Fig. 1

The process of FOA and the process of FOAGRNN reconstruction of temperature and salinity field. The flow chart on the left corresponds to the FOA optimization mini-cycle on the right, S value corresponds to spread parameter, Smell corresponds to RMSE of reconstruction results and training samples; When condition is met, the end of the cycle, and outputs the optimal parameters of spread"

Fig. 2

The changes of RMSE error between original field and SODA reconstruction results/climate state data with water depth. (a) Temperature field, in the worldwide scale and 2016 average; (b) salinity field, in the worldwide scale and 2016 average; (c) RMSE of temperature field between SODA original field and reconstructed results in the Northern/Southern Hemisphere and January/July; (d) RMSE of salinity field between SODA original field and reconstructed results in the Northern/Southern Hemisphere and January/July"

Fig. 3

The selected representative area and Argo floats tracks. NP (North Pacific): 150°—170°E, 30°—40°N; NA (North Atlantic): 40°—20°W, 40°—50°N; EQWP (Equatorial Western Pacific): 170°—170°W, 10°S—0; EQEP (Equatorial Eastern Pacific): 110°—90°W, 10°S—0; SI (Southern indian Ocean): 50°—70°E, 40°—30°S; ANT (Antarctic Ocean): 120°—60°W, 65°—55°S. Argo float ID numbers: (1) 5902460, (2) 5903130, (3) 5905167, (4) 5904090, (5) 2902653, and (6) 6901584. These red curves are the Argo buoy track, and these black dots are the starting point of the tracks; the number of float profiles is between 72 and 146"

Tab. 1

Vertical MRMSE between original and reconstructed SODA field/ climate state in each region"

Fig. 4

Distribution of temperature and salinity field in a zonal section. (a) and (d). SODA reconstructed temperature/salt profiles; (b) and (e). SODA raw data temperature/salt profiles; (c) and (f). their difference. The cross profile is along a latitude passing 00°15′E, and the time is January 29, 2016. The blank space represents land"

Fig. 5

Distribution of temperature and salinity field in a zonal section. (a) and (d). SODA reconstructed temperature/salt profiles; (b) and (e). SODA raw data temperature/salt profiles; (c) and (f). their difference. The cross profile is along a latitude passing 60°S, and the time is January 29, 2016"

Fig. 6

Changes of RMSE between Argo field observation data, satellite data reconstruction results/WOA climate state data with water depth. (a) Temperature field, in the worldwide scale and 2016 average; (b) salinity field, in the worldwide scale and 2016 average; (c) temperature field reconstruction error, in the Northern/Southern Hemisphere and January/July; (d) salinity field reconstruction error, in the Northern/Southern Hemisphere and January/July"

Fig. 7

Argo float track and background field. Argo float number. (a) 5902460; (b) 5904090; (c) 5903130; (d) 6901584; (e) 5905167; (f) 2902653. The red curve is float track, and the blue cross is the starting point of the track, and black cross is the corresponding moment of the surface flow field and SLA"

Fig. 8

Argo float 5902460, located in the North Atlantic Ocean. (a) Argo observed temperature field; (b) satellite data reconstruction temperature field; (c) Argo observed salinity field; (d) satellite data reconstruction salinity field; (e) The Argo/satellite reconstruction/WOA13 temperature profile at the time corresponding to the dotted line in fig. a; (f) salinity field; (g) RMSE of observed temperature field and reconstructed temperature field/WOA13 climate state; (h) salinity field; (i) steric height calculated by Argo profile and reconstructed profile. The red vertical line in fig. a is the corresponding time of the black cross in fig. 7"

Fig. 9

Argo float 5904090, located in the Kuroshio extension. (a) Argo observed temperature field; (b) satellite data reconstruction temperature field; (c) Argo observed salinity field; (d) satellite data reconstruction salinity field; (e) The Argo/satellite reconstruction/WOA13 temperature profile at the time corresponding to the dotted line in fig. a; (f) salinity field; (g) RMSE of observed temperature field and reconstructed temperature field/WOA13 climate state; (h) salinity field; (i) steric height calculated by Argo profile and reconstructed profile. The red vertical line in fig. a is the corresponding time of the black cross in fig. 7"

Fig. 10

Argo float 5903130, located in the South Atlantic Ocean. (a) Argo observed temperature field; (b) satellite data reconstruction temperature field; (c) Argo observed salinity field; (d) satellite data reconstruction salinity field; (e) The Argo/satellite reconstruction/WOA13 temperature profile at the time corresponding to the dotted line in fig. a; (f) salinity field; (g) RMSE of observed temperature field and reconstructed temperature field/WOA13 climate state; (h) salinity field; (i) steric height calculated by Argo profile and reconstructed profile. The red vertical line in fig. a is the corresponding time of the black cross in fig. 7"

Fig. 11

Argo float 6901584, located in the southern Indian Ocean. (a) Argo observed temperature field; (b) satellite data reconstruction temperature field; (c) Argo observed salinity field; (d) satellite data reconstruction salinity field; (e) The Argo/satellite reconstruction/WOA13 temperature profile at the time corresponding to the dotted line in fig. a; (f) salinity field; (g) RMSE of observed temperature field and reconstructed temperature field/WOA13 climate state; (h) salinity field; (i) steric height calculated by Argo profile and reconstructed profile. The red vertical line in fig. a is the corresponding time of the black cross in fig. 7"

Fig. 12

Argo float 5905167, located in the East Australian Current. (a) Argo observed temperature field; (b) satellite data reconstruction temperature field; (c) Argo observed salinity field; (d) satellite data reconstruction salinity field; (e) The Argo/satellite reconstruction/WOA13 temperature profile at the time corresponding to the dotted line in fig. a; (f) salinity field; (g) RMSE of observed temperature field and reconstructed temperature field/WOA13 climate state; (h) salinity field; (i) steric height calculated by Argo profile and reconstructed profile. The blank in (a) and (c) is caused by the lack of Argo data; The blank in (b), (d) and the curve discontinuity in (i) are caused by the lack of satellite data. The red vertical line in fig. a is the corresponding time of the black cross in fig. 7"

Fig. 13

Argo float 2902653, located near the western Pacific. (a) Argo observed temperature field; (b) satellite data reconstruction temperature field; (c) Argo observed salinity field; (d) satellite data reconstruction salinity field; (e) The Argo/satellite reconstruction/WOA13 temperature profile at the time corresponding to the dotted line in fig. a; (f) salinity field; (g) RMSE of observed temperature field and reconstructed temperature field/WOA13 climate state; (h) salinity field; (i) steric height calculated by Argo profile and reconstructed profile. The blank in (d) and the curve discontinuity in (i) are caused by the lack of satellite data. The red vertical line in fig. a is the corresponding time of the black cross in fig. 7"

Fig. 14

Temperature and salinity maps of all standard depths from 0 to 1000 m in each representative area. (a) North Pacific Ocean; (b) North Atlantic; (c) western equatorial Pacific; (d) eastern equatorial Pacific; (e) southern Indian Ocean; (f) Antarctic Ocean. Argo observation data (gray), satellite data reconstruction (green), and WOA climate state (blue)"

Tab. 2

Vertical MRMSE of Argo observation data, satellite observation data reconstruction field and WOA climate state in each region"