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1. Introduction

This document forms the update and extension of deliverable D2.6 for the C3S for Global Shipping project and describes the development and progress of the operational indicators up to and including September 2018 (Previous update was up to May 2018). A detailed introduction is available in the previous update with deliverable title
"C3S_D422Lot1.OSM.2.6(2)_201805_Operational_Indicators_Technical_Note_v1"
Within the document presented here, updates and extended information are given to the RouteCostETA operational indicator and to the Fuel Consumption Model while new sections on Ice Limits for Different Ship Ice Classes and the Availability of New Arctic Routes have been added.
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:

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R_{aw2}= \frac{k \concos \alpha}{2 \omega_e}\int_L b'(x)V_{za}^2dx_b \quad (2)

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• Ship parameters: Draft, centre of gravity, longitudinal (x) coordinates and transverse (y) coordinates can all be obtained from Seaway once the modelling is done and be imported to the code.
• Heading: Heading range is from 0° to 180° with a 10° interval.
• Ship speed: Speed range is ship dependent with a 1 knot interval.
• Wave frequency: Frequency range varies depending on the ship model and one example is shown in Fig. 3; with each ship speed and heading, the code will look-up for 𝜂̂₃, 𝜂̂₅, 𝜙₃, 𝑎𝑛𝑑 𝜙₅.

All inputs are then used to calculate the total resistance transfer function and construct a look-up table in netcdf format for each ship type.

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• P = Calm Water Resistance + Wave Resistance + Wind Resistance • Metocean conditions:
  • SWH set to constant value of 9
  • Mean Wave Period set to constant value of 5 o Wave / Wind / Current directions set to 0 o Wind Speed set to constant value of 9 o Current magnitude set to 0
• DIRECT optimization parameters:
  • Max no. of iterations: 500 o Max no. of functions evaluations: 1500 o Max rectangle divisions: 1000
• ETA parameters:
  • Expected ETA (hours): 100
  • Allowance for late ETA, i.e. how many hours late the ship may be: 0
  • ETAPenalty: 5
• Ship parameters:
  • Max ship speed (kts): 50
  • Min ship speed (kts) (calculated): 20.01 o Average ship speed (kts) (calculated): 35.04 o Average fuel consumption (calculated): 180140 kg
• DIRECT optimization:
  • ETA result: 99.94
  • Minimized fuel consumption result: 433330 kg

3.2.3 Case 3 – Bimini Island to x (short route, more waypoints, no metocean):

Fore Case 1 and Case 2, the full Bimini Island the Bishop Rock route is used, with waypoints separated by relatively large distances along the route. For further advanced testing and analysing local metocean condition impacts, it is imperative to increase the number of waypoints. However, increasing the number of waypoints increases the computational cost of the algorithm as well. For testing purposes, therefore, in Case 3, a sub-part of the route is used, and the number of waypoints is increased.
The results, shown in Figure 7, are of the same type as for Case 1: the optimized route is the same as the input route, with same fuel consumption and same ETA while sailing with the fixed calculated average speed. The algorithm was also tested for uniform metocean fields (as in Case 2), and results are as expected.

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Figure 11: Example plots for ice limits for ship ice classes. The two figures show the off-limit sea ice regions for different decades for the ARC4 ship ice class in the month of Sep. The left panel shows the decade 20252035 and the right panel shows the decade 2055-2065. The ice data is based on the average of 8 different CMIP5 models, and the RCP8.5 climate scenario is applied. 

5. Route Availability Index

5.1 Arctic ship routes

Two different ship routes have been defined and digitized into the standard route format of the project. Both routes utilize the Northeast Passage at two different latitudes. At present, none of the indicators are defined along the Northwest Passage and no standard routes have been created. The reason for this being that model resolution in both ERA-interim and the CMIP5 ensemble are too coarse to resolve the narrow straits east of Greenland. 

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With regards to ice navigation, the Ice limits for different ship ice classes indicator as well as the Route Availability Index indicator have been developed and are ready for implementation into the service.

References

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Boese, P.

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, (1970). Eine Einfache Methode zur Berechnung der Widerstandserhöhung eines Schiffes in Seegang. Institüt für Schiffbau der Universität Hamburg, Bericht Nr 258.

Faltinsen, O.

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7.1 Appendix A – Code for Fuel Consumption Model

The MATLAB code for wave resistance implementation in the Fuel consumption model are delivered in the form of a PDF file together with this document. Filename
"C3S_D422Lot1.OSM.2.6(1)_201805_Operational_Indicators_Technical_Note_AppendixA_code_FC M_waveresistance"

7.2 Appendix B – Code for Route Cost ETA

The MATLAB code files for Route cost ETA are delivered in the form of a zip archive datafile together with this document. Filename "C3S_D422Lot1.OSM.2.6(1)201805_Operational_Indicators Technical_Note_AppendixB_code_RouteCostETA"

7.3 Appendix C – Code for Ice Limits for Different Ship Ice Classes

The Python code files for Route cost ETA are delivered in the form of a zip archive datafile together with this document. Filename "C3S_D422Lot1.OSM.2.6(2)201808_Operational_Indicators Technical_Note_AppendixC_code_Ice_Class_Limits"

References

Boese, P., (1970). Eine Einfache Methode zur Berechnung der Widerstandserhöhung eines Schiffes in Seegang. Institüt für Schiffbau der Universität Hamburg, Bericht Nr 258.

Faltinsen, O. M., Minsaas, K., Liapis, N., and Skjordal, S. O. (1980). Prediction of resistance and propulsion of a ship in a seaway. Proceedings of the 13th Symposium on Naval Hydrodynamics, Tokyo, Japan, 505-529.

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Jensen, J. J., Mansour, A. E., and Olsen, A. S. (2004). Estimation of ship motions using closed-form expression. Ocean Engineering, 31, 61-85.

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