Contributors: Sverre Dokken (OFFSHORE MONITORING LTD), Jacek Gruszka (OFFSHORE MONITORING LTD), Capt. Jorgen Grindevoll (OFFSHORE MONITORING LTD), Constantinos Panteli (OFFSHORE MONITORING LTD), Waqas Qazi (OFFSHORE MONITORING LTD), Siegfried Schmuck (OFFSHORE MONITORING LTD), Kris Lemmens (OFFSHORE NAGIVATION LTD), Capt. Reidulf Maalen, Cruise vessels, Mega-yachts (GLOBAL MARITIME SERVICES), ChernFong Lee (GLOBAL MARITIME SERVICES), Leif Eriksson (CHALMERS UNIVERISTY), Lars Jonasson (CHALMERS UNIVERISTY), Wengang Mao (CHALMERS UNIVERISTY), Capt. Pär Brandholm (LAURIN MARITIME (TEAM TANKERS INTERNATIONAL))

Issued by: OSM / Sverre Dokken

Date: 01/09/2018 Ref:

C3S_D422Lot1.OSM.2.6(2)_201809_Operational_Indicators_Technical_Note_v1

Official reference number service contract: 2018/C3S_D422_Lot1_OSM/SC2

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:

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

Numbers 3 and 4 are based on the development status of number 1, Fuel Consumption Model. Given the advanced state of development of number 1, numbers 3 and 4 are expected to be included in the next update to this document. Number 7, Cost of new Arctic Routes is already well under development, however, documentation on this will only be included in the next update to this document. Numbers 8 and 9 are still at an early stage of development and it is likely that there will be insufficient time left within the project to develop both indicators. Depending on highest feasibility, one of the two will be chosen for further development, however, as noted in the previous update of this document, the main difficulty to produce and/or validate these indicators come from the limited (or no) validation data being available and the likely too coarse spatial resolution of the input data for the indicators to be effective for shipping operations. Number 10 has now been found to be unlikely to be included within this project due to the current state of scientific research on the topic being not advanced enough to allow development within the remaining timeframe of the project.

2. 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 being 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. In the document presented here we describe the progress in terms of wave added resistance calculation w.r.t. ship speed and heading.

2.1 Wave added resistance

The added resistance due to waves is split into two parts namely the resistance due to wave diffraction (R_awd) and resistance due to wave motion (R_awm). Resistance due to wave diffraction was computed using the Faltinsen's Asymptotic formula while the resistance due to wave motion was calculated using Garritsma and Beukelman's Radiated Energy method. The 2D ship model used is shown in Figure 1.

Figure 1: Schematic of 2D ship model strips from Seaway

2.2 Faltinsen's asymptotic formula

A schematic diagram of the ship water plan is shown in Figure 2. The formula is (Faltinsen et al., 1980):

R_{aw1}= \frac{\rho g\zeta_a^2}{2}\int_C \left\{\sin^2(\theta+a)+\frac{2\omega U}{g}[1-\cos \theta \cos(\theta+a)] \right \} \sin \theta dl \quad (1)

 where

2.3 Radiated energy method (method 1)

The added resistance due to ship motions according to the radiated energy method is given as (Gerritsma & Beukelamn, 1972):

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

where

b'(x)=b_{33}-U \cdot \frac{da_{33}}{dx_b} \quad (3)

and V_za is the amplitude of the vertical water velocity:

V_z = \dot\eta_3 -x_b \dot\eta_5 + U \eta_5 - \dot\zeta \ast = |V_{za}| \cos(\omega_et+\epsilon) \quad (4)

As observed, the resistance is approximated to be dependent only on heave and pitch motions.

Figure 2: Schematic of wave diffraction at water plane 

2.3.1 Hydrodynamic coefficients

Referring to Eqn. 3, since the 2D dynamic coefficients are required in the form of a₃₃ and b₃₃, the first step of the calculation is to estimate the 2D hydrodynamic coefficients. In Eqn. 3 however, an assumption has been made to treat a₃₃ as a constant along the ship length to drop the second term; the revised eqn. therefore becomes:

b'(x)=b_{33} \quad (5)

The ship is modelled in Seaway for Windows which allows the 3D hydrodynamic data to be obtained through the software. According to Grim (1959), the damping coefficient b₃₃ can be calculated through Lewis conformal mapping function

b_{33}=\frac{\rho g^2 A^2}{\omega^3} \quad (6)

where factor A is given by (Jensen et al., 2004):

A_i = 2 \sin(\frac{\omega_e^2 b_i}{2g}) e^{- \frac{\omega_e^2 T}{g}} \quad (7)

The 3D damping coefficient B₃₃ can be obtained from Seaway and since it is the integration of 2D damping coefficients along the ship length, it can be deduced approximately that the 2D damping coefficient follows the distribution of factor A. b₃₃ of each strip (see Figure 1) can therefore be estimated using Eqn. 8:

b_{33,i} = \frac{A_i^2}{\sum_{j=1}^{\infty}A_j^2} \times \frac{B_{33}}{(x_{b,j+1}=x_{b,j})} \quad (8)

2.3.2 Motion response

Referring to Eqn. 3, heave and pitch response transfer functions are required to obtain V_za, which can further be expressed in terms of heave and pitch responses according to Eqn. 9. Response amplitudes and phases are obtained through Seaway for each speed and heading and are stored in the form of look-up table. An example is presented in Figure 3.

|V_{za}|=|U \cdot \hat\eta_5 +i \cdot \omega_e(x_b \cdot \hat\eta_5 - \hat\eta_3) + i \cdot \omega \cdot \zeta_a \cdot e^{-kT} e^{-i \cdot k \cdot x_b \cos \alpha}| \quad (9)

where

Figure 3: Heave response at one specific speed and heading in the function of wave frequency

2.4 Integrated pressure method (method 2)

Boese (1970) calculated the added wave resistance through integrating the longitudinal oscillating pressure over the ship hull's wetted surface:

R_{aw1}= \frac{\rho g \zeta_a}{2} \int_L \left[ 1 - \frac{z_{xa}^2}{\zeta_a^2} + \frac{2 \cdot s_a \cdot \cos(-kx_b \cdot \cos \mu - \epsilon_{s \zeta})}{\zeta_a} \right] \cdot \frac{dy_w}{dx_b} \cdot dx_b \quad (10)

where

For deep water, the Eqn. 10 is simplified to become:

R_{aw1}= \frac{\rho g \zeta_a}{2} \int_L s_a^2 \cdot \frac{dy_w}{dx_b} \cdot dx_b \quad (11)

There is a second component due to vertical component of wave force, included as:

R_{aw2}= \frac{1}{2} \cdot \rho \Delta \cdot \omega_e^2 \cdot z_a \cdot \theta_a \cdot \cos(\phi_3 - \phi_5) \quad (12)

The total resistance due to motion is therefore:

R_{awm}= R_{aw1} + R_{aw2} \quad (13)

2.5 Total resistance

The total resistance is simply a summation of the two contributions in Eqn. 1 and Eqn. 2:

R_{aw}= R_{awd} + R_{awm} \quad (14)

2.6 The algorithm

A detailed description of the algorithm is presented below.

2.6.1 The inputs

• 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.

2.6.2 The outputs

For a specific speed and heading combination, a code can be written to look up and output the transfer function of total added resistance R_aw as a function of wave frequency ω or encounter frequency ω_e.

\pmb{R_{aw}} (\omega)= \frac{R_{aw} (\omega)}{\zeta_a^2} \quad (15)

2.6.3 Post processing

Assuming the wave energy spectrum S_ζ(ω) (Pierson-Moskowitz, JONSWAP, ITTC etc.) is used, the mean resistance in irregular waves can be represented as:

\overline{R_{aw}} (\omega)= 2 \int_0^{infty} \frac{R_{aw}(\omega)}{\zeta_a^2} \cdot S_{\zeta} (\omega) \cdot \partial \omega \quad (16)

2.7 Further developments

Test results will be generated to check and validate the code implementation. The range of speeds in the look up tables needs to be extended.

3. Route Cost ETA

The detailed description of the Route Cost ETA operational indicator is given in the earlier version of this document C3S_D422Lot1.OSM.2.6(1)_201805_Operational_Indicators_Technical_Note_v1. As a brief overview, most shipping operations require arrival at a fixed ETA (Estimated Time of Arrival) at the 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.
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.

3.1 Method / algorithm description

The DIRECT (DIviding RECTangles) optimization method is used here for route optimization (refer to C3S_D422Lot1.OSM.2.6(1)_201805_Operational_Indicators_Technical_Note_v1 for input data and method description). The DIRECT method is open-source, with code available in both MATLAB and Python (scipydirect package), and as such is perfectly suited for implementation in the C3S Global
Shipping service scenario. The first version implementation of DIRECT sail planning is done in MATLAB, which will then be ported into Python later. The conceptual framework of DIRECT route optimization is shown in Figure 4.
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 chosen. This route is easy to analyze as it is based on the shortest distance (great circle) on the curved surface of the Earth, and therefore the route optimizer effects are easier to understand. The same route has been used for the fuel consumption model analysis (Sec. 2.3) in C3S_D422Lot1.OSM.2.6(1)_201805_Operational_Indicators_Technical_Note_v1. The route along with its waypoints is shown in Figure 5. The Robinson projection will be used for all maps plotted and shown here.

Figure 4: Conceptual framework for DIRECT route optimization. The algorithm is now "functional" i.e. all basic modules are integrated, and system is fully functional from end-to-end.    

Figure 5: Bimini Island to Bishop Rock great circle fixed route plotted along with its specified waypoints. Map plot produced from fixed route created by BOPEN. 

3.2 Results & discussion

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

where

P: ship power (unit: KW)

V: ship speed (unit: m/s)

H_s: significant wave height (unit:m)

T_z: 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,H_s ≤ 15 m, 4s < T_z <14s; and W < 30 m/s. However, in this case we apply the equation over all possible values.

After testing small sub-components of the code, understanding how the code works, and implementing necessary modifications/enhancements, the algorithm is now "functional": all basic modules are integrated, and system is fully functional from end-to-end. The functional code / system is being tested through various devised test environments and input parameter setups, which follow the basic idea of starting from very simple tests, and then progressing to more complex tests. These tests are described in detail below.

For initialization of the DIRECT sail planning method, a few parameters have to be specified. Some of these important initialization parameters are mentioned below:

i. Route parameters:

• Departure and arrival point locations (latitude and longitude)
• Route waypoints

ii. DIRECT optimization parameters:

• Maximum number of iterations
• Maximum number of function evaluations
• Maximum rectangle divisions

iii. ETA parameters:

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

iv. Ship parameters:

• Maximum ship speed (kts)

In each individual test case description, the values of these input parameters are reported along with the relevant intermediate calculated parameters, output parameters, and graphical / map outputs.
It should be noted in that in the test cases, the input values of ship ETA and speeds are unrealistic; these are specified on purpose to make the optimization run quicker. In next versions of the code, these input variables will be adjusted to realistic values.

3.2.1 Case 1 – Bimini Island to Bishop Rock (no metocean):

The first step in operational testing / verification of the code is to attempt route optimization without any influence of met-ocean conditions. For this, the met-ocean conditions of waves, winds, and currents, are all set to 0 fields. Since the Bimini Island to Bishop Rock great circle route is the shortest distance between the two points, therefore with 0 met-ocean contributions, the optimized route should be the same as the input great circle route.
The results, shown in
Figure 6, are as expected: 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. This verifies the algorithm running correctly in case of no met-ocean contributions.

• P = Calm Water Resistance only
• DIRECT optimization parameters:
  • Max no. of iterations: 500
  • 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 o 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: 99.93
  • Minimized fuel consumption result: 179960 kg

Figure 6: Route optimization results for Case 1. Top panel shows the optimized route, while the bottom panel shows the speed profiles for each waypoint. 

3.2.2 Case 2 – Bimini Island to Bishop Rock (uniform metocean fields):

The case 2 test includes uniform values of metocean conditions of wind and wave magnitudes. In this case, since the metocean contribution is uniform at every location, the optimization system should treat it as 0, however the fuel consumption should be increased due to increased wind and wave resistance components in the fuel consumption model. All the other results should be the same as Case 1.
The results are as expected, where the fuel consumption is increased markedly, but the optimized route, ETA, and speed profiles remain the same. The graphical outputs are exactly the same as for
Case 1 (Figure 6) and are thus not shown for Case 2.

• 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.

• P = Calm Water Resistance only
• DIRECT optimization parameters:
  • Max no. of iterations: 500
  • Max no. of functions evaluations: 1500 / 3000 o Max rectangle divisions: 1000
• ETA parameters:
  • Expected ETA (hours): 30
  • 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): 20.08 o Average ship speed (kts) (calculated): 35.04 o Average fuel consumption (calculated): 54214 kg
• DIRECT optimization:
  • ETA result: 29.98
  • Minimized fuel consumption result: 54215.5 kg

Figure 7: Route optimization results for Case 3. Top panel shows the optimized route, while the bottom panel shows the speed profiles for each waypoint. 

3.2.4 Case 4 – Bimini Island to x (short route, more waypoints, SWH strip):

For Case 4, the short route of Case 3 is taken, and a SWH field is introduced, with a SWH strip along a small part of the route with value of 9; the rest of the SWH field is set to uniform 0 values. This metocean environment setup will help to identify how the route optimizer functions in case of encountering a high SWH strip along its path.
The results are positive and as expected.
Figure 8 shows the output optimized route, which adjusts itself to avoid the high SWH strip and sail as much as possible in the 0 SWH metocean field. The fuel consumption is of course higher than 0 met-ocean conditions fuel consumption due to some part of the route spent in the high SWH zone and also the optimized route covering more distance than the fixed great circle route. The ETA is close to the expected 30 hours still, and therefore the speed profiles remain the same, i.e. sailing at the determined average speed of 35.04 knots.

• P = Calm Water Resistance + Wave Resistance + Wind Resistance • Metocean conditions:
  • Constant SWH field of 0, with a small strip of 9 values within the route o 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 0 o Current magnitude set to 0
• DIRECT optimization parameters:
  • Max no. of iterations: 500 o Max no. of functions evaluations: 3000 o Max rectangle divisions: 1000
• ETA parameters:
  • Expected ETA (hours): 30
  • 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): 20.08 o Average ship speed (kts) (calculated): 35.04 o Average fuel consumption (calculated): 54214 kg
• DIRECT optimization:
  • ETA result: 30.06
  • Minimized fuel consumption result: 56827 kg

Figure 8: Route optimization results for Case 4. Top panel shows the optimized route, while the bottom panel shows the speed profiles for each waypoint.    

3.2.5 Case 5 – Bimini Island to x (short route, more waypoints, SWH patch):

For Case 5, a big SWH patch is introduced in the path of the fixed route, with values of 9, while the rest of the SWH field is set to uniform 0 values. In this case, the patch is so big, that the route may not be able to completely avoid or circumvent it, and the optimizer should take this into account while calculating the optimized route.
The results are positive and as expected.
Figure 9 shows the output optimized route, which adjusts itself to spend less time in the high SWH patch and sail as much as possible in the 0 SWH metocean field. The fuel consumption is of course higher than 0 met-ocean conditions fuel consumption due to some part of the route spent in the high SWH zone and also the optimized route covering more distance than the fixed great circle route. Because of longer route distance, the expected ETA is exceeded while sailing at average speed, which is why there is a higher speed profile near the end of the journey to reach within the specified ETA.

• P = Calm Water Resistance + Wave Resistance + Wind Resistance • Metocean conditions:
  • Constant SWH field of 0, with a square patch of 9 values within the route o 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 0 o Current magnitude set to 0
• DIRECT optimization parameters:
  • Max no. of iterations: 500 o Max no. of functions evaluations: 12000 o Max rectangle divisions: 1000
• ETA parameters:
  • Expected ETA (hours): 30
  • 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): 20.08 o Average ship speed (kts) (calculated): 35.04 o Average fuel consumption (calculated): 54214 kg
• DIRECT optimization:
  • ETA result: 29.93
  • Minimized fuel consumption result: 64020 kg

Figure 9: Route optimization results for Case 5. Top panel shows the optimized route, while the bottom panel shows the speed profiles for each waypoint. 

3.3 Further developments

After successful testing with synthetic configurations of metocean fields, the algorithm will now be tested with direct ingestion of CDS metocean data. The algorithm will be customised to work with more great circle routes in the system as well. Further constraints, such as ETA land avoidance and strong weather avoidance, will be added through penalty functions.

4. Ice Limits for Different Ship Ice Classes

The ice class of a ship refers to a notation given by a national authority or classification society to certify that a ship is able to navigate through ice. Navigating through ice imposes more strain and load on the hull and propulsion of a ship. Different ship classification societies and organizations have made classification charts, which specify the ship-build, which can traverse an ice-infested route like through the Baltic or Artic. These classifications of ship strength of course also take into account the ice parameters like ice-age, ice thickness, ice area, and season. The most well-known and welladapted of these ice class typologies are described below.

4.1 IACS Polar Class

Polar Classes are issued by the International Association of Classification Societies (IACS) and they complement the IMO (International Maritime Organization) Polar Code guidelines for ships operating in Arctic ice covered waters. Seven Polar Classes are defined, ranging from PC 1 for year-round operation in all polar waters to PC 7 for summer and autumn operation in thin first-year ice (Table 1).

Table 1 IACS Polar Class definitions

4.2 Finnish-Swedish Ice Class (FSICR)

Swedish-Finnish Ice Class Regulations (FSICR) are issued by the Swedish Maritime Administration and the Finnish Transport Safety Agency. These class rules are majorly defined for vessels operating in first-year ice in the Baltic Sea and calling Finnish / Swedish ports. Figure 10 demonstrates the interling between the IACS Polar Classes and FSICR classes.

4.3 Russian Marine Register of Shipping

The Russian Marine Register of Shipping (RMRS) maintains sea ice classes based on operations in Russian Arctic waters. The ice class follows three different notations: Ice for non-Arctic ships, Arc for Arctic ships, and Icebreaker for icebreakers. Table 2 describes the Arc ice classes. These ice classes can be applied in parallel with the IACS Polar Classes and FSICR classes.

4.4 Implementation

The ice class and associated tonnage requirements for polar route navigation vary depending on the seasonal sea ice conditions. Some sea ice classes require the assistance of an ice-breaker with the ship to help it navigate through the sea ice. As a result of the increased melting of the Arctic ice, ships with lower ice classes will potentially be able to trade through the Arctic in the future.

Figure 10: Inter-link between the IACS Polar Classes and FSICR classes.    

Table 2: Russian Marine Register of Shipping ice class definitions

Even though it is not possible to connect the ice navigation ability directly to an encountered ice conditions (ice thickness mainly, as well as the ice concentration, etc.) since the criteria may also depends on other ship, cargo and weather related parameters, a simple table is provided for the ice operation scenarios (Table 3). "Assisted" operation corresponds to the scenario where icebreaker assistance is provided or the ice concentration is less than 100%.

Table 3: Implementation example of ship ice classes w.r.t. ice floe thickness

The indicator will be visualized as showing the off-limits areas for different ship ice classes w.r.t. climate projects for different periods. Figure 11 shows an example output for a ship ice class for the month of Sep. in two different decades (2025-2035 and 2055-2065); the results are based on RCP8.5 climate scenario.

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. 

The two Northeast Passage routes are shown in Figure 12 below. The routes have been defined in [Mulherin et. al. 1999] and are created by using historical voyages together with a route optimization model based on ice and weather information. The original routes have been altered in a few locations where the route points were positioned on ERA-interim land points. In these situations, the route points have been moved away from the coast as much as required to be covered by a wet grid cell in ERA-interim. 

Figure 12: Northerly and southerly Northeast Passage

5.2 Route Availability

The Route Availability Index calculates the transit window in days for a Northeast Passage route. The algorithm follows the steps presented in Khon et al., 2016 and utilized the same subset of CMIP5 models. The selected CMIP5 models have been chosen based on their skill in predicting historical transit windows.
An example of the indicator product is shown in Figure 13 below. In this case the calculations are done on the southern Northeast Passage route. The criteria for an open transit are determined using
sea ice concentration threshold for ice-free conditions and the percentage of the daily length of ice free conditions with respect to the full route.

Figure 13: Opening and closing dates of the Northeast Passage. Gray and green shaded areas indicate dates calculated from ERA-interim and CMIP5 RCP4.5 scenarios, respectively. The dashed line shows the one standard deviation spread of the CMIP5 models. 

Step-by-step description of the algorithm

1. Define a route for the North East Passage

2. Interpolate sea ice concentration to the route for each ensemble member 3. Take ensemble average for each route grid point 4. For each time step:
   1. calculate the sea ice concentration in grid points that covers parts of the route.
   2. Apply sea ice concentration threshold and determine if grid point is ice covered
   3. Get the percentage of ice free grid points
   4. Apply transit window threshold and determine if route is open or closed for this time step

5. Summarize open dates for each year

Validation

The algorithm is validated in Khon et al., 2016 and only verification of the implementation are required.

6. 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(1)_201805_Operational_Indicators_Technical_Note_v1 (Period 31 May - 01 September). The description and discussion of two operational indicators have been expanded while two new sections have been added, detailing the development status of two more operational indicators.

The wave resistance w.r.t ship velocity and heading has been implemented in the fuel consumption model. The next steps entail adding more velocity ranges in the look-up tables and validating the code implementation.
The Route cost ETA indicator using the DIRECT sail planning algorithm is now fully functional end-toend. Tests with great circle route with synthetic SWH data are successfully described. Future developments will include testing with actual CDS data, and modifying the system to work with other routes as well.

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.

7. Appendices (Codes used for generating the indicators)

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.

Gerritsma J. and Beukelman W., (1972). Analysis of the Resistance Increase in Waves of a Fast Cargoship. International Shipbuilding Progress, 18(217).

Grim, O. (1959). Oscillation of buoyant two dimensional bodies and the calculation of the hydrodynamic forms. Technical Report 1171. Hamburgische Schiffbau-Versuchsanstalb.

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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