SHI Hongyuan , CAO Xuefeng, LI Qingjie, LI Delei, SUN JiachengYOU Zaijin and SUN Qingying

1) School of Civil Engineering, Ludong University, Yantai 264025, China

2) Institute of Ports and Coastal Disaster Mitigation, Ludong University, Yantai 264025, China

3) National Marine Environmental Monitoring Center, Dalian 116023, China

4) Yantai Marine Environmental Monitoring Central Station, State Oceanic Administration, Yantai 264006, China

5) Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China

Abstract Wave parameters, such as wave height and wave period, are important for human activities, such as navigation, ocean engineering and sediment transport, etc. In this study, wave data from six buoys around Chinese waters, are used to assess the quality of wave height and wave period in the ERA5 reanalysis of the European Centre for Medium-Range Weather Forecasts. Annual hourly data with temporal resolution are used. The difference between the significant wave height (SWH) of ERA 5 and that of the buoy varies from ?0.35 m to 0.30 m for the three shallow locations; for the three deep locations, the variation ranges from ?0.09 m to 0.09 m. The ERA5 SWH data show positive biases, indicating an overall overestimation for all locations, except for E2 and S1 where underestimation is observed. During the tropical cyclone period, a large (about 32%) underestimation of the maximum SWH in the ERA5 data is observed. Hence, the ERA5 SWH data cannot be used for design applications without site-specific validation.The difference between the annual wave period from ERA5 and the mean wave period from the buoys varies from ?1.31 s to 0.4 s.Inter- comparisons suggest that the ERA5 dataset is consistent with the annual mean SWH. However, for the average period, the performance is not good, and half of the correlation coefficients in the four points are less 50%. Overall, the deep water area simulation effect is better than that in the shallow water.

Key words wave hindcasting; reanalysis; ERA5; wave height; wave period

1 Introduction

Waves and wind are important for human activities, such as maritime commerce, oceanographic engineering design,ship design, and hazard mitigation. For engineering applications, the height and crest of waves are the most important among wave characteristics (ISSC, 2015). Datasets with sufficient duration and adequate resolution are required by maritime commerce, oceanographic engineering,etc.These data can be obtained through several techniques, such as the use of voluntary observing ships, synthetic aperture radar, satellite altimetry, and the use of buoys and lasers. Among these observation data, ship data have the longest history; however, its quality varies, and it may lose extreme events due to shipping routes (Gulevet al., 2003). Light vessels and buoys can provide comprehensive and diverse measurements and important information (Bromirskiet al., 2005; Menendezet al., 2008;Genmrichet al., 2011). However, they are limited to discrete locations (Agarwalet al., 2013; Stopa and Cheung,2014). Satellite altimetry can cover a large area of ocean with high precision. Thus, it has been adopted as a worthy resource in the field of climate studies (e.g., Young, 1999;Hemeret al., 2010; Younget al., 2011). However, the orbit of satellites is periodic for the fixed field, varying from 10 days to 35 days (Le Traon, 2013). Hence, the temporal resolution of satellite altimetry is poor, and estimating longterm distributions and extreme events may be difficult (Kumar and Naseef, 2015; Campos and Soares, 2016).

Since World War II, numerical models have been used to predict and hindcast wave and wind conditions. Reanalysis datasets have been produced using numerical models,observations, and data assimilation techniques. These datasets are also used to estimate wind and waves. Simulations can be conducted over a large space without the disadvantages of the irregular and discontinuous data encountered when using synoptic hydrologic observatory data. In recent years, simulations have provided datasets with high spatial and temporal resolution, large coverage area, and long duration and have greatly supplemented various sources of wind and wave measurements. The numerical simulations,such as calculating extreme load design values (Guedes Soares and Trov?o 1991; Guedes Soares and Scotto, 2001),fatigue loads (Guedes Soares and Moan, 1991; Vanem and Walker, 2013), and ensuring safe navigation (Prpic-Or?icet al., 2015), are applied widely. Compared with traditionally recorded data, hindcasts have been increasingly used for design in the last decade and are continuously being developed and improved (Cardoneet al., 2015).

The European Centre for Medium-Range Weather Forecasts (ECMWF) has been operating numerical modeling for at least 20 years. The ERA-Interim (ERA-I) dataset(Deeet al., 2011) is available for all locations worldwide from 1979 to present. ERA5 (ECMWF; Hersbach and Dee, 2016), which also covers data from 1979 to present,is the most updated reanalysis product of the ECMWF.Both datasets are coupled atmosphere-wave models that produce a wind and wave dataset. Archived operational forecasts have provided an important source of wind and wave data for climate studies and commercial activities(Agarwalet al., 2013; Portillaet al., 2013; Shanas and Kumar 2014; Shiet al., 2017; Yiet al., 2018). Model physics, resolution, and assimilation techniques are continuously being updated; thus, datasets are unsuitable for the analysis of multiyear climate signals. Therefore, attention should be shifted to the modeling of ocean wave climate (Regueroet al., 2012; Rascle and Ardhuin, 2013).

Numerical models have become an important tool to obtain the wind and wave characteristics of a region without observation (Stopa and Cheung, 2014; Kumar and Naseef,2015). Many reanalysis datasets are available, and different models are used. A proper evaluation of hindcasts is a key process to improve the wave models and hence the operational forecasts (Cavaleriet al., 2012). Many researchers have performed this work. Caireset al.(2004) assessed the wind speed and significant wave height (SWH) data of several reanalysis datasets using altimeter and buoy data.They concluded that although the quality of the datasets differs from that of the observed data, most of the longscale features are mainly equal across all the data sets.Kumar and Naseef (2015) assessed the ERA-I wave data in the shallow waters around data-sparse India ocean using measured data from six locations. The result shows that ERA-I data overestimate wave height in all regions, except for the northern part of India’s west coast where data are underestimated. Campos and Soares (2016) compared HIPOCAS and ECMWF wind and wave reanalysis twice;one is a comparison between HIPOCAS and ERA-40, and the other is a comparison between HIPOCAS and ERA-I.Under calm and moderate weather conditions, the results relatively agree well. The difference in extreme conditions increased greatly, mainly occurring in winter at middle and high latitudes. Around the globe, the correction of reanalysis products has been conducted (Caires and Sterl, 2005),and several other studies have assessed the quality of ERAI wave datasets in different zones (Stopa and Cheung, 2014;Sharpet al., 2015; Campos and Soares, 2016).

The assessment of the product homogeneity in time and space enhances the confidence of dataset application in wave research and marine businesses. Although ERA5 wave data have been compared with observations at several locations, the potential benefits of this data source have not been examined around Chinese waters due to data sparsity caused by the confidentiality of observation and buoy data. This study addresses this gap by evaluating the skill of the ERA5 model in China using highresolution observations. Section 2 describes the details about the reanalysis datasets and the buoys. The methodology for comparison is shown in Section 3. Section 4 reports the results, and the last section presents the summary and conclusions.

2 Description of Datasets

2.1 ERA5 Dataset

ERA5 is the fifth generation of ECMWF atmospheric reanalysis of the global climate (Deeet al., 2011). This dataset is the most updated reanalysis product of the ECMWF. ERA5 reanalysis covers the modern observation period from 1979, with daily updates continuing forward in time. ERA5 eventually replaced ERA-I, which is increasingly difficult to maintain (ECMWF; Hersbach and Dee, 2016).The Integrated Forecasting System (cycle 41r2) with several added features specifically developed for reanalysis was used in the ERA5 assimilation system(ECMWF; Hersbach and Dee, 2016). Compared with ERAI (Deeet al., 2011), ERA5 is remarkably improved (Menget al., 2018; Czerneckiet al., 2019). ERA5 data have highresolution hourly analysis fields, with a horizontal resolution of 31 km (about 0.25?) on 137 vertical sigma levels from the surface up to 0.01 hPa (approximately 80 km).The number of variables provided by ERA5 has increased from 100 in ERA-I to 240, including the wave height and wave direction provided by the coupled wave model; thus,users can analyze past atmospheric and oceanic states more accurately than before. Many researchers have adopted ERA5 for atmospheric and oceanic studies. Bechtleet al.(2019) adopted the wind dataset whose accuracy is not confirmed by the documentation of the ERA5 reanalysis data for energy resource analysis. Mahmoodiet al.(2019)presented the temporal and spatial characteristics of wave energy in the Persian Gulf on the basis of the ERA5 reanalysis dataset.

2.2 Buoy Data

Wave data obtained by the Directional Waverider MKIIII from six buoys were adopted to evaluate the ERA5 datasets. The location of the buoys is shown in Fig.1 and the details of the stations are shown in Table 1; only four buoys had the wave period recorded. Wave measurement was conducted by the Ministry of Natural Resource of China or the Institute of Oceanology, Chinese Academy of Sciences. The directional wave rider buoy measures free-surface gravity waves with heaves ranging from ?20 m to +20 m, with a resolution of 1 cm and wave periods ranging from 1.6 s to 30 s. The cross sensitivity of the heaves is less than 3%. Data were recorded at a frequency of 1.28 Hz, and the buoys took an hour of procession to produce one record. Default wave characteristics, such as SWH, were recorded in the file in sdt format. Before observation data were used, it should be checked to eliminate singular values.

Table 1 Buoy information statistics at six locations

Fig.1 Observation locations in the research area.

3 Methodology of Comparison and Evaluation

The methodology used in this study is the same as that applied in a previous wave and wind evaluation. We first determined the coincident time and site domain that corresponds to the six buoys. Then, the values in the ERA5 dataset at the buoy locations were obtainedviaspatially linear interpolation. Linearly interpolated data are not strictly consistent in space.

The error metrics applied are as follows: bias, root mean square error (RMSE), scatter index (SI) and correlation coefficient (COR).

whereXis the observations,Yis the reanalysis values, the over bar indicates mean values in time, andndenotes the number of data pairs.

Bias is a statistical quantity that signifies the average difference between the ERA5 and buoy data. The lower the RMSE and SI values, the better fit of data between ERA5 and the observations.

4 Results

4.1 Significant Wave Height

Buoy wave data undergo a phenomenon of missing measurement. In this study, all the data in the missing measurement period were eliminated. The time series of the SWH between ERA5 and the buoy at different locations are shown in Fig.2. Along the Yellow Sea, the measured buoy data show that the annual mean SWH in Y1 and Y2 are 0.67 and 1.06 m, respectively. In the East China Sea,the annual mean SWH are 0.3 m (E1) and 1.2 m (E2). As for the South China Sea, the annual mean SWH in S1 and S2 are 1.19 and 1.75 m, respectively. As shown in Table1,the measurement stations are divided into two groups,namely, shallow (Y1, E1, and S1) and deep (Y2, E2 and S2) stations.

A scatterplot of the ERA5 SWHversusthe buoy SWH and a least-squares linear fit to the datasets are presented in Fig.3. The latter shows that the slopes of the fit line are predominantly close to 1 for deep water locations compared with shallow ones. Furthermore, a large deviation is observed in E1. Comparison statistics also illustrate that the ERA5 SWH data are consistent with the buoy- measured SWH data in the waters around China (Table 2). The values of bias are reasonably small (i.e., no more than 0.1 m), except those for E1 and S1 whose values are 0.35 and 0.30 m, respectively. All the values of bias, except those for E2 and S1, are negative. This result indicates that the SWH of ERA5 is larger than that of the measured one.However, the maximum SWH in the two datasets is inverse (Table 3). Therefore, although ERA5 data are larger than the measured data, it is smaller in maximum SWH simulation. The destructive force of SWH will be underestimated when we adopt the SWH of ERA5 for marine engineering design. The error analysis of the numerical simulation results corresponding to the maximum measured wave height in six stations shows that the error can reach up to 35%. This result shows that ERA5 cannot simulate every wave process well and thus may miss some extreme waves.

The RMSE values in deep locations are reasonably small(i.e., no more than 0.2 m); for shallow locations, the values are less than 0.4 m. SI reflects the dispersion between the measured and ERA5 datasets; the smaller the value,the better the correlation between them. The SI in E1 is the largest, and its correlation coefficient is the smallest(0.68). The SI of other locations are no more than 0.3, and the correlation coefficients are all above 0.89, even reaching up to 0.97 in Y2 and S2.

The present study shows that the underestimation of the annual maximum SWH in ERA5 data is less than 10%, except for E2 and S1 with values of 15.9% and 32.0%, respectively (Table 3). The annual variation of SWH for Y1 and Y2 is similar (nearly 10%); for E2 and S2, the variation is nearly 5%. The biggest difference between the measured data and that of ERA5 is found in E1, with an annual variation of 116.7%; for S1, the value is 26.1%. ERA5’s 90th percentile SWH value for Y1, Y2,and S2 is within 2% of the measured values. For E1, the variation can reach up to more than 70%; for E2 and S1,the variation is 10.9% and 25.4%, respectively. ERA5’s 75th percentile SWH value for Y1, Y2, and S2 is within 4% of the measured values. For E1, E2, and S1, the variation can reach up to 96.4%, 9.6%, and 63.9%, respectively. The large variation between E1 and S1 can be attributed to the small island located east of the E1 site.Islands have a great influence on wave propagation; thus,the measured SWH is smaller than that of ERA5, which took the island as water for SWH calculation. As for S1,the actual water depth is approximately 18 m, which is deeper than the depth adopted in the ERA5 wave model;thus, the measured SWH, especially under extreme conditions (such as typhoons), is larger than that of ERA5.Four typhoons attacked this area during the period of observation. Y1, which is located in shallow waters, is only slightly affected by water depth due the low-to-medium wind speed, resulting in the minimal difference between measured and ERA5 values.

Table 4 shows the monthly biases between the measurement and reanalysis SWH to illustrate the variability of errors over time. The monthly bias and the correlation coefficient for two groups indicate that the shallow locations are strongly influenced by water depth; hence, the monthly bias values were larger (about 0.5 m) in shallow water sites and relatively smaller (less than 0.25 m) bias values were observed in deep sites.

The underestimation is due to the poor data quality of the input wind field used to force the wave model during extreme events (Kumar and Naseef, 2015; Shiet al., 2016).The results show that central wind speed is significantly lower when the atmospheric model simulates a typhoon(e.g., Shiet al., 2016). Nevertheless, most of the wave modeling results show a difference between the measured and modeled SWH (Kumar and Naseef, 2015). Although large SWH values are generated during typhoons, the impact of typhoons on the average annual SWH is not significant because the impact of typhoons only lasts for 3 – 4 days, and the number of cyclones per year is limited.The annual mean SWHs are not significantly influenced by typhoons; thus, the annual mean ERA5 SWH data for regions influenced by a typhoon clone can be used for further studies because ERA5 only underestimates the SWH in the upper percentiles. The present study shows that ERA5 SWH can be used with confidence for locations that are not influenced by typhoons; however, ERA5 overestimates the SWH in most of the locations because the wind speed which is adopted for wave simulation by ERA5 is higher than the measured wind speed (not shown here).

Fig.2 Time series of the SWH between ERA5 and the buoy at different locations.

Fig.3 Scatterplot of ERA5 SWH with buoy SWH for different locations.

Table 2 Statistical results of SWH

Table 3 Annual mean, annual maximum, and the 75th and 90th percentiles of SWH from the buoy and ERA5

Table 4 Average value of SWH for each month from ERA5 and the buoy in all locations considered in the study (unit: m)

4.2 Wave Period

Wave periods can be expressed in many ways. Research shows that the energy wave period is close to the ECWMF wave period (Kumar and Naseef, 2015), but only the mean wave period (Tm) is provided in ERA5. Hence,analysis was conducted by usingTm. For Y2 and S2, no wave period was recorded; thus, four locations were adopted for comparison in this section.

The time series ofTmbetween ERA5 and the buoys at different locations are shown in Fig.4. For E1, the distribution of observationTmis messy and thus considered invalid. Therefore, the data in E1 were not used for evaluation. The statistical results of annual mean, annual maximum, and the 75th and 90th percentiles of theTmfrom the buoy and ERA5 are shown in Table 5. Along the,Yellow Sea, the measured buoy data show that the annual meanTmin Y1 is 4.54 s. In the East and South China Seas the annual meanTmis 5.88 and 3.98 s, respectively. The annual maximum, the 75th and 90th percentiles ofTmfrom the buoy and ERA5 is within 10%, except for the buoy of S1.

Fig.4 Time series of the Tm between ERA5 and the buoys at different locations.

Table 5 Annual mean, annual maximum, and the 75th and 90th percentiles of the Tm from the buoy and ERA5

A scatterplot of the ERA5Tmversus the buoyTmand a least-squares linear fit to the datasets are presented in Fig.5.And the statistical results ofTmare shown in Table 6. The correlation coefficient values between the ERA5Tmand the buoyTmfor two shallow locations along the Chinese waters are 0.47 and 0.79, respectively Higher values of SI(0.11–0.35 s) are found for these locations, indicating a bad fit between the ERA5Tmand the buoyTm. For E2,which is located in deep waters, the correlation coefficient value is 0.84, and the SI value is 0.09 s. The difference annual bias ofTmbetween the ERA5 and the buoy varies from ?1.31 s to 0.4 s, indicating that the value of ERA5Tmis larger in S1 compared with others (Y1 and E2). S1 is shallower in ERA5; thus, the wave spectrum during propagation is converted to low frequency. As a result, the value ofTmis larger than the measurement. For S1, the average difference between the buoyTmand the ERA5Tmis larger (1.3 s) than that of other locations (less than 0.4 s).

Fig.5 Scatterplot of ERA5 Tm with the buoy SWH for different locations.

Table 6 Statistical results of Tm

Wave data in ERA5 were produced on a grid with a resolution of the order of 31 km (about 0.25?). Even though shallow water physics are active in the model, the coupled wave component (Janssen, 2004) is coarser at approximately 31 km, and the average water depth at the point of interest is different from that of the buoy location.This observation is due to the coarseness of the grid. The data adopted for the ERA5 data evaluation in the present study were collected using buoys located 0.4 – 316 km from the coast (Table 1). This difference in water depth might explain the discrepancies between the ERA5 and buoy observations in shallow locations, particularly those of the wave period. In addition, ERA5 does not consider small islands, reefs, or sandbars for simulations. The presence of such land forms causes the wave spectrum to shift to lower frequencies during wave propagation, thus reducing the wave height and increasing the period, such as what happened in E1.

5 Summary and Conclusions

In this study, we evaluated the performance of ERA5 reanalysis SWH andTmdata at six locations around Chinese waters by comparing the obtained data within situbuoy measurements. Half of the buoys were positioned in shallow water, and half were placed in deep water. Observations covering different seasons were used for the study.

Analysis showed that ERA5 overestimates the SWH along the China Seas due to wind overestimation. The difference between the ERA5 SWH and the buoy SWH reaches up to 117% for E1, where a small island is located in the east. Even though the annual average values of bias indicate that ERA5 overestimates the SWH, the underestimation of the SWH under extreme conditions, such as typhoons, is large (1.59 m in S1). The locations off the southeast coast of China are frequently influenced by typhoons, and ERA5 underestimates the maximum SWH in these locations during the cyclone period by about 30%.Hence, ERA5 should not be used for design applications without proper validation. The difference between the buoyTmand the ERA5Tmin shallow water location is large.

As the latest generation of ECMWF’s atmospheric reanalysis of the global climate, ERA5 is greatly improved.Similar to ERA-I, assessing the root causes of the biases and errors of ERA 5 remains difficult when a low- resolution global model is used in a somewhat complex basin within situobservations located in nearshore environments.Orographic effects and bathymetry may play an important role in this situation.

Acknowledgements

The project was financially supported by National Key R&D Program of China (No. 2018YFB1501901), the National Natural Science Foundation of China (No. 519091 14), the Major Research Grant (Nos. U1806227 and U190 6231) from the Natural Science Foundation of China and the Provincial Natural Science Foundation of Shandong,the Open Research Fund of the Key Laboratory of Ocean Circulation and Waves, Chinese Academy of Sciences (No.KLOCW1901), the Open Research Fund of State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences (No.LTO1905). ERA5 data used in this study have been obtained from the ECMWF data server (http://apps.ecmwf.int/ datasets/). We thank the two reviewers for their constructive comments and suggestions, which substantially improved the paper.