Fig. 1
Schematic of the experimental set-up. TRUTH (in grey) is the year 600–710 of a multi-century control run. PERFECT (in red) is initialized from TRUTH at the beginning of each prediction cycle. The 10 EnKF-SST cycles assimilate observations extracted from TRUTH during the analysis period and continued in the prediction cycles. The analysis cycle of EnKF-SST (in blue) and FREE (in black) are initialised from the same initial ensemble (green ellipse) composed from output of the years 251–541 of the control run.
Fig. 2
Time series of monthly RMSE and bias for FREE (black), EnKF-SST (blue) and PERFECT (red) averaged over the 10 cycles. The vertical dashed line separates the analysis phase (year 1–10) from the prediction phase (year 11–20). The RMSE is plotted as a bold solid line and the bias with a dashed line.
Fig. 3
Averaged differences between monthly RMSE in FREE and EnKF-SST, over the 10 analysis cycles. Warm colours indicate that the RMSE in the EnKF is smaller than in FREE. The units are the same as in Table 1.
Table 1. The first column is the monthly RMSE calculated over the whole domain for FREE for the last year of the analysis period averaged over the 10 analysis cycles. The second column shows the corresponding improvements of EnKF-SST relative to FREE [RRMSE given in %; see eq. (6)]
T2M (°C)0.8211Precip (mm/day)0.799ssh (m)0.0610icec (%)0.811sst (°C)0.3654sss (psu)0.1325T[0 225] (°C)0.3145S[0 225] (psu)0.0625T[225 500] (°C)0.1615S[225 500] (psu)0.0311T[500 1050] (°C)0.133S[500 1050] (psu)0.025
Fig. 4
Correlation between the AMOC in EnKF-SST and TRUTH depending on the latitude. The blue line represents the correlation for the yearly time series. The black and red lines are the correlations when a 3- and 5-yr running mean is applied before calculating the correlation. The vertical dashed line indicates the 42°N latitude for which AMOC is calculated in Figures 5 and 7.
Fig. 5
Time series of the AMOC, the SPG, the STG and the AMO over the 10 analysis cycles for TRUTH (black) and EnKF-SST (blue). The blue shading is the ensemble quartile envelope and the blue line is the ensemble mean. For the AMOC, the bold line is the 5-yr running mean while the thin line represents the yearly values. The vertical dashed lines separate each of the analysis cycles.
Table 2. Correlations between EnKF-SST and TRUTH over the 100-yr analysis period for the different indices
AMOC 42°0.61AMOC 42° (5-yr)0.77STG0.82SPG0.59AMO0.93Niño30.96
Table 3. The first two columns are the 1 and 2–5 lead-year averaged RMSE, calculated over the whole domain for FREE. The remaining columns show the corresponding improvements for EnKF-SST and PERFECT relative to FREE [RRMSE given in %; see eq. (6) for each of the time-periods considered]
Prediction year
T2M (°C)0.550.3774137Precip (mm/day)0.480.261151910ssh (m)0.050.0511108583icec (%)0.80.6452919sst (°C)0.30.22183918sss (psu)0.10.091545630T[0 225] (°C)0.210.192255425S[0 225] (psu)0.050.051867345T[225 500] (°C)0.160.161147451S[225 500] (psu)0.030.031178466T[500 1050] (°C)0.120.12308572S[500 1050] (psu)0.020.02549284
Fig. 6
The difference of 1 lead-year averaged RMSE of FREE and EnKF-SST, over the 10 prediction cycles, as in Figure 3.
Fig. 7
The difference of 2–5 lead-year averaged RMSE of FREE and EnKF-SST, over the 10 prediction cycles, as in Figure 3.
Fig. 8
Left panels: time series of different indices are on the left column. Right panels: the correlation relative to the forecast lead-time (in years). Vertical dashed lines separate each of the prediction cycles. The black line is TRUTH, the red line is PERFECT, the blue line is EnKF-SST and the horizontal dashed line is PERSISTENCE. The dashed blue line for the SPG index in the right panel represents the skill of the EnKF-SST when the initial bias is corrected as in PERSISTENCE.
Fig. 9
Time series of the detrended decadally averaged AMO index for TRUTH (thick black line), PERFECT (red line), EnKF-SST (blue line), PERSISTENCE (dashed black line) and EnKF-SST if initial bias is corrected (dashed blue line). Vertical dashed lines separate each of the prediction cycles.
Fig. 10
Correlation with the Niño3 index for PERSISTENCE (black), PERFECT (red) and EnKF-SST (blue). Correlations are computed for 6-month averages. For the first 6 months, EnKF-SST is under PERFECT.
Fig. 11
Prediction of heat content (0–300 m) in different regions of the Nordic Seas. The thick black line is TRUTH, the dashed black line is PERSISTENCE, the red line is PERFECT and the blue line is EnKF-SST. Shaded areas correspond to the quartile envelope. Vertical black lines separate each of the prediction cycles.