). Here, we follow the general approach used by Larsson & Simonsen (2014) for DIRECT sail planning optimization. The DIRECT method is open-source and as such is perfectly suited for implementation in the C3S Global Shipping service scenario. Numerically, the method has fast convergences and does not require a huge number of evaluations at each iteration step. Within convergence, the number of iterations determine the precision of the optimum solution. However, for route optimization, increasing the number of intermediate waypoints will rapidly increase its complexity and computational cost.
The DIRECT algorithm will take the metocean conditions, time steps, input route (start point, end point, and waypoints) as input along with ship characteristics, expected ETA, average ship speed, etc. The optimization object function will be the total fuel consumption, over which minimization is performed. The optimization variables are specified locations of the points along the route and the speed profiles for these journey legs. The output will be the new optimized route waypoints, total shaft power, and velocity profiles along the route segments. The fuel/power consumption can be directly calculated for standardized ship categories considering the extra impact of sea state (CDS) data. The conceptual framework of DIRECT route optimization is shown in Figure 6. The fuel consumption model described in Section 2 cannot be directly integrated with the DIRECT sail planning algorithm in its current iteration due to two different platforms being used for their development. At this time, a simplified fuel consumption model is being used, while at the time of service implementation, it will be replaced by the developed fuel consumption model.
The base DIRECT optimizer code is available as an open-source MATLAB code (Dan Finkel's MATLAB implementation: The first version implementation of DIRECT sail planning will be done in MATLAB, which will then be ported into Python later. The base DIRECT code exists in the public domain as a Python implementation known as the "scipydirect" package (
In its current version, the processing and visualization of this indicator will follow these steps:

  1. Pick a specific route from the library of fixed routes.
  2. Pick a specific month to analyze.
  3. Use the 6-hourly wind and waves data from mean climatology and the monthly means of currents over some wide, buffer, region around the fixed route (in terms of latitude and longitude)
  4. Calculate the optimal route with minimal route cost (minimal shaft power) for the chosen month.

For visualization, the reference fixed route will always be displayed, and the suggested optimal route for the selected month will be displayed on the map additionally. The fuel/power cost for both routes, and fuel/power savings in number and percentage for the optimized route (as compared to the reference great circle route) should also be displayed.

Figure 6:  Conceptual framework for DIRECT route optimization 

Preliminary processing & analysis

In the current version of the DIRECT sail optimization, the monthly mean values of climatology are used, which are replicated for route analysis every 6 hours.
Major time and resources have been spent on testing small sub-components of the code, understanding how the code works, and implementing necessary modifications/enhancements. Some of the major modifications/additions to the code have been:

  1. Replacing the proprietary fuel consumption model with a basic fuel consumption model for testing and analysis
  2. Adjusting the algorithm to use defined fixed routes as initial routes
  3. Adjusting the algorithm to work also with great circle routes instead of only rhumb line routes iv. Writing code to read and ingest CDS metocean data
  4. Modifying the plotting and visualization schemes

The following basic fuel consumption model is being utilized for testing and development purposes:

\[ P = V^{3.2} + 12.5 × H_s^3 × \left(\cos(\theta) + \frac{\pi}{T_Z} \right) + 0.5 × W^{1.5} × \left(\cos(2\theta) + \frac{\pi}{2T_Z} \right) \]

𝑃 = 𝑆ℎ𝑖𝑝 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 (𝑐𝑎𝑙𝑚 𝑤𝑎𝑡𝑒𝑟) 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 + 𝑊𝑎𝑣𝑒 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 + 𝑊𝑖𝑛𝑑 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛


P: ship power (unit: KW)

V: ship speed (unit: m/s)

Hs: significant wave height (unit:m)

Tz: mean wave period (unit: second)

θ: heading angles (unit: rads) W: wind speed (unit: m/s)

W: wind speed (unit: m/s)

The above basic model is valid for V ≤ 12 m/s,Hs ≤ 15 m, 4s < Tz <14s; and W < 30 m/s. However, in this case we apply the equation over all possible values. In addition, all heading angles are set to 0 in this first version of the algorithm.

For algorithm development and prototyping, the fixed great circle route from Bimini Island (near East Coast of USA) to Bishop Rock (Entrance to English Channel) is being used. This route is easy to analyse as it is based on the shortest distance over the curved surface of the Earth (great circle), and therefore the route optimizer effects are easier to understand. The route is shown in Figure 4 and the same route has been used for the fuel consumption model analysis (Section 2.3).

For initialization of the DIRECT sail planning method, a few parameters have to be specified. For current ongoing testing for the chosen route (Bimini Island to Bishop Rock), these are specified as follows:

i. ETA parameters:

Expected ETA (hours): 200
Allowance for late ETA, i.e. how many hours late may the ship be: 15

ii. Ship parameters:

Maximum ship speed (kts): 25
Minimum ship speed (kts): 8
Calculated Average speed (kts): 17.5

iii. DIRECT optimization parameters:

Maximum number of iterations: 200
Maximum number of function evaluations: 1500
Maximum rectangle divisions: 1000

Results from the DIRECT algorithm test runs are at a preliminary stage at this time. We plan to include significant developments and results for this indicator in the next iteration of this deliverable.

Further developments

The algorithm will be tested with various configurations of synthetic metocean fields, and in the next stage, CDS metocean data will be directly ingested for optimization. The algorithm will be customised to work with more routes in the system as well.
Going forward, constraints (such as ETA, land, strong weather avoidance) will be added through penalty functions. If a constraint is violated, the represented value will be multiplied with a penalty parameter leading to an increase in fuel consumption calculated through the object function.


This document presents an overview of the status of the operational indicators for the C3S for Global Shipping project. The complete updated list of operational indicators is given in section 1, followed by a discussion on the feasibility and value of different indicators to the maritime industry. Possible issues with input data and validation data are highlighted as well. For reference, the indicator definitions are also briefly mentioned.
The Fuel consumption/shaft power model operational indicator development, progress, and results are given in section 2. The model is in an advanced stage of development and is functional w.r.t. climatology datasets as input. The next step is to integrate the seasonal forecast datasets within this indicator.
The Route cost ETA indicator uses the DIRECT sail planning algorithm, which is described in detail in section 3. This indicator is undergoing code testing with actual routes, and CDS metocean data, however, testing results, as presented in this document, are at a preliminary stage and will be greatly expanded upon in the coming few weeks. Therefore, significant updates to this indicator are expected in the next iteration of this document.


Bartholomew-Biggs, M. C., Parkhurst, S. C., & Wilson, S. P. (2002). Using DIRECT to solve an aircraft routing problem. Computational Optimization and Applications, 21(3), 311-323.

Custódio, A. L. & Madeira, J. F. (2015). GLODS: Global and Local Optimization using Direct Search. Journal of Global Optimization, 62(1), 1-28.

Dürr, S. & Thomason, J. C. (eds.) (2010). Biofouling. Blackwell Publishing Ltd.

Holtrop, J. (1984). A statistical re-analysis of resistance and propulsion data. International Shipbuilding Progress, 31(363): 272-276.

Holtrop, J. & Mennen, G. G. J. (1982). An approximate power prediction method. International Shipbuilding Progress, 29(335): 166-171.

Jones, D. R., Perttunen, C. D., & Stuckman, B. E. (1993). Lipschitzian optimization without the Lipschitz constant. Journal of Optimization Theory & Applications, 79(1), 157-181. {+}[ |]

Larsson, E. & Simonsen, M. H. (2014), DIRECT weather routing. Master's thesis, Chalmers University of Technology, Gothenburg.

Larsson, E., Simonsen, M. H., & Mao, W. (2015). DIRECT optimization algorithm in weather routing of ships. Proceedings of the 25th International Offshore and Polar Engineering Conference, ISOPE-2015, Hawaii, USA, 21-26 June 2015.

Lin, Y.-H., Fang, M.-C., & Yeung, R. W. (2013). The optimization of ship weather-routing algorithm based on the composite influence of multi-dynamic elements. Applied Ocean Research, 43: 184-194.

Liu, S., Shang, B., Papanikolaou, A., & Bolbot, V. (2016). Improved formula for estimating added resistance of ships in engineering applications. Journal of Marine Science and Application, 15(4), 442451.

Liuzzi, G., Lucidi, S., & Piccialli, V. (2010). A DIRECT-based approach exploiting local minimizations for the solution of large-scale global optimization problems. Computational Optimization and Applications, 45(2), 353-375.

Walther, L., Rizvanolli, A., Wendebourg, M., & Jahn, C. (2016). Modeling and optimization algorithms in ship weather routing. International Journal of e-Navigation and Maritime Economy, 4, 31-45. {+}

Wilson, S., Bartholomew-Biggs, M., & Parkhurst, S. (2009). A global optimization approach to solve multi-aircraft routing problems. In L. Weigang & A. G. de Barros (eds), Computational Models, Software Engineering and Advanced Technologies in Air Transportation. Engineering Science Reference (IGI-Global), pp. 237-259.

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