Regional Comparison of Performance between EnKF and EnOI in the North Pacific
1. Introduction
The North Pacific is composed of several distinctive regions in terms of currents and hydrography. For instance, there is an equatorial current zone where the annual temperature variations are low; however, the currents are characterized by various directions and speeds (e.g., the westward North Equatorial Current and the eastward Equatorial Countercurrent). Thus, the eddy kinetic energy is large; however, the eddy lifespan is relatively short (Fig. 1) (Cheng et al. 2014). Moreover, the sea surface temperature (SST) of the equatorial zone may change depending on large-scale climatic fluctuations, such as El Niño–Southern Oscillation (Alexander et al. 2002; Mysak 1986). Meanwhile, the northwest Pacific region is characterized by distinct seasonal temperature variability, where the Kuroshio flows strongly throughout the year. Furthermore, the northeast Pacific experiences seasonal variations in water temperature without any strong currents (Cheng et al. 2014; Kashino et al. 2009).
Model domain of the North Pacific region. The northwestern Pacific (NWP), central Pacific (CP), northeastern Pacific (NEP), and equatorial (EQ) regions are indicated by the black boxes. Background shading indicates the annual mean eddy kinetic energy (cm2 m−2) from SODA 3.4.2 reanalysis data in 2015.
Citation: Journal of Atmospheric and Oceanic Technology 41, 2; 10.1175/JTECH-D-23-0062.1
The North Pacific is a spatially extensive region that cannot be spatiotemporally covered by oceanic observations from vessels. In this area, SST and sea surface height (SSH) were retrieved from spaceborne observations, whereas temperature profiles were obtained using the Argo profiler. However, existing datasets with ocean variables for this region were scarce for a complete understanding of spatiotemporal variability. The data assimilation approach has been previously applied to alleviate this gap. One of the most widely used data assimilation methods is the ensemble Kalman filter (EnKF) (Burgers et al. 1998; Evensen 1994; Seo et al. 2010), whereas ensemble optimal interpolation (EnOI) is a simplified version of EnKF that has been widely used as well (Evensen 2003).
These two assimilation methods calculate the background error covariance through the ensemble; however, in EnKF, all the ensemble members were updated using data assimilation over time, whereas in EnOI, the historical model data were used as ensemble members (e.g., they are not updated over time). Several studies have compared the performance of EnKF with that of EnOI and concluded that EnOI requires low computational resources, whereas the performance of EnKF was better. For instance, Oke et al. (2007) used a one-dimensional linear advection model to compare their performances using the number of members of the ensemble and length scale localization. They demonstrated that although EnOI was less optimal than EnKF, EnOI with 100 ensembles took less time than EnKF with 50 members. Overall, they reported that EnOI was a reasonable alternative to EnKF. Wan et al. (2010) compared the performance of EnOI and EnKF by assimilating altimetry data in the North Pacific using the Hybrid Coordinate Ocean Model (HYCOM). They used Argo data for intercomparison and showed that EnKF yielded better results in terms of water temperature and salinity than EnOI. Sakov and Sandery (2015) compared the performance of EnKF and EnOI in the East Australian Current separation zone by assimilating satellite altimetry data, satellite SST data, and Argo temperature/salinity profiles. They demonstrated that EnKF exhibited better overall performance and forecasting skills than EnOI. However, previous comparative studies were constrained by the region of study and reported robust estimates for a wide area. To date, the causes of the performance differences have also been understudied, while regional comparisons, considering the spatial–temporal variability of the ocean currents and water temperatures, were lacking. Because the North Pacific consists of various sea subregions, it is essential to select an efficient assimilation method based on the characteristics of physical properties in the target area.
The main aim of this study is to compare the regional and seasonal assimilation performances of EnOI and EnKF in the North Pacific by assimilating spaceborne SST data using the Regional Ocean Modeling System (ROMS) model. The objectives of this study are 1) to compare the regional differences in the performance of EnOI and EnKF in the North Pacific, 2) to elucidate the causes of such differences in performance, and 3) to evaluate an efficient method for obtaining high-quality reanalysis data for each region, considering the regional physical properties. The remainder of this paper is organized as follows. The method is described in section 2, and the results and discussion are presented in sections 3 and 4, respectively. Finally, the conclusions are presented in section 5.
2. Material and methods
a. The ocean model
This study applied ROMS, which represents a free-surface, terrain-following, primitive equation ocean model that is widely used in regional ocean modeling for a diverse range of applications (Di Lorenzo 2003; Haidvogel et al. 2000; Marchesiello et al. 2003; Peliz et al. 2003). For computational efficiency, ROMS utilizes hydrostatic primitive equations for momentum. The primitive equations were vertically discretized over the topography using stretched terrain-following coordinates (Song and Haidvogel 1994). This vertical coordinate can increase the resolution of the thermocline and bottom boundary layers. Moreover, in the horizontal dimension, primitive equations were calculated on a staggered Arakawa C grid.
The model domain used in this study was the North Pacific region (20°S–65°N, 98°E–76°W; Fig. 1). The North Pacific domain includes the northwest Pacific (NWP) region traversed by the Kuroshio, equator region (EQ) with consistently strong westward currents, and northeast Pacific (NEP) region with relatively weak dynamics. The model horizontal spatial grid had 0.25° horizontal resolution, and the time step of the model was 300 s. The model domain had 30 vertical sigma coordinates. The topography was retrieved from a global relief model of Earth’s surface, with a spatial resolution of 1°.
In this study, K-profile nonlocal closure schemes were applied for vertical mixing parameterization as formulated by Large et al. (1994). The K-profile scheme was expanded to include both the surface and bottom oceanic boundary layers. Daily average estimates from the European Centre for Medium-Range Weather Forecasts (ECMWF) interim reanalysis (ERA-Interim) datasets were utilized for atmospheric forcing (Hersbach et al. 2020). The 2-m dewpoint temperature, mean sea level pressure, relative humidity, net shortwave downward radiance, 2-m air temperature, and 10-m zonal and meridional wind speeds were implemented using bulk flux algorithm (Fairall et al. 1996). Simple Ocean Data Assimilation (SODA) version 3.4.1 was utilized for the open boundary data, including the temperature, salinity, and zonal and meridional velocities (Carton and Giese 2008). The initial data of temperature and salinity were obtained from the World Ocean Atlas 2013 version 2, a set of objective analyses, and statistical data. Velocity and SSH were initially set to 0, and a 5-yr spinup was conducted to obtain velocity and SSH suitable for the model. To spin up the model state, the model was implemented five iterations with 2005 forcing. To obtain historical data for the simulations, the model was integrated for 10 years from 2006 to 2015 using the initial data (e.g., the result of spinup). An experiment to compare the performance of the control model, EnKF, and EnOI was conducted in 2015.
b. Observations
We used spaceborne SST observations from the Operational Sea Surface Temperature and Sea Ice Analysis (OSTIA) for the assimilation purposes (Donlon et al. 2012). SST data were provided by the Group for High-Resolution Sea Surface Temperature (GHRSST). Spatial resolution of OSTIA is 0.05°. For data assimilation, OSTIA SST data were subsampled at 1° intervals for the NWP. Temporal resolution of SST data used in this study is daily. Assimilation was performed once every seven days. The OSTIA SST data, which were not subsampled, were used to validate the model performance for SST. The observation errors provided by the OSTIA dataset varied depending on the spatial scale. The total number of observations per assimilation step was 10 369. The independent observation data for the validation of assimilation results were obtained from the gridded altimeter SSH from the French Space Agency’s Center for Archiving, Validation, and Interpretation of Satellite Data in Oceanography (AVISO) and Argo float profiles (https://argo.ucsd.edu/). We used the Argo float profiles from 2015 to compare the performances of the models. As both the ROMS and Argo profiles have different vertical levels for each grid and profile, the standard levels were determined and compared after vertical interpolation for Argo profile. Owing to the difference in the absolute reference levels of the model and satellite SSHA data, the average SSHA of North Pacific from AVISO was subtracted and further compared with model results.
c. EnKF
d. EnOI
The EnKF model can achieve optimal performance because it calculates the step error covariance even under strong nonlinear conditions in various fields, such as engineering and natural sciences. However, the EnKF requires substantial computational resources owing to the number of members of the ensemble required for better performance. Particularly, EnOI is an alternative solution that was first introduced by Evensen (2003). EnOI was designed to reduce the number of computations in the EnKF and used an ensemble based on the results of long historical model runs. Because the background covariance matrix was calculated using a static ensemble, the integration of multiple ensembles was not required. Moreover, there was no feedback from the data assimilation to the background error covariance. This method reduced the computational resources required to integrate all ensembles. Similar to EnKF, EnOI consisted of 51 ensemble members. They were formed using a subsampling field from the historical model data. Five days were sampled each year for a decade. Data for each year from 2006 to 2015 were numbered from day 1 to day 365 (or 366), and then 40 days before and after, 20 days before and after, and the target day were selected. The initial of the reference model state of EnOI is equal to the initial ensemble mean of EnKF. EnOI was localized in the same manner as EnKF, while the same observation window and data assimilation cycle length were used.
3. Results
a. Model validation
In addition to selecting the appropriate assimilation method, it is essential to establish a model system appropriately. To this end, the model validation was performed before the data assimilation. The SSTs from the OSTIA and numerical model simulation without data assimilation were then compared between 1 April and 1 July 2015 (Fig. 2). We observed that both the SSTs were similar. However, we also identified significant differences in the SST estimates in some regions, such as the Kuroshio extension region, North Pacific marginal seas, and equatorial eastern Pacific. For instance, overshooting of the Kuroshio has been previously identified as a problem because of the low horizontal resolution of ocean models (Haidvogel and Beckmann 1999; Seo et al. 2010). The simulations of SSH reproduced the major features in most regions accurately, including the equatorial and northeast Pacific regions (Fig. 3). However, the simulated SSH exhibited a large difference with regard to the observed SSH from AVISO in the NWP, as in SST. This difference indicates that the model is limited to the simulation of complex dynamics in the NWP.
Sea surface temperature of OSTIA on (a) 1 Apr and (b) 1 Jul 2015. Bias in the sea surface temperature between OSTIA and ROMS models on (c) 1 Apr and (d) 1 Jul 2015.
Citation: Journal of Atmospheric and Oceanic Technology 41, 2; 10.1175/JTECH-D-23-0062.1
Sea surface height anomaly of AVISO on (a) 1 Apr and (b) 1 Jul 2015. Bias in the sea surface height anomaly between AVISO and ROMS models on (c) 1 Apr and (d) 1 Jul 2015.
Citation: Journal of Atmospheric and Oceanic Technology 41, 2; 10.1175/JTECH-D-23-0062.1
b. Comparison between the performances of EnOI and EnKF
The RMSE was compared with OSTIA SST data over the entire domain. A comparison of the spatially averaged RMSE time series in SST for the three simulations is shown in Fig. 4. Note that while comparing the performances of EnOI and EnKF, hereafter we denote the control model without assimilation as “NODA.” The observation points used in the assimilation were removed to compare the accuracy of performance. We observed that the RMSEs of both methods were lower than that of the NODA. During summer, the performance of all simulations was relatively poorer than that of the other seasons. However, the average temporal performance over the entire domain between the EnOI and EnKF did not vary significantly. The RMSE of EnOI was slightly lower than that of EnKF.
Time series of RMSE compared with OSTIA SST data. The black line indicates the RMSE in the SST from the simulation without assimilation. The cyan and red lines indicate the RMSE in the SST from EnOI and EnKF data assimilation simulations, respectively.
Citation: Journal of Atmospheric and Oceanic Technology 41, 2; 10.1175/JTECH-D-23-0062.1
To determine the regional differences in performance, the spatial distributions of SST were compared on 31 December 2015 (Fig. 5). The spatial distribution of the OSTIA SST is shown in Fig. 5a, and the SST anomalies of the three simulations from the OSTIA SST are shown in Figs. 5b–d. The difference in SST was reduced by both assimilations compared with NODA. In particular, the error decreased in the eastern equatorial Pacific region for the EnOI and in the Kuroshio extension for the EnKF. The annual time series of the SST RMSE for each subregion is shown in Fig. 6. The assimilation performance during summer was poor, except in the equatorial Pacific (EQ) region. In the NWP and CP regions, the RMSE of EnKF was slightly lower than that of EnOI, whereas the RMSE of EnOI was lower than that of EnKF in the EQ region. The simulations conducted in a specific model domain varied depending on the region. Despite the same number of ensemble members, model settings, and observation data used in data assimilation, some differences in regional performance were observed. The SST RMSE of NODA, EnOI, and EnKF in 2015 is shown in Table 1.
Sea surface temperature of OSTIA on (a) 31 Dec 2015. Absolute difference of sea surface temperature in (b) NODA, (c) EnOI, and (d) EnKF simulations compared with OSTIA SST on 31 Dec 2015.
Citation: Journal of Atmospheric and Oceanic Technology 41, 2; 10.1175/JTECH-D-23-0062.1
Annual time series of regional SST RMSE for free running (NODA), EnOI, and EnKF simulations compared with OSTIA SST in the (a) northwestern Pacific, (b) northeastern Pacific, (c) central Pacific, and (d) equatorial Pacific regions. The black line indicates a free run, and the cyan and red lines indicate EnOI and EnKF simulations, respectively.
Citation: Journal of Atmospheric and Oceanic Technology 41, 2; 10.1175/JTECH-D-23-0062.1
Root-mean-square error (°C) of sea surface temperature from NODA, EnOI, and EnKF with OSITA satellite in 2015. Each RMSE is represented at North Pacific, northwestern Pacific (NWP), northeastern Pacific (NEP), central Pacific (CP), and equator (EQ).
The SSHs from NODA, EnOI, and EnKF were compared with the AVISO spaceborne estimates. As mentioned, they were independent of observation data that were not used for assimilation. Figure 7 shows the time series of the SSH RMSE for the three simulations over the entire domain. The mean RMSE of the SSH in the entire domain exhibited a significant difference between the three simulations for January and February. However, EnOI exhibited a higher RMSE in SSH than in NODA. Meanwhile, we revealed a lower RMSE than NODA for the EnKF from mid-March onward. The difference in the SSH RMSE between the two assimilations was relatively larger than that in the SST RMSE over the entire domain.
Time series of RMSE model for AVISO SSH satellite data with NODA (free run; black line), EnOI (cyan line), and EnKF (red line).
Citation: Journal of Atmospheric and Oceanic Technology 41, 2; 10.1175/JTECH-D-23-0062.1
The differences in the SSH RMSE among the three simulations were not the same in each subregion. The RMSEs of the two assimilation results were similar to or lower than those of NODA in the NWP but did not reveal any significant differences in the CP (Fig. 8). We identified a remarkable improvement in EnKF in the NWP during the entire period, whereas EnOI showed little improvement. However, we discerned poorer EnKF results in NEP from January to July, while they reach the same level as the others thereafter. We did not observe any significant improvement in EnOI during the entire period. For CP, we observed some improvement for EnKF and no improvement for EnOI. Furthermore, EnOI yielded a higher RMSE than NODA in the EQ, and EnKF exhibited no improvement. The SSH also exhibited some differences in regional performance in a specific model domain. There were strong currents with large variability in the NWP and EQ, where EnKF exhibited better performance than EnOI. As the surface current was closely related to SSH, owing to the geostrophic balance, it could affect the distribution of SSH. The ensemble of EnOI from long-term historical data did not reflect the short-term variability of strong currents. Thus, EnKF improved the overall performance better than EnOI in the active current regions. The SSH RMSE of NODA, EnOI, and EnKF in 2015 is shown in Table 2.
Annual time series of regional RMSE for AVISO SSH satellite data in (a) NWP, (b) NEP, (c) CP, and (d) EQ with NODA (free run; black line), EnOI (cyan line), and EnKF (red line).
Citation: Journal of Atmospheric and Oceanic Technology 41, 2; 10.1175/JTECH-D-23-0062.1
Root-mean-square error (cm) of sea surface height from NODA, EnOI, and EnKF with AVISO satellite in 2015. Each RMSE is represented at North Pacific, NWP, NEP, CP, and EQ.
To evaluate the effect on the data assimilation of the subsurface, we also compared the vertical temperature profiles of the three simulations with independent observations (e.g., Argo profiles). Figure 9 shows the RMSEs between the simulations and Argo profiles in 2015. Because the vertical levels of the Argo profiles and model were different, we interpolated them vertically to the standard depth. We observed that the RMSEs were generally higher around the thermocline in all regions. This observation indicates that SST assimilation in the surface layer improved the RMSE in the subsurface. Although the difference in the SST RMSE between the two methods was low in the NWP, the profile result induced a prominent improvement in the EnKF compared to the EnOI. However, we did not observe any significant differences in either method for the NEP. The performance of EnOI was slightly better than that of EnKF in terms of EQ. From the SST perspective, the performance of EnKF was better in the NWP, which exhibited considerable spatiotemporal variations in water temperature. The assimilation of SST at the surface also improved the salinity profile. The RMSE of salinity significantly decreased in the NWP and CP, but the decrease was considerably minor in the NEP and EQ after assimilation. The RMSE of EnKF was lower than that of EnOI in all the regions, as shown in Fig. 10.
Water temperature profile comparison between the Argo profiles available from 1 Jan to 31 Dec 2015 and the model results. The black line indicates the vertical RMSE of free run (NODA); cyan indicates that for EnOI, and red that for RMSE of EnKF. It shows the difference between Argo profiles and model results in the (a) NWP, (b) NEP, (c) CP, and (d) EQ regions.
Citation: Journal of Atmospheric and Oceanic Technology 41, 2; 10.1175/JTECH-D-23-0062.1
Salinity profiles comparison between Argo profiles available from 1 Jan to 31 Dec 2015 and the model results. The black line indicates the vertical RMSE of NODA (free run), cyan indicates that for EnOI, and red that for EnKF. The difference between Argo profiles and the model results are shown in the (a) NWP, (b) NEP, (c) CP, and (d) EQ regions.
Citation: Journal of Atmospheric and Oceanic Technology 41, 2; 10.1175/JTECH-D-23-0062.1
4. Discussion
This study proved that EnKF performed better than EnOI, and these results were consistent with those of previous studies (Oke et al. 2007; Wan et al. 2010; Sakov and Sandery 2015). However, previous studies that used a regional model did not capture regional differences in performance depending on physical properties. They explained the advantages of EnKF by evolving statistical ensemble members (the aforementioned references). However, the effect of the background error covariance on the assimilation performance between variables in each sea area has not yet been examined.
We reported that EnOI in the EQ performed slightly better in the SST but poorer in the SSH. The performance may depend on the ensemble members used in both methods. In particular, EnKF utilized a dynamic ensemble that provided an updated background error covariance matrix, whereas the ensemble member of EnOI was derived from historical model data without evolution in time.
(a) Sea surface temperature (SST) on 2 Dec 2015 from OSTIA satellite data. (b) Sea surface height (SSH) on 2 Dec 2015 from AVISO. SST of ensemble mean used in (c) EnKF and (e) EnOI on 2 Dec 2015. SSH of ensemble mean used in (d) EnKF and (f) EnOI on 2 Dec 2015.
Citation: Journal of Atmospheric and Oceanic Technology 41, 2; 10.1175/JTECH-D-23-0062.1
Figure 12 shows the time series of the ocean Niño index (ONI) from 2006 to 2015 provided by the National Center for Atmospheric Research (NCAR). According to ONI estimates, SSH exhibits large variations (Hu et al. 2017; Lee and McPhaden 2010). Depending on the ENSO phase, the pattern of SSH in the equatorial region changes. Shi et al. (2020) demonstrated that the spatial distribution of SSH anomalies exhibits an opposite pattern during El Niño and La Niña phases. During El Niño phases, positive SSH anomalies were observed in the eastern Pacific, while negative SSH anomalies were evident in the western Pacific. Conversely, during La Niña phases, the distribution showed the opposite pattern. The ONI was high in December 2015, when this experiment was conducted. Figure 13 shows the SSH of the ensemble mean of EnOI in the equatorial region from 2 December 2006 to 2015. The zonally low SSH around 8°N in the western equatorial region developed remarkably in 2015 when the ONI was high and positive (Fig. 13j). The SSH distributions in 2006 and 2009, when the ONI was positive, were similar to that in 2015. However, the low SSH estimate in the western equatorial region was not identified in 2007, 2008, 2010, and 2011 when the ONI was negative (Figs. 13b,c,e,f). The ensemble mean of EnOI (
Time series of the ocean Niño index (ONI) from 2006 to 2015. Red stars indicate the ONI in December.
Citation: Journal of Atmospheric and Oceanic Technology 41, 2; 10.1175/JTECH-D-23-0062.1
Sea surface height (SSH) from historical model data used for the ensemble member of EnOI in data assimilation on 2 Dec. The panel order corresponds to (a) 2006 to (j) 2015.
Citation: Journal of Atmospheric and Oceanic Technology 41, 2; 10.1175/JTECH-D-23-0062.1
This crash mean state adversely affects the correlation of the variables. As SST was directly assimilated by the observational data, there was no significant difference in the assimilation performance between EnKF and EnOI. However, for SSH, the magnitude of assimilation was determined by the correlation between variables from the ensemble members. The correlation coefficient between SST and SSHA exhibited a large difference between EnKF and EnOI. The correlation between SST and SSHA in the EnKF was in line with the observations from the OSTIA SST and AVISO SSH; however, we revealed a large difference for that in the EnOI (Fig. 14). Unlike other regions, the equatorial region is an area where the spatial scale of the spatial correlation between SST and SSH and the ocean current that balances the geostrophic current is significantly different. In the northwest Pacific, the spatial correlation patterns of SST and surface currents are both relatively small scales, and in the northeast Pacific, both are relatively large scales. However, the scale of the spatial correlation of SST in the equatorial region is relatively large, but the scale of the spatial correlation of ocean currents appears small. If long-term historical data are used as an ensemble member at the equator for EnOI, there is a possibility that the correlation between variables may be problematic due to the influence of different regimes. The different correlation patterns in EnOI could induce poor SSH performance. However, the SST performances of EnKF and EnOI in the EQ were similar because the spaceborne SST estimates were directly assimilated as observation data.
Correlation coefficient between SST and SSH at each model grid from the (a) OSTIA-AVISO, (b) ensemble mean of EnKF, and (c) ensemble mean of EnOI.
Citation: Journal of Atmospheric and Oceanic Technology 41, 2; 10.1175/JTECH-D-23-0062.1
The northwest Pacific Ocean has similar spatial variability between SST and currents; however, there is no significant spatial variation in the case of SST in the equatorial region, and there is a large spatial variation in the case of currents that balance with SSH. Therefore, in the case of EnOI in the equatorial region, if long-term historical data are used as an ensemble member, there is a possibility that the correlation between variables may be problematic owing to the influence of different regimes. How does this characteristic affect the forecasting performance of the assimilation window? In NWP, the RMSE of EnOI was lower than EnKF immediately after assimilation, but in common, the RMSE of EnOI increased more between the assimilation windows than that of EnKF. This indicates that although the model field was adjusted significantly by EnOI, this effect did not last longer than that of EnKF. It appears that the model field assimilated by EnKF in almost all regions is a better initial field than the model field generated by EnOI.
In NEP, the SST performances of EnKF and EnOI were similar; however, the SSH performance of EnKF was worse than that of EnOI at the beginning of the experiment. As the ensemble member of EnKF increased, the RMSE of the SSH decreased (the figure is not shown here).
5. Conclusions
In this study, OSTIA SST estimates were assimilated using the ROMS model to compare the regional and seasonal assimilation performances of EnOI and EnKF in the North Pacific. We observed that both methods exhibited better performance for SST simulations compared with the NODA case; however, the assimilation performance was poor during the summer over the entire domain. For SSH, the performance of EnOI was observed to be rather poor, and the performance of EnKF was also poor from spring to early summer, despite the performance being better than that of NODA. The regional evaluation of SST indicated that the performances of EnKF and EnOI were similar in most areas. However, the performance of EnOI was better than that of EnKF in terms of EQ. The regional comparison of the SSH revealed better performance of the EnKF in the NWP and EQ, as well as better performance of the EnOI in the NEP.
We demonstrated that regional differences in performance depend on the ensemble mean. In particular, the poor performance of EnOI in SSH stems from its crushed mean structure. Because long-term historical data were used as an ensemble member, the state vector of the ensemble mean used to calculate the background error covariance did not resolve the narrow zonal structure in the SSH of the equator. The distribution of SSH in the EnOI ensemble mean was revealed to be different from the satellite observations because of the large interannual variability, which resulted in the worst performance compared to the control model. However, the performance difference in SST was not significantly different between EnKF and EnOI due to the direct assimilation of SST, whereas the interannual variability of SST was not as significant as in the SSH. Therefore, even if EnOI is economic and suboptimal from a computational perspective, it is essential to consider the mean of ensemble members for the application of EnOI in each target area.
It is worth noting that, for the entire domain, the performance of EnKF is generally better than that of EnOI and NODA. In addition, for each regional area, we attempted to tune the model configuration and assimilation schemes to obtain similar results; that is, the performance of EnKF was not inferior to the others. However, in this study, when their performances were compared over regional areas instead of the entire domain, their results were slightly different. In addition, depending on the individual assimilated variables or the combination of the assimilated variables, their performance was different. That is, depending on the physical properties of the ocean, the model configuration and assimilation settings should be considered.
In future studies, applicable methods for constructing the ensemble and perturbation should be selected based on thorough consideration of regional characteristics. If not, the assimilated model’s performance could be inferior to that of the control model. The performance of EnKF may vary depending on the perturbation method. Various experiments are required in the future because we only assimilated the SST data. Future studies should focus on assimilating Argo profile data and satellite altimetry data to assess the relative performances of EnOI and EnKF.
Acknowledgments.
This research was supported the by Korea Institute of Marine Science and Technology Promotion (KIMST) funded by the Ministry of Oceans and Fisheries, Korea (20220033), Improvements of ocean prediction accuracy using numerical modeling and artificial intelligence technology (20180447) and National Research Foundation of Korea (NRF) grants funded by the Korean government (MSIT) (NRF-2021R1A2B5B03087097, 2022R1A5A1033624).
Data availability statement.
The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation. Given the large size of the modeling experiment outputs (∼3 TB), the dataset is not stored online and can be shared upon request to the corresponding author.
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