The construction of high precision geostrophic currents based on new gravity models of GOCE and satellite altimetry data
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Abstract: The new gravity field models of gravity field and steady-state ocean circulation explorer (GOCE), TIM_R6 and DIR_R6, were released by the European Space Agency (ESA) in June 2019. The sixth generation of gravity models have the highest possible signal and lowest error levels compared with other GOCE-only gravity models, and the accuracy is significantly improved. This is an opportunity to build high precision geostrophic currents. The mean dynamic topography and geostrophic currents have been calculated by the 5th (TIM_R5 and DIR_R5), 6th (TIM_R6 and DIR_R6) release of GOCE gravity field models and ITSG-Grace2018 of GRACE gravity field model in this study. By comparison with the drifter results, the optimal filtering lengths of them have been obtained (for DIR_R5, DIR_R6, TIM_R5 and TIM_R6 models are 1° and for ITSG-Grace2018 model is 1.1°). The filtered results show that the geostrophic currents obtained by the GOCE gravity field models can better reflect detailed characteristics of ocean currents. The total geostrophic speed based on the TIM_R6 model is similar to the result of the DIR_R6 model with standard deviation (STD) of 0.320 m/s and 0.321 m/s, respectively. The STD of the total velocities are 0.333 m/s and 0.325 m/s for DIR_R5 and TIM_R5. When compared with ITSG-Grace2018 results, the STD (0.344 m/s) of total geostrophic speeds is larger than GOCE results, and the accuracy of geostrophic currents obtained by ITSG-Grace2018 is lower. And the absolute errors are mainly distributed in the areas with faster speeds, such as the Antarctic circumpolar circulation, equatorial region, Kuroshio and Gulf Stream areas. After the remove-restore technique was applied to TIM_R6 MDT, the STD of total geostrophic speeds dropped to 0.162 m/s.
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Key words:
- GOCE /
- gravity field model /
- mean dynamic topography /
- geostrophic current
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Figure 1. Comparison of geoid heights from different GOCE gravity field models. a. DIR_R5-DIR_R6 model, b. DIR_R5-TIM_R5 model, c. DIR_R5-TIM_R6 model, d. DIR_R6-TIM_R5 model, e. DIR_R6-TIM_R6 model, and f. TIM_R5-TIM_R6 model.
Figure 2. Comparison of geoid heights from GRACE and GOCE gravity field models. a. ITSG-Grace2018-DIR_R5 model, b. ITSG-Grace2018-DIR_R6 model, c. ITSG-Grace2018-TIM_R5 model, and d. ITSG-Grace2018-TIM_R6 model.
Figure 4. Standard errors of drifters’ eastward velocities (a) and northward velocities (b).
Figure 5. Standard errors of the total geostrophic speed differences between gravity models and drifter in Kuroshio area (a) and Gulf Stream area (b).
Figure 6. The absolute errors of total geostrophic speeds calculated by different gravity field models. a. DIR_R5-drifter model, b. DIR_R6-drifter model, c. TIM_R5-drifter model, d. TIM_R6-drifter model, and e. ITSG-Grace2018-drifter model.
Figure 7. Mean dynamic topography (shadding) and corresponding geostrophic currents (black arrows) in the Kuroshio area. a. DIR_R5 model, b. DIR_R6 model, c. TIM_R5 model, d. TIM_R6 model, e. ITSG-Grace2018, and f. drifter.
Figure 8. Mean dynamic topography and corresponding geostrophic currents (velocities are displayed as black arrows) in the Gulf Stream area. a. DIR_R5 model, b. DIR_R6 model, c. TIM_R5 model, d. TIM_R6 model, e. ITSG- Grace2018 model, and f. drifter.
Figure 9. Comparison of total geostrophic speeds before and after Remove-restore technique in the Kuroshio current area (a. before remove-restore, b. after remove-restore, and c. drifter) and Gulf Stream area (d. before remove-restore, e. after remove-restore, and f. drifter).
Table 1. Statistics of the different geoid products
Gravity model Mean geoid height/m RMS/m Minmum geoid height/m Maxmum geoid height/m DIR_R5-DIR_R6 0.001 0.147 –1.878 1.853 DIR_R5-TIM_R5 0.006 0.246 –2.624 3.286 DIR_R5-TIM_R6 0.006 0.251 –2.812 2.580 DIR_R6-TIM_R5 0.005 0.209 –2.360 2.167 DIR_R6-TIM_R6 0.005 0.207 –2.785 2.461 TIM_R5-TIM_R6 0.000 0.284 –2.463 3.510 ITSG-Grace2018-DIR_R5 –0.014 0.349 –3.423 2.337 ITSG-Grace2018-DIR_R6 –0.013 0.323 –3.506 2.419 ITSG-Grace2018-TIM_R5 –0.008 0.373 –3.331 2.342 ITSG-Grace2018-TIM_R6 –0.007 0.383 –3.655 3.322 
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Table 2. STD between the geostrophic currents based on GRACE/GOCE models and drifter results
Gravity field model Unfiltered velocity Filtered velocity STD (u)/(m·s–1) STD (v)/(m·s–1) STD (V)/(m·s–1) STD (u)/(m·s–1) STD (v)/(m·s–1) STD (V)/(m·s–1) DIR_R5 0.771 7.830 12.375 0.091 0.367 0.333 DIR_R6 0.765 7.567 12.118 0.091 0.355 0.321 TIM_R5 0.786 7.706 12.251 0.091 0.359 0.325 TIM_R6 0.767 7.404 11.907 0.091 0.353 0.320 ITSG-Grace2018 1.293 11.702 16.186 0.097 0.377 0.344
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Table 3. STD of geostrophic currents between the different MDT and drifter results
MDT models STD of geostrophic current/(m·s–1) STD (u) STD (v) STD (V) TIM_R6 before remove-restore 0.091 0.353 0.320 TIM_R6 after Remove-restore 0.077 0.209 0.162 MDT_CNES-CLS13 0.080 0.233 0.186
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