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ABSTRACT
ABSTRACT
This paper compares and evaluates three wave hindcasts in the North Atlantic Ocean: ERA-Interim, NOAA/CFSR and HIPOCAS. The assessment was performed using satellite data from the GlobWave Project. It concerns the second part of a research project that aims to characterize differences among reanalyses and to calculate wind and wave error maps using satellites. The first step of this study inter-compares the hindcasts within a spatial-temporal approach. Besides, the analysis was also divided into overall conditions and extreme events. The second step evaluates each hindcast independently using satellite data. In order to compare and evaluate the three datasets, coincident periods and grid domain were determined, which corresponds to the interval between 1979 and 2001, latitudes between 15° and 72° North and longitudes between 66° West and 7° East. Results for the overall non-extreme conditions indicate that the three wave hindcasts are very similar and have small errors (less than 0.5 metres); NOAA/CFSR (based on the WAVEWATCH III model) presents the largest waves, followed by HIPOCAS and ERA-Interim (both based on the WAM model). NOAA/CFSR and especially HIPOCAS at European waters tend to overestimate the measurements while ERA-Interim tends to underestimate. For extreme events, the differences increase significantly (up to 2.5 meters) and HIPOCAS presented the highest waves, followed by NOAA/CFSR and ERA-Interim (severely underestimated). A simple joint wind and wave analysis concluded that WAVEWATCH III presented the best modelling in terms of bias but was over-performed by WAM used in the ERA-Interim project regarding the root mean square error and scatter index.
1. Introduction
Winds, waves and currents are essential environmental loads that act on ships and offshore structures. Wave height and wave crest are among the most important wave characteristics for engineering applications (ISSC 2015). In terms of environmental threat to ship and marine structures, Vanem and Walker (2013) consider the significant wave heights perhaps the most important parameter. Bad weather with high waves account for a great number of ship losses and accidents. Some failure modes related to ocean waves are hull girder collapse due to extreme loads that may break the ship into two in extreme sagging or hogging conditions, structural failure due to fatigue, parametric roll and capsize/loss of stability. The most critical conditions will vary between ship types and will depend on the actual design. Other hazards related to ocean waves for various ship types are green water loads, breaking of windows, sloshing of tanks, shift of cargo and loss of containers. Hence, the ocean wave climate is a major concern in ocean engineering applications and for all stakeholders within the maritime industries. Such environmental forces need to be taken into account in the design and operation of marine structures; both the normal conditions and the severe sea state conditions must be considered in design and there is a need for a long-term description of the variability of important sea state parameters. Moreover, Tolman and Alves (2005) describe that apart from high wind speeds and increased mean water levels at landfall, wave heights associated with tropical cyclones pose a major hazard.
Wave buoys, wave staffs, radars, lasers, LASAR and step gauges remain the most important sources of in situ measurements (ISSC 2015). However, locations where high-quality in situ data are available are sparsely distributed, since buoys and platforms data are geographically limited. Although satellite observations offer global coverage, they suffer from temporal scarcity and intermittency, making estimation of long-term distributions and extreme analysis difficult. Traditionally instrumentally recorded data were regarded as superior to model derived data. However, due to limited availability of measurements and improved hindcasts, the latter have become increasingly used in design in the last decade. New improved global wave hindcasts (e.g. ERA-Interim, HIPOCAS, CFSR) are continuously developed (Cardone et al. 2015). Reanalyses have the advantage of high time–space resolution, long duration, large grid domains and data assimilation. Recent progress on wave modelling has been presented at the 13th International Workshop on Wave Hindcasting and Forecasting & 4th Coastal Hazard Symposium, taken place 27th October till 1st November 2013 in Banff, Canada. Roland and Ardhuin (2014) summarise some aspects of these improvements.
The present paper compares three wave hindcasts in the North Atlantic Ocean followed by an evaluation against GlobWave satellite data. The datasets are: ‘Hindcast of Dynamic Processes of the Ocean and Coastal Areas of Europe’ based on the REMO (Jacob & Podzun 1997; Von Storch et al. 2000) wind model (hereafter called HIPOCAS; Pilar et al. 2008); ERA-Interim (Dee et al. 2011) and the recent NOAA wave hindcast based on WAVEWATCH III forced with the Climate Forecast System Reanalysis (CFSR; Saha et al. 2010) described by Chawla et al. (2012). Differences between reanalyses and its possible sources are discussed. The analysis is restricted to the North Atlantic Ocean, which is regarded as the most severe – confirmed by Cardone and Cox (2011) and Cardone et al. (2015). The majority of ocean-going ships are designed to the North Atlantic wave environment as well as the floating production, storage and offloading (FPSO) systems if location-specific wave climate cannot be proved more appropriate (ISSC 2015), which emphasise the importance of the selected domain in the present paper.
Due to the intense activity and severity of the North Atlantic Ocean (as well as other severe locations), the accuracy of hindcasts has become extremely important, as it plays an essential role for disaster prevention. A proper evaluation of hindcasts is a key process to improve the wave models and hence the operational forecasts. Moreover, accurate forecast is important for the eco-efficiently ship operations because of the optimum ship routing that depends significantly on the wave forecast. Several wave modelling simulations were made recently to study extreme events that caused well-known accidents; for example, Cavaleri et al. (2012) studied the accident of the Louis Majesty ship, which took place in the Mediterranean Sea on 3rd March 2010. The ship was hit by a large wave that destroyed some windows at deck number five and caused two fatalities. Using the WAM wave model, driven by the COSMO-ME winds, a detailed hindcast of the local wave conditions was performed. Waseda et al. (2013) have revisited a well-studied marine accident case in Japan in 1980 (Onomichi–Maru incident) and hindcasted the sea states. Bitner-Gregersen et al. (2014) have applied coupling of the wave model WAM and the numerical non-linear wave model based on the Euler equations to investigate statistical properties of surface oscillations during the particularly severe Andrea storm, which crossed the central part of the North Sea on 8th–9th November 2007. More examples about wave hindcasts and associated discussion and evaluation involving wave modelling can be found in Burgers and Makin (1992), Sterl et al. (1998), Alves et al. (2002), Rocha et al. (2004), Padilla-Hernandez et al. (2004), Cavaleri and Bertotti (2004), Caires et al. (2004), Tolman and Alves (2005), Cavaleri and Bertotti (2006), Feng et al. (2006), Ardhuin et al. (2007a, 2007b, 2010), Guedes Soares (2008), Ponce de León and Guedes Soares (2008), Mackay et al. (2010), Cardone and Cox (2011), Young et al. (2011), Appendini et al. (2012), Campos et al. (2012), Chawla et al. (2013), Guedes Soares et al. (2014), Ponce de Leon and Guedes Soares (2014) and Stopa and Cheung (2014).
The wind-generated ocean waves are related to the surface winds and its characteristics of intensity, fetch dimension and duration (Young 1999a). The Joint North Sea Wave Project (JONSWAP; Hasselmann et al. 1973) was an important experiment to quantify the non-linear relation of wave growth related to the surface wind intensity. Many authors describe the importance of the wind input for the numerical wave models and how sensitive is the momentum transfer process (Teixeira et al. 1995; Holthuijsen et al. 1996; Tolman & Chalikov 1996; Ponce de Leon & Ocampo-Torres 1998; Cavaleri et al. 2007; Stopa et al. 2013) – see Equations (5)–(7). Therefore, this present paper also aims to briefly evaluate the impact of the wind error on the final wave error obtained from the comparison using GlobWave satellite data.
2. Description of datasets
The WAM (WAMDI Group 1988) model and the WAVEWATCH III (Tolman 2009) model are the most generalised and tested wave models used for both hindcasting and forecasting purposes and many reanalyses have been produced with them (ISSC 2015). Some recently updated or newly developed metocean databases are: ERA-Interim, ERA-Clim, CFSR, NORA10, GROW12, HIPOCAS, BMT-ARGOSS and Fugro-OCEANOR. The reanalyses ERA-Interim, ERA-Clim and CFSR databases have higher resolution and improved forcing with better quality control of assimilated data (Aarnes et al. 2012; Cardone et al. 2015). Other local hindcasts for specific applications are, for example, GROW (Mediterranean Sea, Sea of Okhotsk, Caribbean Sea and North Atlantic Basin), NAMOS (NW Australia), SNEXT (North Sea), SEAFINE (SE Asia), BOMOSHU (Brazil, Atlantic waters) and WASP (West Africa Swell Project). The two main centres with global reanalyses under continuous improvements are the National Centers for Environmental Prediction (NCEP/NOAA) and the European Centre for Medium-Range Weather Forecasts (ECMWF), responsible for two of the three reanalyses evaluated in this paper, ERA-Interim and CFSR, respectively.
ERA-Interim (Dee et al. 2011) covers the period from 1979 and kept up to date, which increases its utility for near real-time applications and it has a resolution of 0.7° × 0.7° and 6 hours for the wave parameters. The wave model remains the same as all ECMWF reanalyses (WAM), but the source terms were updated as explained by Bidlot et al. (2005, 2007) and Janssen (2008). ERA-Interim also includes data assimilation from satellites for the wave results starting in 1991. The need of atmospheric oceanic model coupling is discussed by Tolman and Alves (2005), Bender and Ginis (2000) and Bao et al. (2000) – it was first implemented by the ECMWF and used in the ERA-Interim project with fully coupled components for the atmosphere, land surface and ocean waves (Dee et al. 2011). The ERA-Interim database can be downloaded (after registration and following the terms and conditions) at http://apps.ecmwf.int/datasets/data/interim-full-daily/.
The global atmospheric reforecast CFSR is based on the Global Forecast System (GFS) model that is run by the NCEP to provide forecasts four times per day. It was used to force WAVEWATCH III ® (Tolman 2009) using the source terms of Tolman and Chalikov (1996) as described by Chawla et al. (2013). The final wave hindcast (hereafter called NOAA/CFSR) covers the period from 1979 to 2009 with a resolution of 0.5° × 0.5° and 3 hours. The NOAA/CFSR database was deeply discussed and validated by Chawla et al. (2013).
HIPOCAS contains 44-year datasets of wind, sea level and waves in the North Atlantic Ocean and areas surrounding Europe. It was a follow-up to the WASA reanalysis (Waves and Storms in the North Atlantic; Güenther et al. 1998), which was not focused on European Coastal areas but on the North and Northeast Atlantic. The wind input fields were generated by the regional atmospheric model REMO (Jacob & Podzun 1997; Von Storch et al. 2000) forced with the 44-year atmospheric reanalysis (Kalnay et al. 1996), from 1958 to 2001, carried out by the National Centers for Environmental Prediction and National Center for Atmospheric Research (NCEP/NCAR). Details about the wind modelling can be found in Weisse and Feser (2003), Weisse et al. (2005) and Sotillo et al. (2005, 2008). The wind fields forced the WAM model cycle 4 (WAMDI Group 1988), which was used in a version allowing two-way nesting (Gomez Lahoz & Carretero Albiach 1997). The procedure resulted in four grids with increasing resolution towards the Iberian Peninsula, described by Pilar et al. (2008). The grid selected for the comparisons has a space–time resolution of 1.0° × 1.0° and 3 hours for the wave parameters. Pilar et al. (2008) provide a complete evaluation of HIPOCAS. Table 1 summarises the grid resolutions of the three reanalyses of this paper.
Comparison and assessment of three wave hindcasts in the North Atlantic Ocean
Published online:
20 July 2016Table 1. Reanalyses approximate resolution and coverage.
The evaluation of ERA-Interim, CFSR and HIPOCAS in this paper was based on GlobWave Satellite data. The GlobWave Project is an initiative funded by European Space Agency (and subsidised by CNES) through the Data User Element (DUE), which is a programmatic element of the third period of the Earth Observation Envelope Programme (EOEP-3), an optional programme of the European Space Agency (GlobWave Product User Guide 2010). According to GlobWave Product User Guide (2010), some of the main goals of the project are: (1) to develop and maintain a GlobWave web portal providing a single point of reference for satellite wave data and its associated calibration and validation information; (2) inter-comparison of different wave data sources; (3) provision of a uniform, harmonised, quality controlled, multi-sensor set of satellite wave data and ancillary information in a common format, with a consistent characterisation of errors and bias. Therefore, this new satellite database represents a standard and reliable source of public data, in accordance with the state-of-the-art in Satellite Altimetry. The quality control and calibration, known to be one of the most time-demanding steps, represents a major improvement of the GlobWave database.
A previous evaluation and comparison of ERA-Interim and NOAA/CFSR hindcast using buoy and altimetry measurements was performed by Stopa and Cheung (2014), who found a systematic seasonal biases, temporal discontinuities, and spatial error trends in terms of wind speed and wave height. They describe that both hindcasts results are reasonably well but ERA-Interim tends to underestimate and NOAA/CFSR overestimates the measurements. Under extreme conditions the authors showed that both hindcasts are underestimated, with a better performance of NOAA/CFSR. For the upper percentiles between 90th and 99.9th ERA-Interim underestimates the wave height by 5–18% while NOAA/CFSR has biases in a more favourable range of 4–8%. Agarwal et al. (2013) also studied the reanalysis ERA-Interim, pointing the same underestimation of the extreme quantiles when compared with estimates obtained from buoy data.
The final wave heights, in terms of over and under predictions, are resulted from both wind input and wave model applied, that is, overestimated winds can generate underestimated waves in case of a low transfer energy rate of the wave model and vice-versa. Many studies have performed sensitivity tests to evaluate specifically the wave models WAM and WAVEWATCH III. Padilla-Hernandez et al. (2004) tested three models, WAVEWATCH III v2.2, WAM4 and SWAN, against measurements. The authors found that all models generally underestimate the peak storm Hs values. They concluded that, although all models provide skillful hindcasts, results show that WAVEWATCH out-performs the other models, in comparison with observed wave data, and SWAN can give slightly better results nested in WAVEWATCH, rather than in WAM. Mackay et al. (2010) show the complexity and the dependence of the final errors in wave models, which exhibit non-linear dependence on multiple factors, seasonal and inter-annual changes in bias and short-term temporal correlation. They concluded that the estimate of Hs from the WAVEWATCH hindcast is consistently lower than the buoy data and the estimate from the WAM hindcast is consistently higher, although, both models underestimate the most intense storm in the analyzed period. In the two datasets (from WAM and WAVEWATCH) examined in the paper, both presented significant biases before calibration performed by Mackay et al. (2010) and, after calibration, the WAVEWATCH hindcast seemed to perform better.
Tolman and Chalikov (1996) developed one of the most used source terms implemented in WAVEWATCH III (ST2). Compared to measurements, the model results in excellent growth behaviour from extremely short fetches up to full development. For intermediate to long fetches, results are similar to those of WAM, but for extremely short fetches the model presents a significant improvement. The authors concluded that WAVEWATCH gives smoother growth curves than WAM. Moreover, in the absence of wind biases, Durrant et al. (2013) show that the source terms of Tolman and Chalikov (1996) actually provide slight underestimations. Ardhuin et al. (2007a) constructed a hindcast of wind and wave conditions in the Mediterranean Sea for two months. Four meteorological models (ECMWF, ALADIN, COAMPS and ARPEGE) and three wave models (WAM-cycle 4, VAG and WAVEWATCH) were used and results were compared with satellite and buoys. The authors found that for low wave heights, WAM and WAVEWATCH perform similarly. However, for growing significant wave heights, there is a progressively increasing underestimation by WAVEWATCH with respect to WAM. Finally, comparing WAVEWATCH with buoys, it seems to underestimate substantially the largest wave heights in the Mediterranean Sea.
These previous evaluations give a brief initial idea about what to expect in the next comparisons and evaluations of ERA-Interim, NOAA/CFSR and HIPOCAS, since HIPOCAS and ERA-Interim are based on WAM, but with different wind inputs and source terms, and NOAA/CFSR is based on WAVEWATCH III.
3. Methodology of comparison and evaluation
The methodology is the same as applied in a previous evaluation of the winds (first part of the same project) and it is divided into two parts: the first of inter-comparison of HIPOCAS against ERA-Interim and HIPOCAS against NOAA/CFSR; and the second part of independent evaluation of the three reanalyses against GlobWave Satellite data. Coincident time and grid domain were determined, which corresponds to 1979–2001, latitudes between 15° and 72° North and longitudes between 66° West and 7° East. The evaluation using satellite data restricted the period to 1985–2001 because of the absence of satellite data before 1985.
ERA-Interim and NOAA/CFSR grids were spatially interpolated to the final resolution of HIPOCAS, equal to 1° × 1°. The lowest time resolution among reanalyses (ERA-Interim) was selected for the comparison, equal to 6 hours. Therefore, the lowest grid resolution (from HIPOCAS) and the lowest temporal resolution (from ERA-Interim) defined the space–time resolution from now on applied. Figure 1 shows the exact grid points where the comparison and evaluation were calculated.
Comparison and assessment of three wave hindcasts in the North Atlantic Ocean
Published online:
20 July 2016Figure 1. Comparison domain and grid. The red points represent two positions of the time series analysed, at 55°N/25°W (Point A) and 25°N/25°W (Point B).
![]({"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/tjoo20/2016/tjoo20.v009.i01/1755876x.2016.1200249/20160808/images/medium/tjoo_a_1200249_f0001_c.jpg"})
Figure 1. Comparison domain and grid. The red points represent two positions of the time series analysed, at 55°N/25°W (Point A) and 25°N/25°W (Point B).
The analysis under extreme conditions selected data above the 95th percentile. Thus, sections are divided into overall conditions and extreme events. Results are also divided into all-year comparison, regarding the entire period, and monthly divided comparison. The error metrics applied are: bias (satellite minus reanalyses), root mean square error (RMSE), scatter index (SI) and correlation coefficient (r):![]({"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/tjoo20/2016/tjoo20.v009.i01/1755876x.2016.1200249/20160808/images/tjoo_a_1200249_m0001.gif"})
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(2) ![]({"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/tjoo20/2016/tjoo20.v009.i01/1755876x.2016.1200249/20160808/images/tjoo_a_1200249_m0003.gif"})
(3) ![]({"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/tjoo20/2016/tjoo20.v009.i01/1755876x.2016.1200249/20160808/images/tjoo_a_1200249_m0004.gif"})
(4) where ![]({"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/tjoo20/2016/tjoo20.v009.i01/1755876x.2016.1200249/20160808/images/tjoo_a_1200249_ilm0001.gif"})
are the measurements (GlobWave satellite data) and ![]({"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/tjoo20/2016/tjoo20.v009.i01/1755876x.2016.1200249/20160808/images/tjoo_a_1200249_ilm0002.gif"})
are the reanalysis values. The over bar indicates mean values through time and ![]({"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/tjoo20/2016/tjoo20.v009.i01/1755876x.2016.1200249/20160808/images/tjoo_a_1200249_ilm0003.gif"})
denotes the number of data pairs. Metrics are called ‘error’ (RMSE) only when it is using measurements; when two hindcasts are compared it is referred as ‘difference’ (root mean square difference, RMSD).
At the end two grid points were selected to visualise the time series and to compare the evolution of wave heights in the winter and summer. The locations were chosen (red points of Figure 1) representing typical overestimation and underestimation areas.
4. Comparison between databases
4.1. Analysis for the overall conditions
This section deals with comparisons between the three reanalyses taking HIPOCAS as the reference and covering the whole datasets, involving all meteorological systems and intensities. Further it will be separated and focused on extreme events only.
4.1.1. All-year comparison
Table 2 summarises the spatial and temporal average of the comparisons. Values of mean difference and RMSD are reasonably small, especially for the comparison between HIPOCAS and ERA-Interim, that is, the table shows that the significant wave heights of HIPOCAS are more similar to ERA-Interim than to NOAA/CFSR. Although these two metrics are small, the scatter index is high, which indicates an important relative difference between hindcasts.
Comparison and assessment of three wave hindcasts in the North Atlantic Ocean
Published online:
20 July 2016Table 2. Spatial wave average of the comparison metrics of all grid points of Figure 1 for the whole dataset.
Table 2 also shows that HIPOCAS has larger waves than ERA-Interim but smaller than NOAA/CFSR; that is, considering the temporal and spatial average, NOAA/CFSR presents the highest waves among hindcasts, followed by HIPOCAS and ERA-Interim. It follows the improving resolution order of reanalyses (Table 1), with NOAA/CFSR having a fine and ERA-Interim a coarse grid resolution – which corroborates with Cavaleri and Bertotti (2006). Some papers have showed that WAVEWATCH tends to underestimate WAM (e.g. Ardhuin et al. 2007a); however, in this case the wind input and(or) different model tuning prevailed on the simulation and final wave fields. Table 2 confirms the results from Stopa and Cheung (2014) who found a significant underestimation of ERA-Interim compared to NOAA/CFSR.
Figures 2 and 3 present the spatial distribution of differences, with a large range of each-site metrics. The colour bars indicate large differences between hindcasts that were hidden in the spatial average of Table 2. From these figures it is possible to conclude that errors and differences among hindcasts are strongly site dependent. The general increase of bias occurs with latitudes, due to the increase of wind intensity and wave heights at mid-high latitudes. However, Figure 2 shows a strong dependence of the longitudinal evolution, in terms of differences between HIPOCAS and ERA-Interim. These differences increase towards Europe, especially at coastal waters and between Scotland and Norway. The west part of the North Atlantic Ocean has ERA-Interim with similar or higher waves than HIPOCAS while in the east part HIPOCAS has much larger waves. It can be interpreted as the cumulative disagreement from the wind input and model parameterisation following the westerly winds; later it will be shown that this is due to a longitudinal decrease of bias of HIPOCAS compared to the satellite data. The RMSD map of Figure 2 highlights the increasing error above 40° North, as expected from the wind comparisons.
Comparison and assessment of three wave hindcasts in the North Atlantic Ocean
Published online:
20 July 2016Figure 2. Wave comparison maps representing the difference (HIPOCAS minus ERA-Interim, in meters, on the top left), root mean squared difference (top right, in metres), percentage difference (scatter index, on the bottom left) and correlation coefficient (bottom right) for the whole wave datasets of HIPOCAS and ERA-Interim.
![]({"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/tjoo20/2016/tjoo20.v009.i01/1755876x.2016.1200249/20160808/images/medium/tjoo_a_1200249_f0002_c.jpg"})
Figure 2. Wave comparison maps representing the difference (HIPOCAS minus ERA-Interim, in meters, on the top left), root mean squared difference (top right, in metres), percentage difference (scatter index, on the bottom left) and correlation coefficient (bottom right) for the whole wave datasets of HIPOCAS and ERA-Interim.
Comparison and assessment of three wave hindcasts in the North Atlantic Ocean
Published online:
20 July 2016Figure 3. Wave comparison maps representing the difference (HIPOCAS minus NOAA/CFSR, in metres, on the top left), root mean squared difference (top right, in metres), percentage difference (scatter index, on the bottom left) and correlation coefficient (bottom right) for the whole wave datasets of HIPOCAS and NOAA/CFSR.
![]({"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/tjoo20/2016/tjoo20.v009.i01/1755876x.2016.1200249/20160808/images/medium/tjoo_a_1200249_f0003_c.jpg"})
Figure 3. Wave comparison maps representing the difference (HIPOCAS minus NOAA/CFSR, in metres, on the top left), root mean squared difference (top right, in metres), percentage difference (scatter index, on the bottom left) and correlation coefficient (bottom right) for the whole wave datasets of HIPOCAS and NOAA/CFSR.
Figure 3 has a different pattern from Figure 2, without important divergences increasing towards Europe. The mean differences map shows the overestimation of NOAA/CFSR in relation to HIPOCAS over the whole North Atlantic Ocean, apart from small regions close to islands and in between Scotland and Norway. The large RMSDs are more concentrated in the northern latitudes. There is a new region with great disagreement between HIPOCAS and NOAA/CFSR from 30° to 40° North in the southwest of domain, possibly due to the influence of tropical storms or the sloped grid coverage of REMO winds used as input of HIPOCAS wave modelling (Pilar et al. 2008) that does not cover the south-western regions (NCEP-NCAR reanalysis was used instead) – see Figures 5 and 6. The correlation coefficient maps of Figures 2 and 3 confirm that HIPOCAS is more similar to ERA-Interim than to NOAA/CFSR.
4.1.2. Monthly divided comparison
The introduction of Figures 2 and 3 to complement conclusions from Table 2 was important to describe the great regionalisation of differences. This section together with Figure 4 will help to identify the seasonal evolution of these differences. All the three graphics of Figure 4 indicate a great seasonality of the absolute and relative differences. The first main graphic of bias (mean differences) shows the same pattern for the two comparisons (HIPOCAS minus ERA-Interim and HIPOCAS minus NOAA/CFSR); however, with a higher variance of HIPOCAS-ERA-Interim. From this map we see that HIPOCAS is more similar to ERA-Interim in the summer and more similar to NOAA/CFSR in the winter. The blue line of HIPOCAS minus NOAA/CFSR has negative values for all months, which means the absolute overestimation of NOAA/CFSR related to HIPOCAS in time. The HIPOCAS–ERA-Interim line, instead, has negative values from May to September and positive for all the other months, that is, ERA-Interim has larger waves than HIPOCAS in the summer and smaller in the other seasons. Considering the two lines together it is possible to conclude that HIPOCAS has a high annual variance of the monthly average of the significant wave heights, with small waves in the summer and large waves in the winter, right below NOAA/CFSR. The RMSD map of Figure 4 shows the better agreement between HIPOCAS–ERA-Interim compared to HIPOCAS–NOAA/CFSR for all months and the RMSD values are higher in the winter, as expected. The scatter index shows a different evolution and it is approximately constant for the comparison HIPOCAS–ERA-Interim but with very high values in the summer for the comparison between HIPOCAS–NOAA/CFSR, which suggests a great disagreement between HIPOCAS and NOAA/CFSR from May to September.
Comparison and assessment of three wave hindcasts in the North Atlantic Ocean
Published online:
20 July 2016Figure 4. Monthly evolution of the spatial integrated differences of wave heights (on the top, in meters), RMSD (bottom left, in metres) and scatter index (bottom right) for the whole wave datasets of HIPOCAS, ERA-Interim, and NOAA/CFSR.
![]({"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/tjoo20/2016/tjoo20.v009.i01/1755876x.2016.1200249/20160808/images/medium/tjoo_a_1200249_f0004_c.jpg"})
Figure 4. Monthly evolution of the spatial integrated differences of wave heights (on the top, in meters), RMSD (bottom left, in metres) and scatter index (bottom right) for the whole wave datasets of HIPOCAS, ERA-Interim, and NOAA/CFSR.
Finally, from Figures 3 and 4 it is possible to conclude that HIPOCAS is more similar to ERA-Interim in the west of the domain and in the summer, while HIPOCAS is more similar to NOAA/CFSR in the east of the domain (including European waters) and in the winter.
4.2. Analysis under extreme conditions
The next tables and maps were constructed following the same procedure of the last section, considering only events above the 95th percentile of each grid point.
4.2.1. All-year comparison
Table 3 compared to Table 2 indicates a clear great increase of the absolute differences among hindcasts. The difference of 0.09 metres between HIPOCAS and ERA-Interim has increased to 1.40 under extreme conditions. Regarding HIPOCAS minus NOAA/CFSR, the negative difference of −0.21 metres (NOAA/CFSR with larger waves than HIPOCAS) has changed to positive 0.53 metres, which points HIPOCAS with the highest waves among the three hindcasts. It confirms the results of Ardhuin et al. (2007a) who found an increasing underestimation by WAVEWATCH in respect to WAM when moving to extreme conditions; however, a proper conclusion must be taken after analysing the input winds (Table 4, Section 5.1). The RMSDs have also increased significantly, confirming the disagreement under extreme events. The scatter index is very important to be analysed because it shows an increase of values for HIPOCAS–ERA-Interim but a reduction of relative differences between HIPOCAS and NOAA/CFSR, that is, HIPOCAS is more similar to NOAA/CFSR for extreme events and more similar to ERA-Interim under moderate and calm conditions. Based on Table 3 it is possible to conclude that for extreme events, HIPOCAS has the highest values of significant wave heights, followed by NOAA/CFSR (very similar to HIPOCAS) and by ERA-Interim with the smallest waves.
Comparison and assessment of three wave hindcasts in the North Atlantic Ocean
Published online:
20 July 2016Table 3. Spatial wave height average of the error metrics of all grid points of Figure 1 for the whole dataset.
Comparison and assessment of three wave hindcasts in the North Atlantic Ocean
Published online:
20 July 2016Table 4. Spatial average of the error metrics of all grid points of Figure 1; evaluation of wind speeds and significant wave heights from HIPOCAS(REMO), ERA-Interim and NOAA/CFSR using GlobWave satellite data.
Figures 5 and 6 illustrate maps of differences for extreme conditions and it is worth to compare with Figures 2 and 3. Figure 5, of HIPOCAS-ERA-Interim, still shows an increasing differences towards Europe, but less evident than Figure 2. It has very large differences for mid-high latitudes above 40° North, reaching 2.5 metres and a large area is seen with differences above 2 metres – the RMSD map confirms this disagreement. The scatter index map has great part of the North Atlantic Ocean with values above 0.2 and the main differences are distributed throughout coastal areas of Europe and Morocco. The small region between Scotland and Norway presents again very large differences between hindcasts and should be further investigated. Pilar et al. (2008) found a pronounced discrepancy close to the UK when compared HIPOCAS against wave buoys.
Comparison and assessment of three wave hindcasts in the North Atlantic Ocean
Published online:
20 July 2016Figure 5. Wind (first line, m/s) and wave (second line, m) comparison maps representing the difference (HIPOCAS(REMO) minus ERA-Interim, on the left), root mean squared difference (centre) and scatter index (on the right) for the datasets of HIPOCAS(REMO) and ERA-Interim under extreme conditions (above the 95th percentile).
![]({"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/tjoo20/2016/tjoo20.v009.i01/1755876x.2016.1200249/20160808/images/medium/tjoo_a_1200249_f0005_c.jpg"})
Figure 5. Wind (first line, m/s) and wave (second line, m) comparison maps representing the difference (HIPOCAS(REMO) minus ERA-Interim, on the left), root mean squared difference (centre) and scatter index (on the right) for the datasets of HIPOCAS(REMO) and ERA-Interim under extreme conditions (above the 95th percentile).
Comparison and assessment of three wave hindcasts in the North Atlantic Ocean
Published online:
20 July 2016Figure 6. Wind (first line, m/s) and wave (second line, m) comparison maps representing the difference (HIPOCAS(REMO) minus NOAA/CFSR, on the left), root mean squared difference (centre) and scatter index (on the right) for the datasets of HIPOCAS(REMO) and NOAA/CFSR under extreme conditions (above the 95th percentile).
![]({"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/tjoo20/2016/tjoo20.v009.i01/1755876x.2016.1200249/20160808/images/medium/tjoo_a_1200249_f0006_c.jpg"})
Figure 6. Wind (first line, m/s) and wave (second line, m) comparison maps representing the difference (HIPOCAS(REMO) minus NOAA/CFSR, on the left), root mean squared difference (centre) and scatter index (on the right) for the datasets of HIPOCAS(REMO) and NOAA/CFSR under extreme conditions (above the 95th percentile).
In comparison to Figure 4, Figure 6 (HIPOCAS-NOAA/CFSR) presents smaller differences, which prove the better agreement of HIPOCAS with NOAA/CFSR under extreme events. The great differences in the south-western part of the domain are found again. The coastal waters of Europe in Figure 6 show much better scatter indexes than in Figure 5, so European analyses based on HIPOCAS and NOAA/CFSR are expected to provide similar results and comparatively different from ERA-Interim. At mid-high latitudes, where the largest divergences occur, it shows relatively small differences and good agreement between HIPOCAS and NOAA/CFSR under extreme conditions, with larger waves of HIPOCAS, showed by the hot colours in the first map of Figure 6.
4.2.2. Monthly divided comparison
The monthly evolution of the comparisons (Figure 7) regards the differences of significant wave heights above the overall 95th percentile (all-year), selecting events that occurred in each month, so the same threshold is applied for all months (one threshold for each grid point regarding the 95th percentile calculated with the whole dataset). It is well known that fewer events are counted in the summer so higher variance and lower confidence in the comparisons are expected during these months. All the three graphics of Figure 7 present the same pattern for the two comparisons, HIPOCAS–ERA-Interim and HIPOCAS–NOAA. The hindcasts, in terms of extreme events, are in better agreement in the winter than in the summer. From December to April all the three metrics show small values for HIPOCAS–NOAA/CFSR and confirms the close agreement between databases. The largest differences are found between HIPOCAS and ERA-Interim.
Comparison and assessment of three wave hindcasts in the North Atlantic Ocean
Published online:
20 July 2016Figure 7. Monthly evolution of the spatial integrated differences of wave height (on the top, in metres), RMSD (bottom left, in metres) and scatter index (bottom right) for the wave datasets of HIPOCAS, ERA-Interim and NOAA/CFSR under extreme conditions (above the 95th percentile).
![]({"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/tjoo20/2016/tjoo20.v009.i01/1755876x.2016.1200249/20160808/images/medium/tjoo_a_1200249_f0007_c.jpg"})
Figure 7. Monthly evolution of the spatial integrated differences of wave height (on the top, in metres), RMSD (bottom left, in metres) and scatter index (bottom right) for the wave datasets of HIPOCAS, ERA-Interim and NOAA/CFSR under extreme conditions (above the 95th percentile).
Therefore, Figure 7 suggests that extreme events are generally in better agreement among hindcasts when it occurs from September until April and the few events found between April and August present large dispersion. Concerning extreme events only, the best agreement and lowest difference occurs between HIPOCAS and NOAA/CFSR in the winter, while the worst case occurs in the summer between HIPOCAS and ERA-Interim.
4.3. Final comparisons in time domain during typical months of winter and summer
The discussion so far has addressed the spatial and seasonal analysis of hindcast differences, without illustrating any time series. This section presents some features of the wave datasets during the winter and the summer at two grid points. Figure 8 shows four graphics concerning one-month (January and July) evolution of the significant wave heights from HIPOCAS, NOAA/CFSR and ERA-Interim at two points (see Figure 1).
Comparison and assessment of three wave hindcasts in the North Atlantic Ocean
Published online:
20 July 2016Figure 8. Time evolution of significant wave height (metres) of HIPOCAS, ERA-Interim and NOAA/CFSR during January (first line) and July (second line) of 1995. Northern point A (55° North, 25° West) on the left column and southern point B on the right column (25° North, 25° West).
![]({"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/tjoo20/2016/tjoo20.v009.i01/1755876x.2016.1200249/20160808/images/medium/tjoo_a_1200249_f0008_c.jpg"})
Figure 8. Time evolution of significant wave height (metres) of HIPOCAS, ERA-Interim and NOAA/CFSR during January (first line) and July (second line) of 1995. Northern point A (55° North, 25° West) on the left column and southern point B on the right column (25° North, 25° West).
The most severe sea state is illustrated by the top left graphic, at the northern point in the winter. It confirms what was discussed before; HIPOCAS has the largest wave heights, which can be verified by the two extreme events on the 5th and 31st of January. These two peaks have significant wave heights about 2 metres higher in HIPOCAS than in the other hindcasts. The second line with the largest waves is NOAA/CFSR and finally ERA-Interim shows the lowest values. Cox et al. (2011) describe that CFSR winds reproduce some but not all extreme events, resulting in under representation of the highest waves. The underestimation of ERA-Interim and other ERA reanalyses are widely discussed and measured (e.g. Caires & Sterl 2001, 2003; Stopa & Cheung 2014). Therefore, the over representation of significant wave heights of HIPOCAS can be interpreted as practical alternative to improve safety in engineering applications. In the same month (January), but in the southern point, NOAA/CFSR becomes the hindcast with the highest values. This month of January contains the same extreme events in the considered domain; however, the northern point is within or close to the extra-tropical storms with the most extreme waves and the southern point receives the swell generated at mid-high latitudes. Hence, the first line of graphics of Figure 8 suggests that the application of WAM model in the HIPOCAS simulation allows more transference of momentum in the wave generation process but has greater attenuation of the swell propagation, when compared to the WAVEWATCH model of NOAA/CFSR.
In the summer at mid latitudes (bottom left graphic) HIPOCAS changes completely and shows the lowest values; NOAA/CFSR and ERA-Interim are in close agreement. On the southern point in the summer (bottom right graphic) once again NOAA/CFSR based on WAVEWATCH has the largest waves. As ERA-Interim was constructed using WAM, with a strong swell attenuation discussed before, the southern point resulted in NOAA/CFSR containing larger waves. The HIPOCAS and ERA-Interim comparison against NOAA/CFSR confirms the difference between WAVEWATCH and WAM in terms of long swell propagation and over-attenuation of WAM – discussed by Tolman and Chalikov (1996).
5. Evaluation of reanalyses using satellite data
The previous sections compared reanalyses without any benchmark, in order to clarify the features of one reanalysis related to another and where and when they are similar or have important differences. Following the same procedure of a wind comparison previously performed in the same project, this section now deals with independent evaluation of HIPOCAS, NOAA/CFSR and ERA-Interim against GlobWave satellite data. It is well known that satellite can also show inaccuracies; however, errors are small under non-extreme conditions in offshore areas as described by the GlobWave Product User Guide (2010) and discussed by Janssen et al. (2007). Therefore, this present section aims to provide an evaluation of HIPOCAS, NOAA/CFSR and ERA-Interim wave reanalyses based on a widely used and quality controlled satellite database. Satellite tracks and measurements were associated with the nearest hindcast grid point and time, which ensures a maximum distance from the satellite measurement to the nearest grid point equal to 0.71° (![]({"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/tjoo20/2016/tjoo20.v009.i01/1755876x.2016.1200249/20160808/images/tjoo_a_1200249_ilm0004.gif"})
, when the satellite measurement position is exactly at the centre of the cell associated with the 1°×°1 grid).
5.1. All-year assessment
Table 4 summarises the spatial and time average of error metrics in the North Atlantic Ocean using GlobWave satellite data. Bias is calculated by the measurement (satellite value of significant wave height) minus the hindcast value, that is, positive bias means underestimation of the hindcast and negative bias means overestimation. The wind intensity (at 10 metres height) assessment was also included in Table 4 to discuss the impact of the wind error on the wave fields. It was based on the same methodology of evaluation and used the same GlobWave satellite database.
From wind bias of Table 4 the reanalyses HIPOCAS and specially NOAA/CFSR are overestimated while ERA-Interim has underestimated wind intensities, which confirm results of Stopa and Cheung (2014). The RMSE and scatter index of NOAA/CFSR winds have the lowest values and show that, although NOAA/CFSR is, in average, significantly overestimated (low accuracy), the precision is better than the other reanalyses. Regarding the wave fields, HIPOCAS has the best performance in terms of bias, a little underestimated, followed by similar absolute bias of ERA-Interim and NOAA/CFSR with respectively underestimation and overestimation. Therefore, NOAA/CFSR is the wave field with the largest significant wave heights, followed by HIPOCAS and ERA-Interim, containing the smallest waves. Comparing the wind and wave bias it is possible to see that HIPOCAS has overestimated winds but underestimated waves, pointing a possible misparameterisation or miscalibration of WAM wave model with a low momentum transference or over-dissipation. ERA-Interim reanalysis presents both winds and waves underestimated as well as NOAA/CFSR presents both overestimated.
Although ERA-Interim showed some underestimation with positive bias, the RMSE and scatter index of waves have the lowest values and consequently the best performance in terms of precision, followed by NOAA/CFSR and HIPOCAS. A common analysis of the three metrics of wave heights indicates that HIPOCAS hindcast has the best accuracy but the worst precision and ERA-Interim has the worst accuracy (together with NOAA/CFSR) but the best precision.
Considering the wind and wave bias together, in regard to the accuracy only, ERA-Interim has the lowest absolute bias of winds and the best wind accuracy but the increasing wave underestimation made HIPOCAS with the best wave accuracy and bias instead of ERA-Interim. This is a consequence of a common underestimation of WAM simulations in HIPOCAS and ERA-Interim; HIPOCAS resulted in the final best wave accuracy simply because it had the strongest winds (overestimated) that compensated the underestimation of the wave model. NOAA/CFSR has both winds and waves overestimated. Therefore, the wave model WAVEWATCH III used by NOAA/CFSR simulation was able to transfer more energy from winds to the wave spectra than the two WAM models applied by HIPOCAS and ERA-Interim – the opposite of what was described by Mackay et al. (2010). It suggests that the overestimation of NOAA/CFSR is not due to WAVEWATCH III parameterisation or calibration problems but due to the overestimated wind input applied.
Now considering the wind and wave RMSE and scatter indexes together, in regard to the precision only, Table 4 shows HIPOCAS with the worst values for both winds and waves. NOAA/CFSR first presented the best precision (lowest RMSE and scatter index) related to wind intensities but then ERA-Interim over-performed NOAA/CFSR on these metrics. It implies a better simulation of WAM wave model configured in the ERA-Interim project than WAVEWATCH III in terms of wave modelling precision.
The basic equations of JONSWAP experiment (Hasselmann et al. 1973) indicate a quadratic dependence of significant wave height to the 10 metres wind and the power of four for the non-linear transfer function. Equation (5), from Hasselmann et al. (1973), shows the minimum momentum transfer from the atmosphere to the wave field for a JONSWAP spectrum, where ![]({"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/tjoo20/2016/tjoo20.v009.i01/1755876x.2016.1200249/20160808/images/tjoo_a_1200249_ilm0005.gif"})
is the air density:![]({"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/tjoo20/2016/tjoo20.v009.i01/1755876x.2016.1200249/20160808/images/tjoo_a_1200249_m0005.gif"})
(5) The same study points an even stronger dependence of the wind associated with the non-linear transfer:![]({"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/tjoo20/2016/tjoo20.v009.i01/1755876x.2016.1200249/20160808/images/tjoo_a_1200249_m0006.gif"})
(6) where ![]({"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/tjoo20/2016/tjoo20.v009.i01/1755876x.2016.1200249/20160808/images/tjoo_a_1200249_ilm0006.gif"})
is a dimensionless function depending on the shape of the spectrum; ![]({"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/tjoo20/2016/tjoo20.v009.i01/1755876x.2016.1200249/20160808/images/tjoo_a_1200249_ilm0007.gif"})
represents the frequency at the maximum of the spectrum and the parameter ![]({"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/tjoo20/2016/tjoo20.v009.i01/1755876x.2016.1200249/20160808/images/tjoo_a_1200249_ilm0008.gif"})
corresponds to the usual Phillips constant. Considering a fully developed sea, WAMDI Group (1988) describes the following quadratic relation between the 10-metres wind and the significant wave height:![]({"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/tjoo20/2016/tjoo20.v009.i01/1755876x.2016.1200249/20160808/images/tjoo_a_1200249_m0007.gif"})
(7) However, it is interesting to note in Table 4 that the relative errors represented by the scatter indexes are smaller in the wave fields than in the wind fields. It highlights the complexity involving the wave growth process and associated wind-wave error propagation, as described by Cavaleri et al. (2007) and Mackay et al. (2010).
Figure 9 illustrates the spatial distribution of the error metrics and presents similar pattern to the comparisons in the last section. The top left map shows the bias of HIPOCAS with a clear longitudinal evolution and increasing overestimation of waves eastwards. The negative values (HIPOCAS greater than GlobWave) represented by the blue colours are evident around Europe while the positive values (GlobWave greater than HIPOCAS) are mainly on the west of the domain. It can be due to the soaring resolution of the grid mosaic applied in the WAM simulations of HIPOCAS. ERA-Interim and NOAA/CFSR have a reasonably homogeneous distribution of bias and smaller errors are found below 35° North as expected. ERA-Interim presents an overall underestimation and NOAA/CFSR an overall overestimation with some underestimation at very high latitudes.
Comparison and assessment of three wave hindcasts in the North Atlantic Ocean
Published online:
20 July 2016Figure 9. Significant wave height evaluation maps using GlobWave satellite data. First line: HIPOCAS. Second Line: ERA-Interim. Third Line: NOAA/CFSR. Error metrics are bias (metres, first column on the left), root mean squared error (metres, second column in the centre) and scatter index (third column on the right).
![]({"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/tjoo20/2016/tjoo20.v009.i01/1755876x.2016.1200249/20160808/images/medium/tjoo_a_1200249_f0009_c.jpg"})
Figure 9. Significant wave height evaluation maps using GlobWave satellite data. First line: HIPOCAS. Second Line: ERA-Interim. Third Line: NOAA/CFSR. Error metrics are bias (metres, first column on the left), root mean squared error (metres, second column in the centre) and scatter index (third column on the right).
Concerning all reanalyses the worst RMSE area is above 40° North, at mid-high latitudes. At these regions, HIPOCAS has the largest errors (above 0.8 metres) followed by NOAA/CFSR (around 0.65 metres) and ERA-Interim (around 0.55 metres). The best performance of ERA-Interim spreads towards north and northeast latitudes so ERA-Interim has much lower RMSE at Southern European and Northern African waters than the other reanalyses. The scatter index figures confirm the best performance of ERA-Interim in terms of wave heights, which is pointed as a result of the WAM source term improvements used in the ERA-Interim project described by Bidlot et al. (2005, 2007) and Janssen (2008).
5.2. Monthly divided assessment
The wave reanalyses’ evaluation against satellite data is now divided in months, as performed in the previous comparisons. An evident seasonal cycle is found on the error metrics again (bias, RMSE and scatter index), found in Figure 10, and also described by Stopa and Cheung (2014). The severe underestimation and high bias of ERA-Interim is reduced in the summer, with values close to zero. The largest seasonal variation of bias is found in HIPOCAS, with large overestimation from November to March and underestimation from May to September. NOAA/CFSR is overestimated throughout all months, showing the best results from August to October.
Comparison and assessment of three wave hindcasts in the North Atlantic Ocean
Published online:
20 July 2016Figure 10. Monthly evolution of the spatial integrated evaluation of the significant wave height of HIPOCAS(REMO), ERA-Interim and CFSR using GlobWave satellite data. Error metrics are bias (on the top, in metres), RMSE (bottom left, in metres) and scatter index (bottom right).
![]({"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/tjoo20/2016/tjoo20.v009.i01/1755876x.2016.1200249/20160808/images/medium/tjoo_a_1200249_f0010_c.jpg"})
Figure 10. Monthly evolution of the spatial integrated evaluation of the significant wave height of HIPOCAS(REMO), ERA-Interim and CFSR using GlobWave satellite data. Error metrics are bias (on the top, in metres), RMSE (bottom left, in metres) and scatter index (bottom right).
The two graphics of RMSE and scatter indexes clearly confirm what was discussed before. The best performance for all months comes from ERA-Interim, followed by NOAA/CFSR and HIPOCAS. Lower RMSE values are present in the summer; however, the largest scatter indexes and worst performance are found in the summer and autumn. Therefore it is not correct to affirm that better wave results are expected in the summer, only based on small bias, since the worst relative errors are found in these seasons for all hindcasts.
There is no assessment of the hindcasts using GlobWave data restricted to extreme events in this present paper due to the scarcity of satellite measurements at each grid point and the well-known short duration of the peak of the storms. Reliable measurements under extreme wind and waves conditions remain a big challenge and a better method could be applied using both satellite data and buoy measurements to validate model results (triple collocation; Caires & Sterl 2003; Janssen et al. 2007); however, buoy data are confined to a few locations only and the scope of the present paper is to focus on the entire North Atlantic Ocean.
6. Conclusions
This paper analysed the differences between three wave hindcasts and the independent associated errors in the North Atlantic Ocean by following three approaches. First it was considered the time–space average, summarising the error metrics in three tables (one single value of error per hindcast per metric). Although the space and time average can hide important dependences regarding the error distributions, it is a quick way to evaluate a large domain as the North Atlantic Ocean and to determine relative under and over estimations of hindcasts. The second approach considered the comparison and error maps, where figures concluded that errors and differences among hindcasts are strongly site dependent. And the third approach investigated the seasonal evolution, where figures indicated a great seasonality of the absolute and relative differences as well as the error metrics, also described by Young (1999b). Therefore, wave hindcast error is a complex multivariate function and it must be taken into account by calibration methods, otherwise oversimplified calibrations can deteriorate the original database and increase the final errors.
The first analysis in this paper showed that for the overall non-extreme conditions, the three wave hindcasts are very similar, differences are less than 0.5 metres at most grid points, corroborating with most of comparison papers and the common sense. The reanalyses assessment using satellite data suggests that NOAA/CFSR presents the largest waves among hindcasts (0.2 metres higher, in average), followed by HIPOCAS and ERA-Interim. The larger waves of NOAA/CFSR compared to ERA-Interim confirm the results of Stopa and Cheung (2014). The inter-comparison indicated HIPOCAS more similar to ERA-Interim than to NOAA/CFSR for the overall non-extreme conditions. In terms of spatial distribution, there is a general increase of bias with latitudes, due to the increase of wind intensity and wave heights at mid-high latitudes. However, HIPOCAS shows a strong longitudinal evolution of the relative increasing significant wave height in comparison to other hindcasts and satellite data, containing overestimated waves close to Europe and underestimated waves in the west of the domain. Gaslikova and Weisse (2006) also mentioned the overestimation of HIPOCAS when compared to wave buoys in the coast of the UK. This overestimation is extremely seasonal dependent, as shown by Figures 4, 7 and 10, that point HIPOCAS with the largest seasonal variation of bias, containing large overestimation from November to March and underestimation from May to September.
Under extreme conditions it was found important differences among hindcasts at mid-high latitudes above 40° North, reaching 2.5 metres and a wide area is seen with differences above 2 metres. For extreme events, HIPOCAS has the highest values of significant wave heights, followed by NOAA/CFSR (very similar to HIPOCAS) and by ERA-Interim with the smallest waves. Apparently it could agree with the results of Ardhuin et al. (2007a), that found an increasing underestimation by WAVEWATCH (used by NOAA/CFSR) in respect to WAM (used by HIPOCAS) when moving to extreme conditions; however, Table 4 indicates that the larger waves of HIPOCAS come from the very intense wind input applied. Figure 8 also confirms the largest waves of HIPOCAS at the peak of the storms, where it is common to have problems of underestimation (e.g. Padilla-Hernandez et al. 2004).
Compared to satellite data, Table 4 indicates that the wind reanalyses HIPOCAS, and especially NOAA/CFSR, are overestimated while ERA-Interim has underestimated wind intensities, which confirm the results of Stopa and Cheung (2014). Regarding the waves, HIPOCAS has the lowest bias (0.06 metres) followed by similar absolute bias (0.12 and 0.13 metres) of ERA-Interim and NOAA/CFSR with respectively underestimation and overestimation. Although HIPOCAS hindcast has the best accuracy, it resulted in the worst precision (high RMSE and scatter indexes) while ERA-Interim has the worst accuracy (together with NOAA/CFSR) but the best precision. Table 4 also shows that HIPOCAS presented overestimated winds but underestimated waves, pointing a possible misparameterisation or miscalibration of WAM wave model with a low momentum transference or over-dissipation. On the other hand, NOAA/CFSR has both winds and waves overestimated, which indicates that the wave model WAVEWATCH III used by NOAA/CFSR simulation was able to transfer more energy from winds to the wave spectra than the two WAM models applied by HIPOCAS and ERA-Interim – a conclusion based on the bias solely.
When considering the RMSE and scatter index, the ERA-Interim reanalysis (that initially has a worse precision of the wind intensities than NOAA/CFSR) presented the best precision of significant wave height among the three hindcasts (Figure 9 and Table 4), which suggests a better simulation precision of WAM wave model configured in the ERA-Interim project than WAVEWATCH III in NOAA/CFSR. The better performance of WAM model used by ERA-Interim than the WAM version used by HIPOCAS can be a consequence of the more recent source term improvements described by Bidlot et al. (2005, 2007) and Janssen (2008) and later implemented in WAM for the ERA-Interim project. In terms of spatial distribution of the errors and differences, Figures 2, 3, 5, 6 and especially 8 show that NOAA/CFSR (WAVEWATCH model) has the largest waves at low latitudes below 30° North. Figure 8 exemplifies the over-attenuation of the extreme waves propagation simulated by WAM (HIPOCAS and ERA-Interim) in comparison with WAVEWATCH III (NOAA/CFSR). Therefore, from the wind and waves error comparison, we conclude that WAVEWATCH III showed the best modelling in terms of the accuracy but was over-performed by WAM used in the ERA-Interim project regarding the precision of the wave simulation. General conclusions about wave performance and under and over predictions of WAM and WAVEWATCH must be considered with cautious, since these models are easily tuned and customised and difference source terms are available nowadays, which leads to totally different results. One example is the differences of wave modelling of HIPOCAS and ERA-Interim, both based on WAM model, but with distinct performances. We also must to consider that HIPOCAS was constructed before ERA-Interim and the wave modelling performance is comparable with ERA-40 (Uppala et al. 2005), an ERA-Interim precursor.
Finally, considering the threats associated with waves (Vanem & Walker 2013; ISSC 2015) and the severity of the North Atlantic Ocean (Cardone & Cox 2011; Cardone et al. 2015), and the need to be safe in practical engineering applications the observations may support the choice of HIPOCAS for high sea states in mid-high latitudes, close or within the storms, and NOAA/CFSR for surrounding areas and lower latitudes. For non-extreme analyses, ERA-Interim would be the choice.
Acknowledgements
The authors acknowledge the European Centre for Medium-Range Weather Forecasts, the National Oceanic and Atmospheric Administration and the GlobWave Project for providing the data used in this paper.
Disclosure statement
No potential conflict of interest was reported by the authors.
ORCiD
C. Guedes Soares http://orcid.org/0000-0002-8570-4263
| Grid res. | Time res. (hours) | Initial date | Final date | |
|---|---|---|---|---|
| HIPOCAS | 1.0° × 1.0° | 3 | 1958 | 2001 |
| ERA-Interim | 0.7° × 0.7° | 6 | 1979 | Up-to-date |
| NOAA/CFSR | 0.5° × 0.5° | 3 | 1979 | 2010 |
| Variable | Mean Difference (m) | RMSD (m) | Scatter Index |
|---|---|---|---|
| HIPOCAS–ERA-Interim | 0.09 | 0.61 | 0.22 |
| HIPOCAS–NOAA/CFSR | −0.21 | 0.71 | 0.26 |
Note: First comparison between HIPOCAS and ERA-Interim. Second comparison between HIPOCAS and NOAA/CFSR.
| Reanalyses | Mean difference (m) | RMSD (m) | Scatter index |
|---|---|---|---|
| HIPOCAS–ERA-Interim | 1.40 | 1.69 | 0.23 |
| HIPOCAS–NOAA/CFSR | 0.53 | 1.35 | 0.19 |
Note: First comparison between HIPOCAS and ERA-Interim. Second comparison between HIPOCAS and NOAA/CFSR under extreme conditions (above the 95th percentile).
| Reanalyses | Bias | RMSE | Scatter Index | |
|---|---|---|---|---|
| HIPOCAS | Wind (m/s) | −0.16 | 2.43 | 0.30 |
| Waves (m) | 0.06 | 0.67 | 0.24 | |
| ERA-Interim | Wind (m/s) | 0.04 | 2.12 | 0.26 |
| Waves (m) | 0.12 | 0.40 | 0.14 | |
| NOAA/CFSR | Wind (m/s) | −0.28 | 1.96 | 0.24 |
| Waves (m) | −0.13 | 0.50 | 0.18 |