1. Introduction
Rogue waves present a serious threat on the ocean. They are defined as a wave with height H that greatly exceeds the background wave height, quantified by the significant wave height Hs. Leading to the criteria of a rogue wave of H > zHs, where a common factor of z is 2.2. Only a few rogue waves in high sea states have been observed directly. The most notable among them (“Draupner” wave, “Andrea” wave, and “Killard” wave) exceed Hs by a factor of up to 2.3 (Haver 2004; Cavaleri et al. 2016; Donelan and Magnusson 2017; Fedele et al. 2016). Encounters with rogue waves have resulted in damage to marine structures and vessels, and have resulted in loss of lives. Compiled lists of extreme waves occurrences cite numerous injuries, loss of lives, damage to ships and coastal infrastructure (Didenkulova et al. 2006; Didenkulova 2020). Despite the hazard that rogue waves present, current rogue wave forecasts have limited skill in forecasting the risk of encountering these freak waves.
Forecasting large storms bringing big waves is important; however, in this work the interest is not only in the accurate prediction of the sea state, but in providing a practical probability forecast for rogue waves. This work’s domain of interest is the northeast Pacific where a recent record of a 17.6-m rogue wave was observed 17 November 2020 in coastal waters off British Columbia’s (BC) coast (Gemmrich and Cicon 2022). The nondimensional wave height (H/Hs) recorded was 2.9, which is likely the largest normalized wave height recorded worldwide. The northeast Pacific is also known for severe storms and large waves produced by strong winter lows (Tillotson and Komar 1997). To present a possible rogue wave risk forecast in high seas, we study a large storm event that occurred 21–22 October 2021 in the northeast Pacific. The storm made news headlines due to the MV Zim Kingston container ship losing over 100 containers at the mouth of the Juan de Fuca Strait and subsequently catching fire while at anchorage just off Victoria, British Columbia (http://www.tsb.gc.ca/eng/enquetes-investigations/marine/2021/M21P0297/M21P0297.html). The vessel, traveling from South Korea, was drifting at the mouth of the Juan de Fuca Strait when extreme weather caused an excessive listing resulting in the collapse of the containers, which were lost overboard. Only four containers were salvaged with some reported to have floated as far as Vancouver Island’s Northwest coast approximately 370 km away. The Transportation Safety Board of Canada (TSB) is performing a class 2 investigation of this incident (http://www.tsb.gc.ca/eng/lois-acts/evenements-occurrences.html).
There are two dominant theories to explain rogue waves in the absence of localized effects like current interactions or focusing effects; namely, (i) nonlinear effects like modulational instability (MI), and (ii) random linear superposition with nonlinear corrections (Dysthe et al. 2008; Gemmrich and Garrett 2011; Adcock and Taylor 2014). Modulational instability implies that rogue waves are generated by third-order nonlinear four wave interactions (Janssen 2003; Zakharov and Ostrovsky 2009). Essentially, in a weakly nonlinear, uniform wave train, small sideband frequencies exchange energy over time and reinforce each other. This results in instability and transient events of abnormally large waves. For a wave packet with a narrow spectrum, MI is well described by the nonlinear Schrödinger equation (Zakharov 1968). Theoretically, these rogue waves occur when the waves are sufficiently steep, for nonlinear focusing to overcome the spreading of energy by linear dispersion. Therefore, spectral bandwidth in combination with steepness can instigate or limit the modulation instability condition (Janssen 2003). This initiated the introduction of the Benjamin Feir index (BFI), which is the ratio of steepness to bandwidth as a proxy for rogue wave risk (Janssen 2003). MI through the BFI forms the basis of a routine rogue wave forecast at the European Centre for Medium-Range Weather Forecasts (ECMWF) (Janssen and Bidlot 2009). However, there is increasing evidence that MI is not the leading contributing factor to rogue waves as the narrow bandwidth and unidirectional conditions required for MI rarely occur in the real ocean (Garett and Gemmrich 2009; Fedele et al. 2016; Häfner et al. 2021b). An alternative theory is that rogue waves are a consequence of random linear superposition with nonlinear Stokes corrections. Stokes theory uses a perturbation series approach, known as the Stokes expansion with respect to steepness to obtain approximate solutions of the wave equation for nonlinear wave motion (Kinsman 1965). The superposition due to random phase alignment of Stokes waves with correction up to fourth order have been shown to account for the rogue wave occurrences observed in the ocean (Gemmrich and Garrett 2011; Gemmrich and Cicon 2022). This mechanism explains rogue wave generation as a linear superposition of multiple steep waves controlled primarily by bandwidth effects.
Rogue waves cannot be predicted from standard forecasts in any deterministic fashion. Phase averaged spectral models used for wave forecasting treat the wave field as a stochastic phenomenon and do not reproduce the sea surface explicitly. Therefore, a probabilistic approach is necessary to correlate spectral sea state characteristics to rogue wave probability. As of now, there is no robust rogue wave probability forecast, which is what this study aims to address. Building on the results of Häfner et al. (2021b), we reexamine proposed influential parameters in rogue wave dynamics in the northeast Pacific. We then expand on the work in Häfner et al. (2021b) by testing and evaluating the approach using a numerical system based on the WAVEWATCH III1 (WW3) wave model (WAVEWATCH III Development Group 2019).
We begin by investigating the relationship between rogue wave probability and r and a simple rogue wave probability forecast is proposed for the northeast Pacific. We then evaluate the ability to model the relevant parameters; namely, crest–trough correlation and significant wave height, using a regional WW3 wave model. This paper also assesses the newly developed northeast Pacific regional system by evaluating the model for the 5 October 2019–11 July 2021 period and a storm case study. The WW3 model forecast is evaluated for a storm on 21–22 October 2021, and a novel rogue wave probability product is demonstrated. The buoy data and wave model details are discussed in section 2. Section 3 introduces the method of generating a rogue wave probability forecast, the results from the observational dataset, and the evaluation of the WW3 model’s forecast. Section 4 presents the results of the storm case study and finishes with conclusions in section 5.
2. Data sources
a. Buoys
Thirteen buoys are used for the rogue wave analysis and the evaluation of the wave model’s forecast. Buoy data are provided by Environment and Climate Change Canada (ECCC), the Pacific Regional Institute for Marine Energy Discovery (PRIMED) at the University of Victoria, and MarineLabs Data Systems, Victoria, BC (Fig. 1). The ECCC buoys data are quality controlled and stored by the Marine Environment Data Section (MEDS) of the Department of Fisheries and Oceans, Canada (DFO) (Department of Fisheries and Oceans Canada 2021). The archives span several decades; however, here we use data from 2010 to 2021. The ECCC buoys include three open-ocean 6-m NOMAD buoys and the remainder are 3-m discus buoys. They record vertical acceleration at 1-Hz sampling rate for 34 min every hour and output bulk wave statistics and one-dimensional frequency spectra. Following a quality control procedure some buoy records and data sections are omitted. Buoy records from the Strait of Georgia are excluded from this analysis as the sheltered strait represents a different wave regime and is not in the scope of this work. In addition to these monitoring buoys, we utilize data from two buoys deployed primarily for research purposes. A 1.1-m TRIAXYS “Nearshore” buoy operated by PRIMED was deployed 2 km off Wickaninnish Beach in the Pacific Rim National Park Reserve in 25-m depth, and a 0.9-m CoastScout, operated by MarineLabs, was deployed about 7 km offshore from Ucluelet, BC, in 40-m depth. The two research buoys provide the surface elevation time series, in 20-min segments every 30 min at 1.3 Hz. The combined records of the Nearshore and MarineLabs buoys result in 28 months of sea surface elevation data.
Bathymetry of the unstructured computational grid with buoy locations marked by circles. Numbered buoys are missing the prefix “C46” for the ECCC buoys. “Nearshore” buoy is labeled N-S and MarineLabs buoys is M-L.
Citation: Weather and Forecasting 38, 11; 10.1175/WAF-D-23-0074.1
b. Wave model
A northeast Pacific wave prediction system, based on WW3 was developed in partnership with ECCC to be incorporated into their operational wave forecast suite. The model domain extends from northwest and southwest corners located at approximately (60°N, 145°W) and (40°N, 134°W) to the coast (Fig. 1). The coastline for the grid was obtained from the GSHHG coastline database provided by the National Centers for Environmental Information (Wessel and Smith 1996). The bathymetry data are a blend from the global relief ETOPO1 (NCEP 2016) with NONNA 100 survey data from the Canadian Hydrographic Service (https://data.chs-shc.ca/map). The model uses a triangular unstructured grid with variable resolution of 1 km nearshore to 5 km offshore generated with OceanMesh 2D in Matlab (Roberts et al. 2019). An implicit solving scheme with global time step of 600 s is used. The model resolves 36 frequency bins from 0.035 to 0.98 Hz corresponding to periods of approximately 1–29 s, and 36 direction bins spaced every 10°. The standard ST4 package is applied to parameterize wind input and dissipation (Ardhuin et al. 2010). In addition, nonlinear four wave interaction using the discrete interaction approximation, DIA (Hasselmann et al. 1985), JONSWAP bottom friction (Hasselmann et al. 1973), depth-limited breaking (Battjes and Janssen 1978), triad interactions (Eldeberky et al. 1996), and a linear input term are employed for the computations. The ST4 growth parameters and the proportionality constant for DIA were tuned using the Cyclops optimization method presented in Gorman and Oliver (2018).
The model is forced with hourly 2.5-km resolution winds from the High Resolution Deterministic Prediction System (HRDPS) (Milbrandt et al. 2016). Boundary conditions are imposed hourly at the western and southern open boundary nodes extracted from the 0.25° Global Deterministic Wave Prediction System (GDWPS) every 5 km (Bernier et al. 2016). In this work we present a 48-h forecast and also refer to a 6-h forecast. The 6-h forecast is the first 6 h of the 48-h forecast and forms the basis of the model continuous cycle. Over a 24-h period, the wave forecast system is driven using surface wind inputs and lateral boundary wave forcings stitched together using successive forecasts of the HRDPS and GDWPS, respectively. Since the HRDPS is run four times daily (0000, 0600, 1200, 1800 UTC) the 24 wind fields used to drive the wave model are obtained by using 6 wind fields obtained from each of the four daily forecasts. The GDWPS is run twice daily (0000 and 1200 UTC). In this case, the boundary conditions over each 24-h period are the result of 12-hourly input of each of the two daily runs.
3. Rogue wave probability forecast
a. Estimation of rogue wave probabilities
The methodology thus far relies on having the full surface elevation record to extract the individual wave heights Hi, and determine the number of rogue waves and non-rogue waves in each recording interval. A per wave estimation of p can then be computed following the method described above. Only the two research buoys report the surface elevation time series for 20-min recording intervals every hour. However, the analysis can be modified to incorporate the hourly output of bulk spectral parameters and Hmax measurements from the ECCC monitoring buoys. The monitoring buoy report a single Hmax measurement in a 34-min recording interval, and corresponding bulk spectral parameters for that interval. To convert this to a per wave estimation of p, rather than a per recording interval estimation of p, we estimate the number of waves in the recording interval by the mean period. The rogue wave probability for the ECCC buoy records is then calculated from the normalized maximum wave height Hmax/Hs and the total number of waves in each 34-min recording interval. This indirect method implies that the number of flagged rogue waves in a recording interval is limited to a maximum of one.
The predictive power is used to evaluate the degree of variability of p with parameter x defined as,
b. Observational rogue wave risk forecast
To develop the rogue wave risk prediction system, the rogue wave probability p was evaluated with various sea state parameters by flagging the number of rogue and non-rogue waves in each parameter bin. The parameters evaluated are crest–trough correlation r, measures of spectral bandwidth including narrowness σN and peakedness σP (Serio et al. 2005), steepness ε (Serio et al. 2005), and BFI (Thomson et al. 2019). As BFI is the ratio of steepness to bandwidth we evaluate a BFI computed with narrowness for the bandwidth parameter as
Variation in rogue wave probability p = P(H/Hs > 2) in blue and p = P(H/Hs > 2.2) in gray with sea state parameters (a) crest–trough correlation r, (b) steepness ε, (c) spectral bandwidth narrowness σN, (d) spectral bandwidth peakedness σP, (e) Benjamin Feir index using narrowness BFIN, and (f) Benjamin Feir index using peakedness BFIP. The shaded area is the 95% credible interval for p. The point markers are plotted at the mean sea state parameter in the bin, and the dashed vertical lines are the maximum and minimum observations of the sea state parameter.
Citation: Weather and Forecasting 38, 11; 10.1175/WAF-D-23-0074.1
We quantify the variation of p with sea state parameters by the “predictive power”
Predictive power of sea state parameters. Error bars represent 95% credible interval bounds. Where the correlation between p and the sea state parameter is negative (negative
Citation: Weather and Forecasting 38, 11; 10.1175/WAF-D-23-0074.1
Modifying the analysis slightly we can also evaluate crest–trough correlation as a rogue wave probability predictor at offshore locations by using the long term time series of hourly Hmax and Hs from the ECCC buoys. This work includes data from 1 January 2010 to 15 August 2021 which had received a quality control check. An additional visual inspection of the data was performed where suspicious data sections were removed, such as periods with excessive amounts of extreme rogue waves indicating likely instrumentation or logging errors for Hmax. Due to outages in service and erroneous data, the time series from the ECCC buoys are variable in length and do not necessarily span the full 11 years. A caveat with this data source is that without the sea surface elevation data it is impossible to verify the Hmax measurement in the context of the preceding and following waves to ensure that the rogue wave is physical and not an erroneous measurement. The data which passed quality control includes 15 000 individual 34-min recording intervals in which Hmax/Hs > 2 and 3500 in which Hmax/Hs > 2.2. This is a lower bound of the true number of rogue waves measured by the buoys as the number of rogues in a recording interval is limited to a maximum of one as only the single Hmax value is given, excluding the possibility of multiple rogue waves in the recording interval. It has been observed in the 1.5 billion wave dataset of Häfner et al. (2021a), that there exists a relatively high number of multiple rogue waves in rapid succession, which corresponds to about 3% of all rogue events. Therefore, the true number of rogue waves in the ECCC records would be expected to be roughly 3% more numerous, as the lower of two rogue waves occurring in rapid succession in one recording interval is not recorded. Subsequently, if the forecasts are assumed to accurately reflect observations, then the forecast rogue wave probability will be lower than in reality. The modified analysis method using Hmax and the number of waves in each recording interval was first tested on the combined surface elevation time series of the Nearshore and MarineLabs buoys before applying it to the ECCC buoy records. Only 3 rogue events out of 160 were unaccounted for with the Hmax simplification and the rogue wave probabilities produced were consistent with the full surface elevation analysis.
The evaluation of the rogue wave probability as a function of the crest–trough correlation is split into three regional buoy categories: “open ocean,” “open coastal,” and “sheltered” (Fig. 1). Open ocean buoys are buoys far from the coast. Open coastal buoys are coastal buoys that are subject to open ocean swell. Sheltered buoys are coastal buoys that are somewhat sheltered from the influence of the open ocean. Bins with fewer than 10 rogue waves are omitted. This threshold can be larger with the longer time series of the ECCC buoys with more rogue wave observations, compared to the shorter time series of the Nearshore and MarineLabs buoys. In all categories a similar strong trend of high correlation between p and r is present which resembles a semilog linear relationship (Fig. 4). This demonstrates that r is an effective rogue wave predictor not only in coastal areas, but is an effective parameter for the full domain of the operational wave forecast.
Variation in rogue wave probability p with crest–trough correlation r, where (left) p = P(Hmax/Hs > 2) and (right) p = P(Hmax/Hs > 2.2). Shaded area is the 95% credible interval for p. The number in brackets in the title is the number of buoys in the category. The point markers are plotted at the mean r value in the bin and the dashed vertical line are the maximum and minimum observation of r.
Citation: Weather and Forecasting 38, 11; 10.1175/WAF-D-23-0074.1
Semilogarithmic fit of return period
Citation: Weather and Forecasting 38, 11; 10.1175/WAF-D-23-0074.1
c. Evaluation of forecasts
Scatterplots of observations vs WW3 model output for (a) significant wave height Hs, (b) crest–trough correlation r, and (c) r where Hs from the model is greater than 3 m. (d) A scatterplot of r vs Hs of buoy data. Data used are from 21.5-month model time series from 5 Oct 2019 to 11 Jul 2021 and for all buoys available in the wave model domain for that period. The solid black line is the 1:1 line, and the dashed gray line is the linear fit. Statistical scores for correlation coefficient R, bias b, and scatter index SI are given on the plot.
Citation: Weather and Forecasting 38, 11; 10.1175/WAF-D-23-0074.1
The 48-h WW3 forecast model performance was evaluated for Hs and r for winter (November and December 2020) and summer (July and August 2021). For both parameters Hs and r, the bias remains nearly constant with a weak increase of SI with forecast lead time (Fig. 7). Although the optimization was in theory fair for both seasons, the wave model is more favorably tuned for the winter for Hs as there is larger bias in July and August compared to November and December. The larger SI in the summer months can be mainly attributed to lower sea state observations in the summer. This bias toward better forecasts in the winter is favorable as the forecast in winter months is arguably more important due to large storms with higher risk. The average bias in the forecast for r is negative, close to zero in the summer, and roughly −0.02 during winter, opposite to the seasonal behavior of the bias in Hs. Similarly to Hs, the scatter for r is smallest in the winter, with SI increasing from 10% at the 6-h forecast to 12% for the 48-h lead time. During summer, SI of r is almost twice as high as in winter.
Bias and scatter index (SI) for (a) Hs and (b) r with forecast lead time for winter months (November and December 2020) and summer months (July and August 2021).
Citation: Weather and Forecasting 38, 11; 10.1175/WAF-D-23-0074.1
4. Case study
The fall storm highlighted in this work was caused by an extratropical cyclone with a central low pressure of 952 hPa. The low pressure system progressed from the Gulf of Alaska toward the coast bringing strong winds and driving large seas. The storm enters the model domain at approximately 0600 UTC 21 October 2021 and dissipates by 1800 UTC 22 October 2021. The maximum wind speed and maximum wave height recorded by the open ocean buoy C46036 was 20.3 m s−1 and 9.5 m, respectively. It has been reported that the Zim Kingston container ship experienced excessive listing, which resulted in containers being lost overboard while drifting outside the mouth of the Juan de Fuca Strait. At the time of this analysis (spring 2023) an exact location and time where the vessel lost the containers has not been published. However, the automatic identification system (AIS) data published by NOAA (https://coast.noaa.gov/htdata/CMSP/AISDataHandler/2021/index.html) indicates the ship drifting at approximately (48.36°N, 125.61°W) outside the Juan de Fuca Strait, consistent with the TSB report, and therefore the best estimate for the location of the excessive listing.
Here we evaluate the WW3 models forecast with lead time to the storm using three buoys, C46036, C46206 and C46207 in the storms reach. Forecasts discussed in this section are 48-h forecasts produced every 6 h over the period of 15 October 2021–1 November 2021. For the rogue wave risk analysis, the wave spectra were output every 1/4° within the model domain. Crest–trough correlation is not a standard WW3 output parameter, and r has been initially tested without modifying WW3. Therefore, r is computed from the spectra in postprocessing at 1/4° resolution. Outputting the spectra for each grid node would be too costly. Following the promising results discussed in this study, calculations of r should be incorporated directly in WW3. This would make r readily available at every grid node, just like Hs.
a. Forecast performance
The WW3 model performs relatively well for the storm with the main discrepancies occurring at the peak of the storm, where the largest error is in the open ocean. Based on the forecasts the projected Hs at the coastal buoys C46207 and C46206 are well represented by the model; however, the storm peak is greatly underestimated at the open ocean buoy C46036 (Fig. 8a). The forecast at C46036 does improve with decreasing lead time to the storm, but still misses the peak. There is a slight systematic underestimation of large Hs by the model, demonstrated in the quantile–quantile plot of Hs (Fig. 9). In general wave models have a tendency to underestimate the largest wave heights, and in particular the peaks of storms (Cavaleri 2009). This is due to wave models being tuned to the bulk of the data, which does not include the rare extreme events. However, this considerable underestimation is more largely attributed to the significant drop in wind speed in the HRDPS forecast (Fig. 8b). The misrepresentation of the wind at the open ocean buoy is due to the low pressure system being forecast slightly more south than in reality. This is verified by the ERA5 reanalysis data of the wind field at 2000 UTC 21 October 2021 (Hersbach et al. 2018). The difference between ERA5 and HRDPS wind forecast with decreasing lead time to the storm demonstrates the underestimation of the winds at the C46036 buoy (Fig. 10). The HRDPS wind forecast does approach the ERA5 wind field with decreasing lead time to the storm peak, but not quite timely enough for the peak to be captured at C46036. Elsewhere, wind forecasts are more representative of actual conditions and so the model predicts the storm well up to 24 h of lead time.
The 48-h forecasts, where only every other forecast is plotted for (a) Hs and (b) wind speed. Dashed vertical lines corresponds to times of peak Hs reported by the respective buoys.
Citation: Weather and Forecasting 38, 11; 10.1175/WAF-D-23-0074.1
Hs quantile–quantile plot of buoy observations against the WW3 model output for the full model time series of 6-h forecasts from 5 Oct 2019 to 11 Jul 2021. The black line is the 1:1 line, and the red line is the linear fit through the data. The Hs markers have been downsampled for plotting.
Citation: Weather and Forecasting 38, 11; 10.1175/WAF-D-23-0074.1
Difference between the ERA5 reanalysis wind field and HRDPS forecast wind field wind for 2000 UTC 21 Oct 2021 from the (a) 0000 UTC 21 Oct 2021 model forecast, (b) 1200 UTC 21 Oct 2021 model forecast, and (c) 1800 UTC 21 Oct 2021 model forecast. The ERA5 wind field has been interpolated onto the unstructured grid nodes to compute the difference. Positive values mean the ERA5 wind speed is larger than what was predicted by the HRDPS. Gray marker is location of buoy C46036.
Citation: Weather and Forecasting 38, 11; 10.1175/WAF-D-23-0074.1
b. Rogue wave risk evaluation
As an example of a potential rogue wave risk prediction, we evaluated the forecast of r and Hs for the storm. The wave model time series of r at C46036, C46207 and C46206 captures the overall variability in r (Fig. 11). However, the forecast of r is far more stable with regards to variations in the wind and boundary forcing compared to Hs. At the approximate peak of the storm at 0000 UTC 22 October 2021 there is a pocket of higher rogue wave likelihood in the open ocean at approximately (50°N, 135.5°W). The significant wave height in this region is forecast as approximately 7 m (Fig. 12). The r value in this pocket corresponds to a probability of a wave exceeding 2Hs (14 m) once every 1.1 days and a wave exceeding 2.2Hs (15.5 m) once every 3.4 days. The probability and return period for rogue waves is computed using the fitted equations for rogue wave probability (5) and the mean wave period
The 48-h forecasts of crest–trough correlation, where only every other forecast is plotted. Dashed vertical lines corresponds to times of peak Hs reported by the respective buoys.
Citation: Weather and Forecasting 38, 11; 10.1175/WAF-D-23-0074.1
Field maps of (a) rogue wave height Hrogue = 2.2Hs, (b) crest–trough correlation r, (c) return period for waves of height given in (a), and (d) probability of a rogue wave H > 2.2Hs. All panels are for 22 Oct 2021, which is approximately at the peak of the storm. Greyed out areas are regions where Hs < 3 m and no reliable rogue wave forecast is available.
Citation: Weather and Forecasting 38, 11; 10.1175/WAF-D-23-0074.1
Time series of Hs and crest–trough correlation r outside the Juan de Fuca Strait (48.36°N, 125.61°W). The vertical dashed line is the storm peak from the model Hs output. Dotted lines are the Hs and r forecasts from 0600 UTC 21 Oct 2021 (T06Z), which is approximately 24 h prior to the storm peak.
Citation: Weather and Forecasting 38, 11; 10.1175/WAF-D-23-0074.1
5. Conclusions
In the northeast Pacific domain presented here, we have found additional evidence that crest–trough correlation r is a plausible parameter as a rogue wave risk predictor and should be considered to be included in standard wave forecasts. There is a strong correlation between rogue wave probability and r in coastal areas as well as the open ocean, where rogue wave probability p increases in sea states with high r. The dependence on r is a reflection of bandwidth controlled linear superposition being the dominant rogue wave generation mechanism. Identifying a spectral sea state parameter that informs on rogue waves risk means that a rogue wave risk prediction can be produced by standard wave models. The crest–trough correlation r is forecast by the northeast Pacific regional wave model with moderate accuracy compared to the higher skill of predicting Hs. Based on the comparison of long-term time series from buoy observations, r has large scatter in low Hs sea states. Therefore, in a rogue wave probability forecast based solely on r, p should be omitted where Hs is low, as is demonstrated in Fig. 12. Crest–trough correlation being adequately forecast in large seas is especially beneficial as rogue waves in large seas are particularly threatening. The skill of the combined Hs and r prediction is demonstrated in the case study of the large storm 21–22 October 2021. The output of Hs is adequately forecast by the model 24 h prior to the storm peak where the winds from the HRDPS are accurately forecast. A large underestimation of Hs at the storm peak at one of the buoys is primarily due to inaccurate localization of the wind and secondarily to a small systematic underestimation of large Hs by the wave model. This emphasizes the importance of the wind forecast for wave forecasting as well as the challenges of capturing the peak of large storms. The r forecast for the storm performs reasonably well and captures the overall variability in r.
Through this work we demonstrate the production of accurate forecasts by the newly implemented northeast Pacific model. This paper reiterates that rogue wave probability is highly correlated to crest–trough correlation and further demonstrates that r is reasonably well predicted by a standard WW3 wave model. A combination of Hs and r has the potential to provide a simple practical risk assessment for rogue waves. However, it should be noted that the relationship between r and p presented here can be considered a lower bound of the true rogue wave probability as the Hmax measurements used do not account for the recording of rogue waves in rapid succession. Furthermore, this proposed forecast does not include any localized rogue wave generation effects due to current interactions and topographical focusing. Following steps are to include r in WW3 to be calculated along with the other spectral parameters and explore its usefulness in global deterministic and wave ensemble forecast systems. Improvements to the empirical expression of rogue wave exceedance probability could include exploring multivariable dependencies.
WAVEWATCH III is a registered trademark of the National Weather Service.
Acknowledgments.
This work was funded by Search And Rescue New Initiatives Fund (Public Safety Canada) Grant SN201907. We thank the Pacific Regional Institute for Marine Energy Development PRIMED (University of Victoria), and MarineLabs Data Systems (Victoria, BC) for access to the buoy data.
Data availability statement.
The wave model data are available from the corresponding author on reasonable request. Data access is restricted to research and educational applications. ECCC buoy data can be accessed at https://meds-sdmm.dfo-mpo.gc.ca (MEDS). Forecasts from the Global Deterministic Wave Prediction System (GDWPS) can be accessed at https://eccc-msc.github.io/open-data/msc-data/nwp_gdwps/readme_gdwps_en/. Forecasts from the High Resolution Deterministic Prediction System (HRDPS) can be accessed at https://eccc-msc.github.io/open-data/msc-data/nwp_hrdps/readme_hrdps_en/. Forecasts for the northeast Pacific model, which is included in the Regional Deterministic Wave Prediction System (RDWPS), can be accessed at https://eccc-msc.github.io/open-data/msc-data/nwp_rdwps/readme_rdwps_en/.
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