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An evaluation of sea surface height assimilation using along-track and gridded products based on the Regional Ocean Modeling System (ROMS) and the four-dimensional variational data assimilation
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Chaojie ZHOU1, 2, Xiaohua DING1, Jie ZHANG2, Jungang YANG2, *, Qiang MA1
Acta Oceanologica Sinica | 2018, 37(9) : 50 - 58
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Acta Oceanologica Sinica | 2018, 37(9): 50-58
• Physical Oceanography, Marine Meteorology and Marine Physics •
An evaluation of sea surface height assimilation using along-track and gridded products based on the Regional Ocean Modeling System (ROMS) and the four-dimensional variational data assimilation
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Chaojie ZHOU1, 2, Xiaohua DING1, Jie ZHANG2, Jungang YANG2, *, Qiang MA1
Affiliations
  • 1 Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China
  • 2 The First Institute of Oceanography, State Oceanic Administration, Qingdao 266061, China
Published: 2018-09-25 doi: 10.1007/s13131-018-1225-1
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Remote sensing products are significant in the data assimilation of an ocean model. Considering the resolution and space coverage of different remote sensing data, two types of sea surface height (SSH) product are employed in the assimilation, including the gridded products from AVISO and the original along-track observations used in the generation. To explore their impact on the assimilation results, an experiment focus on the South China Sea (SCS) is conducted based on the Regional Ocean Modeling System (ROMS) and the four-dimensional variational data assimilation (4DVAR) technology. The comparison with EN4 data set and Argo profile indicates that, the along-track SSH assimilation result presents to be more accurate than the gridded SSH assimilation, because some noises may have been introduced in the merging process. Moreover, the mesoscale eddy detection capability of the assimilation results is analyzed by a vector geometry–based algorithm. It is verified that, the assimilation of the gridded SSH shows superiority in describing the eddy’s characteristics, since the complete structure of the ocean surface has been reconstructed by the original data merging.

ROMS  /  4DVAR  /  sea surface height assimilation  /  along-track  /  gridded product
Chaojie ZHOU, Xiaohua DING, Jie ZHANG, Jungang YANG, Qiang MA. An evaluation of sea surface height assimilation using along-track and gridded products based on the Regional Ocean Modeling System (ROMS) and the four-dimensional variational data assimilation[J]. Acta Oceanologica Sinica, 2018 , 37 (9) : 50 -58 . DOI: 10.1007/s13131-018-1225-1
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1 Introduction
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An efficient simulation of ocean could make a significant contribution to the prediction of oceanic dynamic progress and climate change. Using the consistency constraints with laws of time evolution and physical properties, the estimation of an ocean model state could be enhanced, when the observed information is accumulated into the oceanic model states by data assimilation technology (Bouttier and Courtier, 2002). Remote sensing has collected large mount observations with high temporal and spatial coverages, such as sea surface temperature (SST) and sea surface height (SSH). According to the research of Kurapov et al. (2011) and O’Dea et al. (2012), the accuracy of model simulation could be enhanced when the remote sensing products, such as SSH and SST, are assimilated in the model. Therefore, an excellent assimilation strategy in ocean data assimilation is becoming a meaningful issue in the oceanographic research.
Since the remote sensing observations mainly focus on the surface, the three-dimensional (3-D) ocean structure characteristics could hardly be captured directly. Cooper and Haines (1996) proposed a new algorithm to assimilate the sea surface pressure by displacing the water columns vertically. With surface pressure data assimilated every 9 d, the simulation error was reduced accordingly, but this method was designed for Cox (1985) model and cannot be applied to a free-surface model. White et al. (1990) presented an assimilation procedure of continuous altimetric sea level observations, into a realistic wind-driven numerical synoptic ocean model. The sea level observations were dynamically interpolated onto a regular grid, and then the gridded information was assimilated. Xiao et al. (2006) performed an assimilation experiment of the altimeter data based on the Princeton Ocean Model (POM), and the evaluation indicates that the accuracy of ocean currents is obviously improved. Shu et al. (2009, 2011) assimilated the SST and CTD data into a coastal model by an ensemble Kalman filter method. Benefited from the assimilation, both temperature-salinity (T-S), velocity and water mass characteristics were well simulated. Ratheesh et al. (2012) explored the usefulness of satellite-derived surface data for nowcasting of oceanic circulation features, including the SST and the sea level anomaly (SLA). Surface information was projected into the vertical using predetermined correlation functions firstly, and then both original and vertical projected observations were assimilated into the ocean model, resulted in an enhanced nowcasting capacity. Moore et al. (2011a, b, c) developed a four-dimensional variational data assimilation (4DVAR) module in the ROMS. In the 4DVAR, all the available observations over a finite time interval were taken into consideration, in order to identify the global optimal estimation of ocean states.
The assimilation would be benefited when the SSH is introduced into the ocean model efficiently. Regularly, the altimeter missions sample the sea level along their ground tracks every 7 km, result in the limited coverage of the along-track SSH data. Considering the continuous variation characteristics of the sea level (Gill, 1982), a gridded SSH product named Archiving Validation and Interpretation of Satellite Oceanographic (AVISO) is generated by merging the multi satellite altimeter data. Compared with the along-track observations, the complete structure of the ocean surface is reconstructed.
In this paper, we will analyze the impact of the two SSH data sets on the assimilation, based on the ROMS and an incremental strong constraint 4DVAR method. First, the model configuration, the twin experiment and the validation data are introduced in Section 2; Section 3 is the main body, both the accuracy and the eddy detection capability of the experiment results are discussed. In Section 3.1, the accuracy analysis is conducted with the EN4 data set and Argo (array for real-time geostrophic oceanography) T-S profiles, while the evaluation of eddy detection capability is presented in Section 3.2. At last, some final remarks are given in Section 4.
2 Experiment configuration and data
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2.1 Model configuration
The ROMS is a free-surface, hydrostatic, primitive equation model discretized with a terrain following vertical coordinate system (Shchepetkin and McWilliams, 2005). The model domain covers the whole South China Sea (SCS) and its adjacent area from 1° to 30°N, 99° to 134°E (Fig. 1), with an eddy-resolved horizontal resolution of 0.1°×0.1° (about 10 km) and 30 S-coordinate layers in the vertical. The level 2.5 Mellor Yamada (1982) scheme is adopted as the parameterization of the vertical mixing process. The temperature and salinity fields are initialized by the Levitus climatology data set, while the free surface and velocity are set as 0. The ETOPO1 data (Amante and Eakins, 2009) is employed to produce the bathymetry field, and the minimum and maximum depths in the whole domain are set to be 10 and 5 000 m, respectively. The wind field employs a daily mean wind field from the Cross-Calibrated Multi-Platform (CCMP) ocean surface wind product (Atlas et al., 2011) with a horizontal resolution of 0.25°×0.25°, which is converted into the wind stress using the bulk formula given by Large and Pond (1982). The other daily atmospheric forcing fields, including heat fluxes, solar radiation fluxes, evaporation-precipitation (E-P), air temperature and specific humidity, are obtained from the National Centers of Environmental Prediction (NCEP) reanalysis with a horizontal resolution of 1.875°×1.875° (Kalnay et al., 1996). Finally, the lateral boundary conditions, including the monthly temperature, salinity, sea surface height and velocity field are provided by the Simple Ocean Data Assimilation (SODA) data set.
2.2 Assimilation configuration
The model comes to an ocean dynamic balanced state after 5 a integration starts from January 1, 2002. Then the SSH assimilation experiment is conducted during January 2007. In the data assimilation progress, the forcing and the boundary fields remain the same as prior model simulation. Advanced Very High-Resolution Radiometer (AVHRR) SST provided by the NOAA is employed for its high quality. It is a gridded product with a resolution of 0.25°×0.25° and is produced by merging the satellite observations and in situ measurements based on the optimal interpolation (Reynolds et al., 2007). To facilitate the calculation, the AVHRR is reduced to 1°×1° by selecting every four grids.
The SSH used in the experiment is provided by the AVISO, with the support from the Centre National D’études Spatiales (CNES). The gridded product is available every day since July 2006, and the spatial resolution is 0.25°×0.25°. The corresponding along-track SSH observations merged in the gridded products are also available. In the experiment, the original along-track observations and the gridded product from the AVISO are assimilated to evaluate their impact on the assimilation. To ensure the comparability, we use the original along-track observations of the gridded product merging in the assimilation, and the SSH derived from Jason-1, GFO and Envisat is gathered for the twin experiment. Since the reference level of the SSH and ROMS free surface is different, the steric signal is removed firstly using the result of Willis et al. (2004). The AVISO sea surface height anomalies (SSHA) with the steric signal removed is then added to the mean model height (Fig. 2). Compared with the processed AVISO “SSH”, the main spatial characteristics have been captured by the prior model simulation. According to the study of Powell et al. (2008) focus on the assimilation interval, a 7 d assimilation interval on the model solutions is chosen in this paper.
The goal of 4DVAR is to identify the best estimate circulation (commonly referred to as the analysis or posterior), by minimizing the difference between the model and the observations in a least-squares sense, with a prior hypothesis about errors and possibly additional constraints. Moreover, the errors and uncertainties of initial conditions, surface forcing, and boundary conditions are all taken into consideration in the cost function. Therefore, the three fields are referred to as control variables, and the problem in the 4DVAR is reduced to identifying the appropriate combination of control variables that yield the best estimation over a finite time interval.
The choice of parameters for modeling the background error covariance matrix (D) and the observation error covariance matrix (R) are designed as Moore et al. (2011b). The background errors of all initial condition control variable components of the background error covariance matrix are considered to be correlative for 50 km in the horizontal and 30 m in the vertical. Horizontal correlation scales chosen for the background surface forcing error components of the background error covariance matrix are 300 km for wind stress and 100 km for heat and freshwater fluxes. The correlation lengths for the background open boundary condition error components of the background error covariance matrix are chosen to be 100 km in the horizontal and 30 m in the vertical. Observation errors are assumed to be uncorrelated in space and time, and the variances along the main diagonal of the observation error covariance matrix are assigned as a combination of measurement error and the error of representativeness. The measurement errors of the AVISO SSHA and the AVHRR SST are chosen as the following standard deviations: 0.02 m for the SSHA, 0.4°C for the SST.
In order to explore the impact of the two SSH data on the assimilation, four cases are designed as Table 1. The 1°×1° reduced SST is assimilated in both the four cases. Case 1 is designed as the control experiment and no SSH is assimilated, while the reduced gridded SSH of 1°×1° is assimilated in Case 2, the gridded SSH with an original resolution (0.25°×0.25°) is considered in Case 3 and the along-track SSH observations are employed in Case 4. Here Case 2 is designed to make the strength of gridded products clearer.
2.3 Validation data
To evaluate the accuracy of the experiment results, the EN4 data set and Argo T-S profiles are employed as the validation data. The EN4 gridded data set is a global monthly objective analyzed ocean T-S product, generated by Hadley Centre of the UK Met Office. It covers the period from 1900 to present. Observations from all types of ocean profiling instruments with T-S information are ingested into the data set (Good et al., 2013). The spatial resolution is 1°×1° in the horizontal and 42 layers in the vertical.
The Argo project is designed to observe large-scale subsurface ocean T-S profiles globally. The observation starts from the surface and may reach 2 000 m depth, with a complete cycle of 10 d (Roemmich and Gilson, 2009). In this paper, the Argo temperature profiles are obtained from the China Argo Real-Time Data Center and the Global Data Assembly Centre (Argo, 2000). After temporal-spatial matching and quality control, 35 profiles are left and the distribution is shown in Fig. 3.
3 Results
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The gridded SSH products are supposed to hold the complete reconstructed structure on the surface, but the resolution (0.25°×0.25°) is lower than the original observations (7 km) along the orbit of altimetry. Owning to the different strength of the two SSH data, the assimilation results would present different properties accordingly. In this section, both the accuracy and eddy detection capability of the outcomes would be discussed.
3.1 Accuracy analysis
To analyze the accuracy of the experiment globally, the results of the cases are compared with the EN4 data. First, monthly average of the result is calculated, and then interpolated to 3-D grid of EN4 from the vertical and horizontal, respectively. A horizontal absolute bias (HAB, ba, h) and vertical absolute bias (VAB, ba, v) above 5 000 m are calculated as follows:
${b_{{\rm{a}}, {\rm{h}}}} = \frac{1}{{{N_1}}}\sum\limits_{k = 1}^{{N_1}} {\left| {M\left({i, j, k} \right) - E\left({i, j, k} \right)} \right|} , $
${b_{{\rm{a}}, {\rm{v}}}} = \frac{1}{{{N_2}{N_3}}}\sum\limits_{j = 1}^{{N_2}} {\sum\limits_{i = 1}^{{N_3}} {\left| {M\left({i, j, k} \right) - E\left({i, j, k} \right)} \right|} } , $
where $M$ and $E$ represent the assimilation result and EN4 data; ${N_1}$ is the total vertical layers of EN4 above 5 000 m; ${N_2}$ and ${N_3}$ stand for the horizontal dimensions of EN4.
As shown in Fig. 4, Cases 2–4 with the SSH assimilation both achieve a promotion in the vertical and horizontal. Respectively, the HAB of ocean temperature of the southern SCS and the northeastern Taiwan obtains a remarkable enhancement, and may reach up to 2°C; the VAB distribution in Fig. 4b indicates that, the absolute bias would also decrease after the SSH assimilation. Case 4 with along-track observations assimilated obtains the best performance, followed by Case 3. The VAB mainly occurs in the 200–1 200 m and the absolute bias could exceed 1°C. In order to present the impact of different SSH products expressly, the global averaged absolute bias between the four cases and EN4 are collected. As shown in Table 2, Case 4 seizes the smallest temperature (0.87°C) and salinity (0.076) error, while the gridded SSH assimilation cases get the medium ones.
In the following section, the Argo profile is applied to validate the accuracy of the four cases locally. Considering the micro enhancement of salinity in the assimilation experiment, we mainly concentrate our attention on the comparison of temperature. The outcomes of the assimilation are interpolated to the measure position of each Argo profile sequentially, first in the vertical and then in the horizontal. Ultimately, 2 113 matched temperature measurements of Argo are obtained. To evaluate the results’ accuracy, both an absolute bias (A-Bias) and a root mean square error (RMSE) are calculated. As shown in Fig. 5, Cases 2–4 have an accuracy promotion after the SSH assimilation, no matter which SSH data were ingested. Generally, the difference mostly occurs in 10–25°C and the model outcome seems to be the higher one. Moreover, the Case 3 with original gridded SSH assimilated seizes the best accuracy (A-Bias: 0.77°C, RMSE: 1.14°C), which is contrary to the comparison with EN4. Here, the unbalanced distribution of the Argo profiles ought to be punished, because more Argo profiles are located beyond the altimetry track, making the conclusion one-sided.
Furthermore, compared with the location of altimeter track, the temporal matched Argo profiles are divided into two parts: along the track or beyond the track. The spatial interval 25 km of the gridded SSH product is chosen as the threshold value, and 11 along-track and 24 beyond-track profiles are obtained, respectively. The representative classification of Argo profiles of 2007-01-01 and 2007-01-26 is presented in Fig. 6. The accuracy analysis of the two separated profile groups is illustrated in Fig. 7, and the A-Bias and the RMSE are appended as well. Compared with Case 1, Case 4 performs the best with a reduction of 0.154°C (RMSE) and 0.08°C (A-Bias) along the altimeter track. Accordingly, Case 3 holds an enhancement of 0.147°C and 0.05°C. Beyond the altimeter track, similar promotion of accuracy can hardly be obtained in Case 4, due to the limited influence of the along-track observations. However, there still exists some slight promotion, by the benefit of the global optimization capacity of the 4DVAR.
3.2 Eddy detection capability
According to the research of Zhang et al. (2014), a mesoscale eddy plays an important role in the oceanic transports of heat, salt, fresh water, dissolved CO2, and other tracers. Therefore, an accurate simulation of eddy is necessary in the research of ocean dynamics. In our experiment, the model is configured with an eddy-resolved horizontal resolution 0.1°×0.1°, and is enough to capture the main structure of eddy. In this section, the vector geometry–based eddy detection algorithm (Nencioli et al., 2010) method is employed, to evaluate the eddy detection capability of the four assimilation cases.
As presented in Fig. 8, Case 1 without the SSH assimilation has already gained the ability in eddy capture, and the eddies derived from the Kuroshio Current could be well characterized. Moreover, the detection of eddy are strengthened after the SSH assimilation. To acquire a quantitative analysis, we calculate the radius and eddy kinetic energy (EKE, Ek, e) of the detected eddies during January 2007. The specific algorithm (Penven et al., 2005) is given as follows：
$R = \sqrt {\frac{A}{{\text{π }}}} \;,$
${E_{{\rm{k,\ e}}}} = \frac{1}{{2N}}\sum\limits_{i = 1}^N {({u'_i}^2 + {v'_i}^2)}\;, $
where $A$ represents the area of the eddy; $R$ is the radius of a circle with the same area $A$; $N$ means the total number of grids involved in an eddy; and ${u'_i}$ and ${v'_i}$ are the horizontal velocity anomaly of grid $i$, here $i = 1, 2, \; \cdots, \;N$.
The distribution of radius and EKE of detected eddies are shown in Fig. 9. We can see that, the radius and EKE of the detected eddies are smaller than 150 km and 1 500 cm2/s2, which meets the conclusion of Cheng and Qi (2010) well. Besides, the number, radius and EKE of detected eddies are presented in Table 3. The total number of detected eddies increases significantly after the SSH assimilation. However, both the averaged radius and EKE of Cases 2 and 4 are tending to decay, because of the low resolution and bad coverage of the SSH. After all, the capability of Case 4 seems to be the most remarkable one in ocean mesoscale eddy detection, as the complete structure characteristics of eddy have been reconstructed by the merging procedure.
4 Conclusions
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In order to explore the impact of the SSH types (along-track and gridded) on the data assimilation, a twin experiment with four cases is conducted based on the ROMS and the 4DVAR. In the accuracy analysis, the EN4 data set and the Argo profiles are employed to validate the assimilation results globally and locally. The comparison with EN4 indicates that, Case 4 with the along-track SSH assimilation seizes the best accuracy. Though the gridded SSH is equipped with the better coverage, the “valid” observations are limited because the 0.25°×0.25° resolution is lower than the density of altimeter original measurements (7 km). Difference occurs in the comparison with the Argo profiles. The averaged error of the gridded SSH assimilation in Case 3 presents an optimal accuracy, where the centralized distribution of validation profiles in the analysis should be punished. Then the validation profiles are divided into two groups: along-track and beyond-track, by considering their distance with the nearest altimeter observations. Case 4 with the along-track SSH assimilation presents a higher accuracy promotion along the track, while slight error reduction beyond the track.
Besides, the mesoscale eddy detection capability of the model result is discussed. In this paper, the statistical characteristics of the detected eddies, including the number, the radius and the EKE is studied. Because the complete ocean structure is reconstructed in the gridded SSH products, more reasonable eddies are detected out in Case 3. Totally speaking, both the along-track and gridded SSH products have a significant effect on the data assimilation. The along-track SSH product has more real observations, while the gridded one contains more complete characteristics. When assimilated into the ROMS, higher accuracy can be achieved by the benefit of real observations with the along-track observations, and more reasonable ocean mesoscale eddy characteristics can be detected with the gridded product.
Funding
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  • The National Key Research and Development Program of China under contract No. 2016YFC1401800; the National Natural Science Foundation of China under contract Nos 41576176 and 11401140; the Key Project of Science and Technology of Harbin Institute of Technology at Weihai of China under contract No. 2014 DXGJ14.
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Year 2018 volume 37 Issue 9
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Article Info
doi: 10.1007/s13131-018-1225-1
  • Receive Date：2018-03-08
  • Online Date：2026-04-14
  • Published：2018-09-25
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  • Received：2018-03-08
  • Accepted：2018-03-27
Funding
The National Key Research and Development Program of China under contract No. 2016YFC1401800; the National Natural Science Foundation of China under contract Nos 41576176 and 11401140; the Key Project of Science and Technology of Harbin Institute of Technology at Weihai of China under contract No. 2014 DXGJ14.
Affiliations
    1 Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China
    2 The First Institute of Oceanography, State Oceanic Administration, Qingdao 266061, China

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表12种不同金属材料的力学参数
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Number of
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Number of
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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