In this section, results from the analysis period 1960 to 2009 are compared with observations. The earlier period is not considered, since sub–surface observations are scarce. The global ocean temperature from surface to 310 m simulated by the analysis were compared with HadISST 1.1 and EN4 temperature objective analyses (Good et al., 2013), and in terms of structure and strength were within the uncertainties of these temperature products.
Improvements in correlation and RMS error between these two runs (original SST nudging and new ensemble-based SST nudging) are shown in Figs 3 and 4, respectively. The improvement here means the new ensemble-based SST nudging updating run has a higher simulation skill in correlation and smaller RMS errors than the original SST nudging run. The improvements in correlation can be found within the global mixed-layer, due to the ocean variability is strongly correlated to the variability of SST field. Globally, the improvements are not concentrated at the surface layers, and mostly improved the variability the mixed-layer. Below 100 ms, the significant improvements are mostly concentrated over the Tropical Pacific, and the oceans with deep thermocline structure, such as over the northwest Pacific Ocean, the southern Indian Ocean, and the northern Atlantic Ocean. And the improvements in correlation over these regions can reach to more than 300 ms deep.
Figure 3. Improvements in correlation of temperature from surface to subsurface between the new ensemble-nudging scheme and original nudging scheme. The shaded area indicates the simulation skill has been improved in correlation.
Figure 4. Reductions in RMSE of temperature from surface to subsurface between the new ensemble-nudging scheme and original nudging scheme. The shaded area indicates the simulation error has been reduced (°C).
Correlations are high improved throughout the equatorial Pacific. In particular, in the Pacific along the thermocline (Fig.5), the improvements of correlation coefficients are ranging from 0.02 to 0.1 (i.e., the percentage of improvement equals to 3%–18%), and the maximum values of the RMS error reduction are around 0.3°C. The weaker correlations about the dateline mark the nodal point in interannual variability in the Pacific. High improved correlations are also found in the subsurface water of the equatorial Indian Ocean and Atlantic Ocean. The reduced RMS errors are relatively weak in the equatorial Indian Ocean and Atlantic Ocean. The difference between the Pacific and the Atlantic are consistent with interannual variability in the Indian and Atlantic on these timescales being significantly weaker. Outside the tropics correlations are weak as expected: In the extra-tropics on seasonal-interannual timescales atmospheric anomalies generally drive SST anomalies.
Figure 5. Simulation differences over the tropical oceans between the new ensemble-nudging scheme and original nudging scheme, (a) is for the improvements in correlation coefficients of temperature, and (b) is for the reductions in RMS errors. The shaded area in (a) indicates the simulation skill has been improved in correlation, and the shaded area in (b) indicates the simulation error has been reduced over the tropical oceans (°C).
As most of the improvements concentrate over the upper 100 m, a new diagnostic variable is chosen here (OHT_100 m: average potential temperature in the upper 100 m). To validate whether this ensemble-based subsurface temperture correction method can improve the relationship between surface and subsurface temperature fields, as designed in Table 1, the validation experiments are carried out for improving the OHT_100 m analysis.
Experiment Name Experiment description Nudg_SST (NSST) Restoring the observed SST into the modeled SST to generate the analysis fields Upd_Tsub Adopting the long-term NSST results to construct the SST and subsurface temperature relationship, and updating the temperature fields when restoring the observed SST into the modeled SST Upd_Tsub_1 Same as in the Upd_Tsub experiment, but adopting the long-term Upd_Tsub results to construct the SST and subsurface temperature relationship Upd_Tsub_2 Same as in the Upd_Tsub experiment, but adopting the long-term Upd_Tsub_1 results to construct the SST and subsurface temperature relationship Upd_Tsub_3 Same as in the Upd_Tsub experiment, but adopting the long-term Upd_Tsub_2 results to construct the SST and subsurface temperature relationship
Table 1. Experiment design for the five analysis experiments
For the “Nudg_SST (NSST)” experiment, the observed SST is stored into the modeled SST to generate the analysis fields, as performed as the original SST nudging scheme in Section 3.1. Furthermore, based on the “NSST” experiment, the “Upd_Tsub” experiment can adopt the (1960–2009) long-term simulation results to construct the SST and subsurface temperature relationship, and then we performed the new ensemble-based SST nudging scheme in Section 3.1 to update the temperature fields when restoring the observed SST into the modeled SST. This application also can consider the 20-century condition besides of the pre-industry condition in these experiments. Again, when performing the “Upd_Tsub_1” experiment, we can adopt the long-term “Upd_Tsub” results to construct the SST and subsurface temperature relationship during restoring the observed SST into the model. The “Upd_Tsub_2” and the “Upd_Tsub_3” experiments have the same design as the “Upd_Tsub_1” experiment, and each experiment is adopting the previous experiment to construct the SST and subsurface temperature relationship during the SST nudging process.
Figure 6 compares the variations in RMS errors from different experiments, we can find the RMS errors of these experiments can converge to one possible value, and the SST nudging scheme gets the worst score of all the experiment. There are nearly no differences in RMS errors between the Upd_Tsub_2 and Upd_Tsub_3 experiments, indicating that the OHT_100 m has been updated to a limit due to the directly adjusting of the subsurface temperature field. Also, as shown in Table 2, the temporal averaged RMS error for the OHC_100 m over global, or over 60°S–60°N, or over 30°S–30°N, can all access to a minimal value, and the differences in the temporal averaged RMS error of OHC_100 m between the Upd_Tsub_2 and Upd_Tsub_3 experiments can be neglected. These comparisons indicate this ensemble-based SST nudging method can represent the relationship between SST and subsurface temperature field well, and can update the temperature field over the upper ocean to an optimal state for initialization.
Experiments Temporal averaged RMS error
for the OHC_100 m/°C
Global 60°S–60°N 30°S–30°N Nudg_SST (NSST) 1.09 1.07 0.98 Upd_Tsub 0.96 0.94 0.84 Upd_Tsub_1 0.83 0.82 0.77 Upd_Tsub_2 0.78 0.76 0.72 Upd_Tsub_3 0.75 0.74 0.69
Table 2. Temporal averaged RMS error of the OHC_100 m for each experiment
Figure 6. Temporal variations in the averaged RMS error of the OHC_100 m over global, or over 60°S–60°N, or over 30°S–30°N from five different analysis experiments. The black line represents the results from the NSST experiment, the red line represents the results from the Upd_Tsub experiment, the green line represents the results from the Upd_Tsub_1 experiment, the blue line represents the results from the Upd_Tsub_2 experiment, and the light blue line represents the results from the Upd_Tsub_3 experiment, respectively.
An ensemble-based SST nudging method proposed for correcting the subsurface temperature field in climate model
- Received Date: 2019-08-27
- Available Online: 2020-04-21
- Publish Date: 2020-03-01
- ensemble-based nudging method /
- ECHAM5/MPI-OM /
- SST assimilation /
- simulation of subsurface temperature field
Abstract: An ensemble-based assimilation method is proposed for correcting the subsurface temperature field when nudging the sea surface temperature (SST) observations into the Max Planck Institute (MPI) climate model, ECHAM5/MPI-OM. This method can project SST directly to subsurface according to model ensemble-based correlations between SST and subsurface temperature. Results from a 50 year (1960–2009) assimilation experiment show the method can improve the subsurface temperature field up to 300 m compared to the quality-controlled subsurface ocean temperature objective analyses (EN4), through reducing the biases of the thermal states, improving the thermocline structure, and reducing the root mean square (RMS) errors. Moreover, as most of the improvements concentrate over the upper 100 m, the ocean heat content in the upper 100 m (OHT_100 m) is further adopted as a property to validate the performance of the ensemble-based correction method. The results show that RMS errors of the global OHT_100 m convergent to one value after several times iteration, indicating this method can represent the relationship between SST and subsurface temperature fields well, and then improve the accuracy of the simulation in the subsurface temperature of the climate model.
|Citation:||Xingrong Chen, Hui Wang, Fei Zheng, Qifa Cai. An ensemble-based SST nudging method proposed for correcting the subsurface temperature field in climate model[J]. Acta Oceanologica Sinica, 2020, 39(3): 73-80. doi: 10.1007/s13131-020-1568-2|