Identification of early warning criteria for rough sea ship navigation using high-resolution numerical wave simulation and shipboard measurements

The analysis of ocean surface waves are essential to ensure a safe and economical navigation. Since 2010, different on-board observation data from a bulk carrier have been collected for 6 years, including high-risk shipping regions in the Southern Hemisphere with strong ocean currents. For four rough sea cases, high-resolution numerical simulations of ocean waves, including the effect of wave-current interaction on ship navigation, have been performed using the WAVEWATCH III model. The simulations considered the ocean surface wind force from the widely used grid point value database NCEP-FNL 15 and ERA-Interim. Aimed at providing practical suggestions for safe navigation by avoiding possible high-risk ocean regions as well as the construction of a more effective and efficient optimum ship routing system, the model results were validated based on on-board observations, followed by discussions on the responses of ship motion and navigation to wave states at different levels. Finally, identification of the early warning criteria, including various operational ocean parameters, is provided for ballast and loaded ships sailing in rough seas. 20

navigation is essential for safe, economical, and environment-friendly ship navigation, from the viewpoint of ship weather routing.
Statistical analysis of ship accident database has been used as an important method by several researchers to find out the relationship between sea states and ship safety as well as make identification of warning criteria.
an agreement with the general conditions of a possible occurrence of dangerous waves based on the statistical analysis. The relationship between rough seas and ship navigation situations was not mentioned due to the lack of necessary ship information.
Statistical analysis of sea states and related ship accidents from the database can give notification of the most dangerous sea 55 parameters on different ship accidents. However, due to the lack of detailed ship motion and dimension information on each ship accident, they underestimated ocean states because of the coarse resolution of the meteorological databases they used and the possible underestimation of wave steepness resulting from the lack of consideration of wave-current interaction; their conclusions may need further improvement using validation with on-board observations and higher-resolution information of more accurate ocean states, in spite of their unneglectable contribution to provide some worthy information and suggestions 60 to the ship operators.
Besides poor weather and dangerous sea states leading to ship losses or accidents such as hull breaking, grounding, and capsizing; the unexpected rough seas are also an important factor leading to negative influences on ship safety and navigational economics. For example, waves can affect the structural integrity and ship stability through the direct action of waves on ship hull; waves can also produce an indirect influence on ship stability such as the water on deck and rolling, and the improper 65 crew operations can also increase the risk of ship accidents due to rolling caused by waves. Besides, the added resistance due to waves can increase the engine burden and speed loss, bringing a high risk of engine failure and then the out-of-control movement. Additionally, a large ship motion amplitude such as pitch, roll, deck wetness, slamming, and propeller racing as well as other coupling phenomena caused by ocean waves are also resulting in unexpected influences on ship safety and navigational economics. 70 As a continuation of previous studies focusing on the wave modelling of high wind seas in typhoon periods (Chen C. et al., 2013;Chen C., et al., 2015) and the study on wave-current interactions accounting for the Kuroshio current in the East China Sea (Chen C., et al., 2018), the present study further analyses the relationship between ocean states and ship navigational responses. This study employs a combination of high-resolution numerical wave modelling and detailed on-board observations of ship motion information, which is affected by rough weather conditions. The study is aimed at providing ship operators 75 practical suggestions for safe navigation by identifying the high risk ocean states and also provides a few possible warning criteria, especially for rough-sea navigation.
For this study, a six-year on-board observation of weather, ocean, and ship motion was performed since 2010, using a 20,000 DWT class bulk carrier covering high-risk shipping regions in the Southern Hemisphere. Two rough sea navigation cases have https://doi.org/10.5194/nhess-2019-399 Preprint. Discussion started: 28 January 2020 c Author(s) 2020. CC BY 4.0 License.
To understand the relationship between sea state parameters and rough sea navigation more, we have selected 4 observation cases from all the experiment period for analysis. The crew almost lost control while recording in the logbook (Case 1). 100 Information on navigation time, ship location and ship loading condition in each case is shown in Table 2.  ship accidents have been reported. (Kjeldsen, 2004) https://doi.org/10.5194/nhess-2019-399 Preprint. Discussion started: 28 January 2020 c Author(s) 2020. CC BY 4.0 License.
The coloured rectangle in Fig. 1 indicates all ocean regions set for high-resolution wave model simulation for these 4 cases. In Fig. 2, (Toffoli et al., 2003) proposed a worldwide ship accidents (1995)(1996)(1997)(1998)(1999) map due to severe weather, using Lloyd's Marine Information Service (LMIS) casualty database. Peter Kjeldsen (Kjeldsen, 2004) identified 21 ocean areas where unconventional waves occur, causing ship accidents, as shown in Fig. 3. 120 A comparison of these three figures illustrates the high navigational risk of the selected 6 rough sea navigation cases, especially by the number 12, 13, and 18 provided in Fig. 3, which show a higher risk of experiencing unconventional waves. In addition, according to (Cattrell et al., 2018), the frequency of occurrence of unconventional waves and their generating mechanism is not spatially uniform, and each location is likely to exhibit unique sensitivities. Thus, unconventional waves occurring in ocean regions of different characteristics are a result of different reasons such as the opposite current effects in the Kuroshio region, 125 the swell and wind sea interactions in the Southern Hemisphere, and the severe storms in the tropical regions. Therefore, detailed information of the on-board observation and the high-resolution wave model simulation are used here for a clear investigation.
The measurements of these observation cases mainly include navigational parameters such as weather data (wind speed, wind direction, etc), engine data (engine revolution, engine power, and fuel oil consumption as well as the exhaust gas temperatures 130 on all six cylinders of the main engine), voyage data (ship speed, ship position, ship course, loading condition, etc), and the ship's motion (pitch, roll, and yaw). Additional detailed information on this observation instrument and the measurement parameters have been provided by (Sasa et al., 2015). To obtain detailed ship information for an accurate analysis, the ship motion was treated as significant values generated using the zero-up cross method for a 10-min time series with an interval of 0.1 s, and all other parameters are results of the averaged values for a 10-min time series obtained every 1 s. 135

Model descriptions
As a third-generation phase-averaged wave model, the WAVEWATCH III (WW3 model; version 4.18) (Booij and Holthuijsen, 1987;Tolman, 1989;Tolman, 2014) has been used for hind cast wave simulations of all the above-mentioned 4 cases. With 140 an implicit assumption of random phase spectral action density balance equation as those properties of medium (water depth and current) as well as the wave field itself vary on time and space scales that are much larger than the variation scales of a single wave, the WW3 model can solve wavenumber-direction spectra. By explicitly parameterizing all physical processes, such as wind input growing actions, nonlinear resonant wave-wave interactions, wave-bottom interaction, and whitecap dissipation, the spectra action balance Equation can be solved as follows (Tolman, 2014): where N is the vector wavenumber spectrum, is the wave group velocity, is the current velocity, is the coordinate in the direction of θ, is the coordinate perpendicular to ，and is the net source term for the spectrum, is the intrinsic wave radian frequency. In this study, S was determined as the summation of the linear input ( ) to provide more realistic initial wave growth for the consistent spin-up of a model from quiescent conditions (Cavaleri and Malanotte-Rizzoli, 1981); wind input ( ) and wave dissipation ( ) (Tolman and Chalikov, 1996) calculated by a non-dimensional wind-wave interaction 155 parameter; nonlinear wave-wave interaction ( ) using the discrete interaction approximation (DIA) (Hasselmann et al., 1985); and wave-bottom interaction ( ) (Hasselmann et al., 1973) with the empirical, linear JONSWAP parameterization for additional processes in shallow water areas. High-order conservative numerical schemes are used for spatial discretization, and a Courant-Friedrichs-Lewy (CFL) condition exists, binding the discretizations in time and in space.

Model settings and input data
A two-way nesting method (ww3-multi) with the horizontal resolution of 0.5° and 0.1° for a large (global) domain and the inner-nested (local) domain was used. Considering the CFL condition, the minimum wave propagation time step was set as 330 s and 300 s for the larger and inner domain. For all rough sea cases, the wave model has a spectral resolution of 10° 165 covering 36 directions. Calculated wave frequencies were set from 0.0345 Hz, with a logarithmic frequency factor of 1.1 for 38 steps. Additionally, a one-month spin-up before the time period of ship motion analysis has been run for all cases to start the model from a resting condition.
To simulate an ocean wave model accurately, a critical input is the "forcing" by wind fields: a time-varying map of wind 170 speed and directions. Meanwhile, the most common sources of errors in wave model results are the errors in the wind field. Therefore, to reduce the model uncertainty originating from the sensitivity of the wind input, as illustrated by the studies such resolution of approximately 80 km (0.75°). Both these wind input sources are updated every 6 h. A linear interpolation method was utilized for applying these two GPV databases (1° and 0.75°) to wave modelling (0.5° and 0.1°).

180
To calculate the wave-current interaction, the ocean current data Ocean Surface Current Analysis Real-time (OSCAR), which is generated by Earth Space Research (ESR), has been used for wave modelling (Bonjean and Lagerloef, 2002). The ocean current data on a 1/3 degree grid has also been interpolated into 0.1°. Furthermore, the wave-ice interactions are also calculated using the wave model WW3. Thus, sea ice and icebergs have been included in the calculation. For these 4 cases, the sea ice coverage was calculated in the global domain, using the Nimbus-7Scanning Multichannel Microwave Radiometer, the Defense 185 Meteorological Satellite Program's Special Sensor Microwave Imager, and Special Sensor Microwave Imager Sounder (Cavalieri et al., 1996).

Distributions of ocean surface wind and waves by model simulations 190
The ocean waves were calculated using the WW3 model, and the detailed settings are provided in section 3.2. The surface wave distributions at the moment of the maximum pitch motion of all rough sea cases are presented in Fig. 4. Low pressures and swells resulted in strong head, bow, or beam waves during rough sea ship navigation.

Validations of simulation results with ship on-board observations
As mentioned at the end of Section 1, observed wind speed of all cases has been averaged for a 10-min time series obtained every 1 s for validation with WRF results, as shown in Fig. 5. Generally, the GPV wind data reasonably replicated the temporal variation of both wind direction and speed, while the NCEP tends to perform better for peak wind than the ERA-205 Interim.

5.
Relationship between ocean state parameters and ship responses

Ocean states
The correlation among the significant wave height, which is representative of sea severity, and other wave parameters generated by the WW3 model of all these rough seas is focused on as the first stage, as shown in Fig. 6. The formulas used in 215 the wave model for generating those wave parameters are also presented in Table 3. Here, the wave energy is E = ∫ ∫ ( , )  To improve the ship safety in rough seas and the efficacy of optimum ship routing in reality, different loading conditions should be included. Here, three different groups are divided as the "Half-Loaded" (Case 3, 4), "Ballast" (Case 1, 2), and "Total" (Case 1, 2, 3, 4), which represent the cases of Half-Loaded conditions, Ballast conditions, and the whole cases, respectively. The numbers inside each panel indicate the correlation coefficients of the relevant two-wave parameters. A 10-225 min average of a time duration approximately 30 days results in a total of 3000 data for these cases, covering high-risk shipping regions in the Southern Hemisphere, as shown in Fig. 1 and Table 2. https://doi.org/10.5194/nhess-2019-399 Preprint. Discussion started: 28 January 2020 c Author(s) 2020. CC BY 4.0 License. As shown in Fig. 6, regardless of the ocean states encountered by the two different loading conditions, there are small differences of MDS and wave steepness between the half-loaded and ballast cases. For instance, the wave height has a strong positive correlation coefficient with a wave steepness of 0.85, and the mean directional spread is found to decrease with an 235 enhancement of the significant wave height, with a negative correlation coefficient of 0.66.
However, a stronger correlation exists in the half-loaded cases than that in the ballast cases, when considering other ocean parameters such as the wavelength, wave period, and wave direction, although the correlation is relatively weak for these wave parameters. This can be attributed to the larger effects from ocean waves, such as the resonances induced by similar 240 length and period of ship and encountered waves, are needed for generating ship responses of the half-loaded cases to the same extent with those of the ballast ones. Details of these ocean states and corresponding ship responses are provided in section 5.3.

Ship responses 245
In addition to those wave parameters, the correlation among observed ship navigation and motion parameters of all rough sea cases are also considered, as presented in Fig. 7. A relatively strong positive correlation can be found between the pitch and roll motion (0.660), ship speed and engine RPM (0.760), whereas a strong negative correlation is found between the pitch motion and ship speed (-0.854). 250 As shown in the top-left panel in Fig. 7, a stronger correlation between roll and pitch motion can be found in the ballast (0.838) than that in the half-loaded cases (0.510), indicating a larger influence of ocean waves on the ship motion in ballast conditions.

255
As observed in the top-middle panel, as the pitch amplitude increases, the ship operators tend to further reduce the engine RPM (a higher correlation coefficient of -0.717), but later (when the pitch motion reaches approximately 3 degree in the half-loaded cases than in the ballast ones (-0.513 and less than 2 degree).
As for the correlation between pitch motion and ship speed, as in the top-right panel, it is observed that the ship operators 260 preferred to maintain the ship speed to a similar level in both loading conditions by reducing the engine RPM (as mentioned above) to balance the wave effects and ship motion.

265
The bottom-left panel shows that the engine RPM and ship speed loss are more highly correlated in the half-loaded cases than in the ballast ones, indicating a harder control of the ship speed in the ballast conditions due to the more complex coupled pitch-roll motions induced by ocean waves, while the pitch motion occupies a relatively large part of the ship motion in the half-loaded cases.

270
As observed from the bottom-middle and bottom-right panels, the correlations between the roll motions with other ship responses in the ballast loading cases have a stronger relationship than those in the half-loaded ones, owing to the higher centre of gravity in the ballast loading conditions. For instance, a correlation difference in the relationship between roll motion and engine RPM as well as ship speed for ballast and half-loaded cases are found as large as around 0.46 and 0.43,

respectively. 275
Lastly, for the half-loaded cases, a pitch motion approximately 3 degrees or a roll motion of approximately 5 degrees can bring a significant drop in engine RPM (less than 100) and SOG (less than 5 knots), as shown in the top-middle, top-right, bottom-middle and bottom-right panels "Engine RPM vs. Roll" and "Ship Speed vs. Roll"; the reason for this can be found in the top-left panel "Pitch vs. Roll" that the pitch motion is large when the ship suffered a 5-degree roll motion, where the 280 possible pitch-induced ship motion in the longitude direction such as slamming, deck wetness, and propeller racing may lead to a manual operation on the engine and then the voluntary speed loss. For the ballast cases, a pitch motion around 5 degrees or a roll motion around 20 degrees can lead to a drop of engine RPM and SOG. https://doi.org/10.5194/nhess-2019-399 Preprint. Discussion started: 28 January 2020 c Author(s) 2020. CC BY 4.0 License.

Ocean states and ship responses 285
According to the correlation between these wave parameters and ship responses of all rough sea cases, as shown in Table. 4, both the wavelength and mean wave period have a weak correlation with the ship responses. Therefore, the other four-wave parameters including the Hs, RWD, MDS and the wave steepness will be focused on in the following analysis. Compared with the roll motion and engine RPM, the wave states tend to have a stronger correlation with the pitch motion and ship 290 speed.

Significant wave height 295
The significant wave height is representative of sea severity. During rough sea navigations, relatively high values significantly influence ship motion and operation. As shown in Fig. 8

310
The impact of waves on a ship strongly depends on the relative wave direction, as defined in Fig. 9. As an example, the head and bow waves can reduce ship speed by inducing large pitch motion while the beam and quartering waves can affect ship stability and then the reduction of engine RPM and ship speed. Therefore, ships usually navigate perpendicular to the crests in rough seas, with very low forward speed.
https://doi.org/10.5194/nhess-2019-399 Preprint. Discussion started: 28 January 2020 c Author(s) 2020. CC BY 4.0 License. As shown in Fig. 10, both the largest amplitude of ship motion and significant drop of engine RPM and SOG occurred when the relative wave direction was less than 60 degrees (including both head and bow waves). The relative wave direction increases from 0 to 120 degrees; its effects on the pitch motion decrease faster than that for the roll motion. When it comes to 320 the correlation coefficients, a difference of 0.3 can be found from two loading cases in the relationship of roll motion and RWD, showing a larger influence of RWD on the roll motion in ballast cases.
https://doi.org/10.5194/nhess-2019-399 Preprint. Discussion started: 28 January 2020 c Author(s) 2020. CC BY 4.0 License. It can be seen in the top-left panel that the maximum pitch motion occurred in the head and bow seas in the cases of halfloaded and ballast cases, respectively, and the top-right panel shows that there is another peak of roll motion when the relative wave direction was around 240 degrees in the half-loaded cases, indicating a quartering wave coming from the stern 330 part. Therefore, head, bow and beam waves brought larger effects in both loading cases. Following quartering waves could also be dangerous because they can induce large roll motion in the half-loaded cases.
The two panels shown below clearly indicate that the head waves exert larger negative effects on the reduction of engine RPM and speed loss in the half-loaded cases, whereas the bow waves reduced them further in the ballast cases. 335

Wave steepness
As a parameter that points at enhancement of risk of extreme waves, the wave steepness is supposed to have a close relationship with ship motion (e.g. pitch) and navigation (e.g. speed loss). (Toffoli et al., 2005) pointed out that more than 340 50% of the incidents took place in sea states characterized by steepness larger than 0.035 (fully developed seas).
As shown in the top-left panel of Fig. 11, a high positive correlation of 0.836 can be found in the relationship between wave steepness and pitch motion, while the wave steepness and roll motion are relatively less-correlated, especially in the halfloaded cases of 0.523. A correlation difference of 0.25 indicates a larger influence of wave steepness on roll motion in the 345 ballast cases than in the half-loaded cases.
The ship operators started reducing the engine RPM as the wave steepness approached 0.015 in the ballast cases, whereas this reduction was conducted later when the wave steepness was larger than 0.03 in the half-loaded cases, as shown in the bottom-left panel.

Mean directional spread 355
According to the experimental tests of two-component directionally spread irregular waves with varying frequencies, directional spreading and component crossing angles made by (Luxmoore et al., 2019) and the reduction of the component directional spreading can increase both the kurtosis and exceedance probabilities. As an important factor to predict the kurtosis and estimate the probability of extreme waves, the mean directional spread is of great importance to identify 360 dangerous ocean regions. Therefore, the mean directional spread was also investigated to better understand the directional information of ocean waves and their effects on ship navigations.
For the whole cases, the pitch and roll motions are negatively correlated with the MDS with coefficients of -0.636 and -0.545, as shown in the top-left and top-right panels in Fig. 12. The MDS had little influence on half-loaded cases (-0.466) when compared with the ballast cases (-0.685), but the effects of MDS on roll motion reduced more quickly as the MDS increased in the ballast cases, while in the half-loaded cases the MDS kept relatively large effects as the MDS increased and there was a second peak of roll motion when the MDS was around 70 degrees.

375
Influences of two different loading conditions on ship responses are discussed. As shown in Fig.13, correlation coefficients of ship responses with different loading conditions to ocean states were compared. Ship responses such as the pitch motion ( Fig.13-A ), engine RPM ( Fig.13-C ) and ship speed (Fig.13-D ) in ballast conditions are of an equal or slightly smaller amplitude than those in the half-loaded ones; large differences exist in the case of roll motion (Fig.13-B ). Owing to a high GM value and stronger parametric roll resonance in irregular high waves, ocean states including the Hs, MDS, RWD, and steepness have larger influences on roll motion in the ballast conditions than those in the half-loaded cases, and the differences of correlation coefficients are not less than 0.2. Therefore, compared with other ship responses affected by ocean waves in the half-loaded conditions, the roll motion should be paid more attention when the ship is in ballast conditions. As mentioned before, the ship operators usually reduced the engine RPM more but later in the half-loaded cases than they did in the ballast ones. 390

Identifications of warning criteria in ocean states of different levels
To provide practical suggestions to the ship operators for their decision-making on identifying and avoiding high-risk ocean states, it is of great importance to figure out the various amplitudes of ship responses induced by rough seas of different levels. In addition to the correlation between each ocean state and each ship response given above, the ship responses are 395 divided into 3 ranges to find out the ship responses to ocean states of different levels, and the detailed values are given in Table. 5.   When it comes to the averaged RWD for each ship response, a difference of 53 degrees, 100 degrees, and 20 degrees can be 420 found between two loading conditions for the large, modest and small ship responses, respectively. Head seas generate modest and large ship response in half-loaded cases, while beam seas tend to affect more in ballast cases.
For half-loaded cases, large ship responses also occurred in ocean regions with a wave steepness of 0.031 (0.0346 is for fully developed wave, according to the Pierson-Moskowitz spectrum), while (Toffoli et al., 2005) found that 60% of ship 425 accidents occurred in sea states with wave steepness of 0.03~0.045 from his studies on the relationship of ocean states and ship accidents, shown in Fig. 15. On the other hand, a smaller wave steepness of approximately 0.02 was experienced for large and modest ship responses in ballast cases, indicating a weaker capability to operate the ship over ocean regions with high steepness as that in the half-loaded cases.

430
Similarly, an MDS difference of around 10 degrees is found between half-loaded and ballast cases for both large and modest ship responses. Also, corresponding with a limited MDS of 25 degrees, the crossing seas are of high probability (98%) for ship accidents (Toffoli et al., 2005), which can also be found in Fig. 14 and Fig. 15 that large and modest ship responses of the half-loaded cases occurred in similar ocean regions. In addition, (Bitner-Gregersen & Toffoli, 2014) also found that the https://doi.org/10.5194/nhess-2019-399 Preprint. Discussion started: 28 January 2020 c Author(s) 2020. CC BY 4.0 License. maximum wave height was affected by crossing angle with a peak around 40 degrees in their numerical studies using 435 directionally spread crossing seas, while the ship in ballast conditions also experienced modest (35.7 degrees) to large responses (37.5 degrees) in our study.  Different from model tests focusing on wave effects on ship models with human-designed waves, a detailed analysis of the relationship between ship responses and ocean states was done in real rough seas with real-time observations in combination 445 with high-resolution wave hind cast. Information on ship motion, engine operation, ship speed loss, and ship dimension is available for every moment in these rough seas by on-board data-recording devices. Two widely used GPV datasets including the NCEP-FNL analyses and ERA-Interim have been used to provide ocean surface wind force to the wave model.
The ocean surface wind was validated using the on-board observations, and the relationship between simulated wave parameters and observed ship responses were quantitatively analysed and suggestions for ship safety under severe weather 450 conditions were also given.
At first, the relationship among different wave parameters in actual rough seas was studied using high-resolution wave models, showing a strong positive correlation of 0.85 between the Hs and wave steepness and a negative correlation of 0.66 between Hs and mean directional spread. Generally, the relationships between Hs and other parameters such as the 455 wavelength, wave period, wave direction as well as the relative wave direction were not strong, although a stronger correlation of these relationships has been found in the half-loaded cases than that the ballast-loaded ones.
Secondly, an analysis of the correlation among the observed ship responses shows a strong positive correlation between the pitch and roll motion (0.66), ship speed and engine RPM (0.76); a strong negative correlation relationship between the pitch 460 motion and ship speed (-0.85). The ship operators reduced the engine RPM more, but later in the half-loaded cases, than they did in the ballast ones. Additionally, due to a higher gravity center, the correlation between roll motions with other ship responses is stronger in the ballast cases than that in the half-loaded cases, and the differences of correlation coefficients are not less than 0.2.

465
Thirdly, studies on the ship responses to ocean states show a stronger correlation between ocean states with the pitch motion and ship speed than those with roll motion and engine RPM, and the wave parameters such as wavelength and mean wave period have a relatively weak correlation with ship responses. With the enhancement of ocean states such as the Hs and wave steepness, the amplitude of pitch and roll motion increases while the engine RPM and ship speed decrease. In addition to the head, bow and beam waves, the following quartering waves could also be dangerous because they could also induce large 470 roll motion in the half-loaded cases.
Lastly, important ship responses to ocean states of different levels are also given, quantitatively showing the relationship among ship navigational parameters such as pitch and roll motion, engine RPM and speed loss with those ocean parameters including the significant wave height, relative wave direction, mean directional spread and wave steepness. For ships of 475 similar dimensions, these results can provide practical suggestions to ship operators on identifying and avoiding the possible https://doi.org/10.5194/nhess-2019-399 Preprint. Discussion started: 28 January 2020 c Author(s) 2020. CC BY 4.0 License.
high-risk ocean regions, thus enabling them to reduce the negative effects on navigational safety and economy induced by unexpected large ship responses, as recorded in the logbook for one case (the first case in the Tasman Sea) that the crew almost lost the control of the ship in the high waves. In addition, such practical suggestions will also help improve the safety of Autonomous Surface Vehicles operation in harsh ocean environments in future studies.