Introduction
The Arctic sea-ice cover has decreased in all months since satellite observations began in the late 1970s (Stroeve and Notz, Reference Stroeve and Notz2018). In particular, sea-ice extent (SIE) in September exhibits a decreasing trend of 12.8% per decade (National Snow and Ice Data Center, 2018, http://nsidc.org/arcticseaicenews/). The decline in Arctic sea ice influences the climate system not only in the Arctic region but also in the midlatitudes (e.g., Mori and others, Reference Mori, Kosaka, Watanabe, Nakamura and Kimoto2019) and economic activity via the Northern Sea Route (e.g., Khon and others, Reference Khon, Mokhov, Latif, Semenov and Park2010; Liu and Kronbak, Reference Liu and Kronbak2010). These factors indicate that there is a need for accurate seasonal-to-interannual sea-ice forecasts (Eicken, Reference Eicken2013).
Initialized predictions using climate models have shown that the summer SIE can be predicted up to 2–7 months ahead (e.g., Sigmond and others, Reference Sigmond, Fyfe, Flato, Kharin and Merryfield2013; Wang and others, Reference Wang, Chen and Kumar2013; Msadek and others, Reference Msadek, Vecchi, Winton and Gudgel2014; Bushuk and others, Reference Bushuk2017). On the other hand, perfect model ensemble prediction experiments have suggested that the Arctic SIE has a potential predictability of 1–2 years (Blanchard-Wrigglesworth and others, Reference Blanchard-Wrigglesworth, Bitz and Holland2011). There is still a gap of a few months to 1 year in the predictable periods between initialized predictions and perfect model experiments. For this reason, further work is needed to improve the forecast accuracy of the real sea ice. The key variables for improving predictive skill are sea-ice thickness (SIT) and subsurface water temperatures (e.g., Day and others, Reference Day, Tietsche and Hawkins2014a), which are thought to be a memory for sea-ice variability. Hence, the initialization of these physical quantities is very important for seasonal-to-interannual sea-ice forecasts.
Previous studies have pointed out the importance of SIT when predicting the summer sea ice. For example, the SIT in winter to spring is considered to be a key predictor of the SIE in summer (e.g., Kauker and others, Reference Kauker2009; Kimura and others, Reference Kimura, Nishimura, Tanaka and Yamaguchi2013). The SIT initialization has considerably improved the predictive skill of the Arctic sea ice (e.g., Day and others, Reference Day, Hawkins and Tietsche2014b; Collow and others, Reference Collow, Wang, Kumar and Zhang2015; Dirkson and others, Reference Dirkson, Merryfield and Monahan2017; Blockley and Peterson, Reference Blockley and Peterson2018; Kimmritz and others, Reference Kimmritz2018; Zhang and others, Reference Zhang2018). Some studies have also shown that the persistence of SIT could contribute to the skilful prediction of the September SIE (e.g., Bushuk and others, Reference Bushuk2017; Ono and others, Reference Ono, Tatebe, Komuro, Nodzu and Ishii2018). However, the sensitivity of the predictions to initializations for different regions for the Arctic sea ice has not yet been thoroughly investigated.
Motivated by the above studies, we investigate the impact of the initialized SIT in April on the predictability of Arctic SIE in September following Day and others (Reference Day, Hawkins and Tietsche2014b) because they did not examine the impact of SIT initialized in spring. To this end, control and perfect model ensemble prediction experiments are first conducted using a climate model, under the Arctic Prediction and Predictability on Seasonal-to-Interannual Time Scales (APPOSITE) project (Day and others, Reference Day2016). When performing sea-ice forecasts with coupled global climate models, forecast errors arise from errors in the initial conditions and an incomplete representation of physical processes in the model. In the perfect model experiments, the model can predict itself with ideal initial conditions and no biases (e.g., Collins, Reference Collins2002). However, it is noted that the predictive skill of a perfect model is not necessarily an upper bound of the predictability, as the climate in the model may be more predictable than in reality or vice versa (Kumar and others, Reference Kumar, Peng and Chen2014). Second, critical areas for the improvement of forecast accuracy in the September Arctic SIE are identified based on comparisons of predictability metrics. This will help inform the effective use of the limited ice thickness data for initialization and provide information for target sites focusing on ice thickness observations.
Methods
The climate model used in this study is the Model for Interdisciplinary Research on Climate (MIROC) version 5.2 (Tatebe and others, Reference Tatebe, Tanaka, Komuro and Hasumi2018). The horizontal resolution of the atmospheric component is a T42 spectral truncation (~300 km), and there are 40 vertical levels up to 3 hPa. The warped bipolar horizontal coordinate system of the MIROC5 oceanic component has been replaced by a tripolar coordinate system (Murray, Reference Murray1996). The horizontal resolution of the oceanic component is a nominal 1° to the south of 63°N and ~60 km over the central Arctic Ocean. There are 62 vertical levels, the lowermost level of which is located at the 6300 m depth. The sea-ice component implements one-layer thermodynamics (Bitz and Lipscomb, Reference Bitz and Lipscomb1999), elastic–viscous–plastic rheology (Hunke and Dukowicz, Reference Hunke and Dukowicz1997) and a subgrid ice thickness distribution (Bitz and others, Reference Bitz, Holland, Weaver and Eby2001) with five categories. The detailed framework and parameters have been described in Komuro and others (Reference Komuro2012).
This study is based on perfect model simulations, which is the same approach used in Ono and others (Reference Ono, Tatebe and Komuro2019). The experiments performed in this study are briefly summarized in Table 1. A control experiment (CTRL) with radiative forcing fixed at present-day levels (year 2000) is conducted following the APPOSITE project framework (Day and others, Reference Day2016). The model is newly integrated for 1000 years, arbitrarily labelled 1–1000, with the initial conditions from the CTRL of Ono and others (Reference Ono, Tatebe and Komuro2019).
Table 1. Overview of simulations considered in this study
A series of perfect model ensemble prediction experiments are carried out to assess the predictability of sea ice. The start date is 1 April of the same year. An ensemble of eight members is generated for the start date. As in Ono and others (Reference Ono, Tatebe and Komuro2019), only eight ensemble members were used in the perfect model experiments based on the APPOSITE protocol. However, care should be taken when interpreting the results because 10–15 ensemble members are required to effectively capture the internal variability (Jahn and others, Reference Jahn, Kay, Holland and Hall2016). The initial conditions are taken from CTRL, and each member differs only by a perturbation of the sea surface temperature, which is generated by spatially uncorrelated Gaussian noise with a std dev. of 10–4 K following the APPOSITE project. Each ensemble is run for 3 years and 9 months from 1 April. The above experiments are referred to as INIT.
Ensemble prediction experiments with the same setup as in INIT but without the initialization of SIT are also conducted following Day and others (Reference Day, Hawkins and Tietsche2014b). To remove the initial memory of the SIT, the grid-averaged SIT is replaced by a climatology for which the monthly mean values during the period of 1–1000 are used, but with the grid-averaged sea-ice concentration (SIC) and snow depth held fixed. The replaced ice thickness for the ith category $\lpar {\rm IT}_{{\rm REPL}}^i \rpar$
is represented as ${\rm IT}_{{\rm REPL}}^i = {\rm IT}_{{\rm CTRL}}^i + {{{\rm \Delta SIT}} \over {{\rm SI}{\rm C}_{{\rm CTRL}}}}$
, where ${\rm IT}_{{\rm CTRL}}^i$
is the thickness of the ice for the ith category of CTRL, ΔSIT ( = SITCLIM − SITCTRL) is the difference in the grid-averaged SIT between the climatology and CTRL, and SICCTRL is the grid-averaged SIC of CTRL. Consequently, the replaced grid-averaged SIT is calculated as $\mathop \sum \nolimits_{i = 1}^5 {\rm IC}_{{\rm CTRL}}^i {\rm IT}_{{\rm REPL}}^i \lpar { = {\rm SI}{\rm T}_{{\rm CLIM}}} \rpar$
, where ${\rm IC}_{{\rm CTRL}}^i$
is the ice concentration of the ith category of CTRL. However, there is a case where the ice thickness of the ith category is outside of the upper and lower thickness limits (see Table 3 of Komuro and others (Reference Komuro2012) for the limits). In that case, the initial values for the ice concentration and thickness, snow depth on ice and temperature in the ice for the ith category are redistributed so that the ith category ice thickness is within the limits. The above experiments are referred to as CLIM. As will be explained in detail later, two additional experiments are also conducted to confirm this paper's hypothesis based on the INIT and CLIM results.
Results
Control experiment
Before showing the results, we briefly review here the basic performance of the model used in this study. As shown in Ono and others (Reference Ono, Tatebe and Komuro2019), MIROC5.2 largely reproduced the observed features for the mean state, variability and diagnostic predictability of sea ice, indicating that it is a useful model for investigating sea-ice predictability. Note that anomalies for all variables are defined as the deviation from the 1000-year climatology of CTRL. In the present study, we did not consider the climatology using a shorter window, as suggested by Cruz-García and others (Reference Cruz-García, Guemas, Chevallier and Massonnet2019), because there is no significant difference in climatology between a 1000-year period and a shorter period (not shown).
Figure 1 shows the time series of the SIE anomaly in September for CTRL. The 1000-year climatology of the CTRL is 7.10 million km2 and the std dev. is 0.47 million km2. The interannual variability in SIE is broadly similar to that of the observations, and dozens of extreme anomalies exceeding ± 2 std dev. occur during the 1000 years. A low-frequency variability is also found in the time series, which is characterized by the persistent positive and negative anomalies over the decadal-to-multidecadal timescales. This might be related to longer climate variability, but sea-ice predictability at longer timescales is beyond the scope of this study. For the perfect model ensemble prediction experiments, ten cases will be chosen from CTRL based on the 100-year interval (vertical lines in Fig. 1). There are two positive and eight negative anomalies in SIE from ten cases (Table 2). While the highest SIE is in the model year 151, the anomaly of 0.35 million km2 is less than one std dev. The lowest SIE is in the model year 751, where the anomaly of −1.35 million km2, which ranks as the lowest minimum SIE over the 1000 model years, is considerably more than two std dev. below the 1000-year climatology of the CTRL. Among the ten cases, model years 151 and 751 also have the highest positive and negative anomalies, respectively, in sea-ice volume (SIV).
Fig. 1. Time series of the September sea-ice extent (SIE) anomaly relative to the 1000-year climatology of CTRL. Plus and minus two std dev. boundaries are indicated by horizontal dashed lines. Vertical lines denote the ten cases used for perfect model ensemble prediction experiments. Positive anomalies are shown in red and negative in blue.
Table 2. September sea-ice extent (SIE) (million km2) and volume (SIV) (thousand km3) for 10 model years and their anomalies from the climatology of CTRL (values for the year shown in Figs 4 and 5 are indicated in bold)
In most cases for the negative SIE anomalies, the sea ice widely retreats in the Beaufort, Chukchi, East Siberian and Laptev Seas and the thickness anomaly is smaller near the ice edge, especially in model years 51, 751 and 851 (Fig. 2). In contrast, the thickness anomalies in the model year 151 are positive in most areas of the Pacific sector of the Arctic Ocean except for the East Siberian Sea, leading to the positive SIE anomaly. It is likely, at least in MIROC5.2, that the September SIE anomaly is determined by sea-ice variability in the Pacific sector under the influence of the atmospheric circulation anomaly.
Fig. 2. Sea-ice thickness (SIT) anomalies in September for ten cases in regions from 60 to 90°N. The black lines denote the 15% contours of sea-ice concentration. Dashed lines show latitude 70° and 80° and longitude 0°, 90°, 180° and 270°.
Perfect model ensemble prediction experiments
Figure 3 shows the spatial distribution of SIT on 1 April in model year 51 for INIT and CLIM, together with the difference, as an example of the SIT replacement. The sea ice in CLIM is thicker in the Pacific sector and the western part of the Kara Sea and thinner in the Barents Sea, the northern part of Greenland and the Baffin Bay when compared to INIT.
Fig. 3. Sea-ice thickness (SIT) used as an initial value for (a) INIT (1st April 51 model year), (b) CLIM and (c) the difference in sea-ice thickness between INIT and CLIM in regions from 60°N to 90°N (latitude circles of 70°N and 80°N are drawn by dashed circles).
Before assessing the prediction skill of sea ice, it might be more useful to compare the results in INIT with those in CLIM for a specific model year. Figure 4 shows the time series of the SIE and SIV anomalies for model years 251 (nearly-climatology case) and 751 (highly-extreme case). For the year 251 (Figs 4a and c), the SIE of CTRL remains continuously within the ensemble spread up to the second November (lead month 20) in INIT. In CLIM, it remains within the ensemble spread during the first two lead months (April and May) and freezing seasons (October–March) but not during the first and second melting seasons (April–September). With regard to the SIV, the result of CTRL remains within the ensemble spread over longer lead-times in both prediction experiments because the SIV in the year 251 is close to the climatology. For the year 751 (Figs 4b and d), however, the SIE of CTRL is outside of the ensemble spread in the first September by ~0.2 million km2 even in INIT. These results are consistent with the previous study by Ono and others (Reference Ono, Tatebe and Komuro2019), who showed that predictions started in April have no significant skill for a drastic ice reduction in September. In CLIM, the SIE during the melting season is far from CTRL up to the second prediction years. Similar features are also found in the SIV.
Fig. 4. Time series of sea-ice (a, b) extent (SIE) and (c, d) volume (SIV) anomalies in INIT (blue) and CLIM (red) started from 1 April for model years (a) 251 and (b) 751. Black lines indicate the CTRL results. Blue and red shadings denote the ensemble spread for INIT and CLIM.
Figure 5 shows the spatial distribution of the September SIT anomaly for model years 251 and 751 in INIT and CLIM. For the year 251, the sea-ice edge in CLIM (red line) is inconsistent with those in INIT (blue line) and CTRL (black line) between the East Siberian and the Laptev Seas. These differences lead to the differences in the predictions of the SIE, as shown in Figure 4. For the year 751, even in INIT, the sea-ice retreat lags behind that in CTRL in the northern part of the East Siberian and Laptev Seas (black and blue lines in Fig. 5b). One of the reasons for this is that predictions started on 1 April do not reproduce the Arctic dipole anomaly in sea-level pressure formed in June–August of year 751 (not shown). In contrast, the sea-ice retreat in CLIM is delayed further as a result of the replacement with the thicker climatology, therefore leading to the positive SIE and SIV anomalies.
Fig. 5. September sea-ice thickness (SIT) anomaly in INIT and CLIM for model years (a) 251 and (b) 751 in regions from 60°N to 90°N (latitude circles of 70°N and 80°N are drawn by dashed circles). The 15% contours of sea-ice concentration in September are indicated by black, blue and red curves for CTRL, INIT and CLIM, respectively. In INIT for model years 251 and 751, the 15% contours for each ensemble member are also denoted by thin blue (INIT) and red (CLIM) lines.
Next, the prediction skill for SIE and SIV is assessed based on the root-mean-square error (RMSE) presented in Day and others (Reference Day, Hawkins and Tietsche2014b). In perfect model experiments, each ensemble member is assumed to be the truth, and the sufficient sample size can be increased by taking each member in turn as the truth and every other member as a forecast. Therefore, the ensemble RMSE is defined as
where x ij (t) is a certain variable (such as SIE) at lead time t for the ith member of the jth ensemble, n d ( = 10) is the number of start dates, and n m ( = 8) is the number of ensemble members. The state is said to be predictable at lead time t, if ${\rm RMSE}\,\lpar t\rpar \lt\! \sqrt 2 \sigma$
where σ is the climatological std dev. of CTRL (Collins, Reference Collins2002). As in Day and others (Reference Day, Hawkins and Tietsche2014b), the RMSE of INIT is calculated in such a way that x kj is considered to be the truth and each x ij the forecast. Similarly, the RMSE of CLIM is calculated by replacing x ij in the above equation with y ij, which is the equivalent member from CLIM. The difference between these two RMSE values gives the gain in skill between the climatological and perfect initialization of the SIT field. The significance of the difference is calculated based on an F test with n d (n m − 1) = 70 degrees of freedom.
Figure 6 shows the time series of the normalized RMSE of SIE and SIV (normalized by $\sqrt 2 \sigma$
) in INIT and CLIM, which were initialized on 1 April. The normalized RMSE in CLIM (Fig. 6a) exceeds 1.0 from June (lead month 3) to October (lead month 7), and thus SIE in September is not predictable. In contrast, the INIT predictions indicate that SIE is continuously predictable up to the third September (lead month 30). A significant difference between them is found in lead months 3–7 (Fig. 6a), which is somewhat better than the predictions started on 1 January in Day and others (Reference Day, Hawkins and Tietsche2014b). This difference is likely impacted by April being a shorter lead time than January. In this study, there are also significant differences in the second August and September. This is likely because of the summer-to-summer re-emergence mechanism associated with the persistence of ice thickness (Day and others, Reference Day, Hawkins and Tietsche2014b). Similarly, there are significant differences in SIV over longer lead times, compared to those in SIE, as in Day and others (Reference Day, Tietsche and Hawkins2014a). As shown in Cruz-García and others (Reference Cruz-García, Guemas, Chevallier and Massonnet2019), since the autocorrelation structure of SIV in MIROC (also see Fig. 3c in Ono and others (Reference Ono, Tatebe and Komuro2019)) is larger than in other models, there is the potential for unrealistically high SIV predictability. Therefore, the predictability of SIV in INIT and CLIM might be influenced by the autocorrelation structure of SIV in MIROC.
Fig. 6. Time series of the normalized RMSE of sea-ice (a) extent (SIE) and (b) volume (SIV) in INIT (blue) and CLIM (red) initialized on 1 April. Dots indicate where differences between INIT and CLIM are significant at the 5% levels based on a one-sided F test.
Focusing on the first forecast year (lead months 1–9 or April–December), we investigate the area underlying the prediction skill of the September SIE. Figure 7 shows the spatial distribution of the difference in the RMSE of SIT and concentration between INIT and CLIM. For the SIT RMSE, the difference for the first lead month (April) is significant in most regions of the Arctic Ocean. In the fourth to sixth lead months (July–September), the difference in SIT RMSE decreases except for the Pacific sector (Fig. 7a). For the SIC RMSE, there are no significant differences in most of the Arctic Ocean in the first 3 months (April–June). During lead months 4–6 (July to September), the differences become significant in the Beaufort, Chukchi, East Siberian and Laptev Seas (Fig. 7b). Initial errors in the April SIT cause errors in the July to September SIC in the Pacific sector and influence the prediction skill of the September SIE. Therefore, the initialization of ice thickness in the Pacific sector is thought to be crucial. These results are supported by Ono and others (Reference Ono, Tatebe, Komuro, Nodzu and Ishii2018), who found a significant relationship between the September SIE and the sea-ice fields in the Pacific sector during the melting season. Additionally, the impacts of initializing predictions with different SIT in April on other variables are shown in Figure S1. Significant differences in RMSE are found in most of the Pacific sector, where the differences in SIC and SIT RMSE are significant (Fig. 7).
Fig. 7. Spatial distribution of the difference in the RMSE of sea-ice (a) thickness (SIT) and (b) concentration (SIC) in April (lead month 1), July (lead month 4), August (lead month 5) and September (lead month 6) in regions from 60°N to 90°N (latitude circles of 70°N and 80°N are drawn by dashed circles). All coloured grid points are significant at the 5% level based on a one-sided F test.
To confirm whether the thickness of April sea-ice fields in the Pacific sector of the Arctic Ocean determines the September SIE variability, two additional ensemble prediction experiments started on 1 April with the SIT initialization only in (PSINIT) and except for (PSCLIM) the Pacific sector (the area enclosed by thick lines shown in Fig. 8c) are conducted until the first December (lead months 9). The normalized SIE RMSE of PSINIT (green line) is generally consistent with that of INIT (blue line), except for lead months 1 and 3 (April and June), indicating that the September SIE is predictable (Fig. 8a). The normalized SIE RMSE of PSCLIM (black line) is larger than that of INIT (blue line), as in CLIM (red line). In contrast, the normalized SIV RMSE is significantly higher in both PSINIT (green line) and PSCLIM (black line) than in INIT (blue line) up to lead months 9 (Fig. 8b). From these results, the RMSE in the sea-ice fields of PSINIT is expected to be small compared to CLIM. In fact, in PSINIT (Figs 8c and d), differences in the RMSE of SIC and SIT in September (lead months 6) decrease substantially in the Pacific sector when compared to CLIM (Figs 7a and b). As pointed out in previous studies (e.g., Bushuk and others, Reference Bushuk2017; Ono and others, Reference Ono, Tatebe, Komuro, Nodzu and Ishii2018), the persistence of sea ice is the source of predictability for the September SIE. These results therefore suggest that initialization of the April SIT only in the Pacific sector improves the forecast accuracy of the September SIE.
Fig. 8. Time series of the normalized RMSE of sea-ice (a) extent and (b) volume in INIT (blue), CLIM (red), PSINIT (green) and PSCLIM (black) initialized on 1 April. Blue dots indicate where differences between INIT and PSINIT are significant at the 5% levels based on a one-sided F test. Spatial distribution of the difference in the RMSE of sea-ice (c) concentration (SIC) and (d) thickness (SIT) in September (lead month 6) between INIT and PSINIT in regions from 60°N to 90°N (Latitude circles of 70°N and 80°N are drawn by dashed circles). All coloured grid points are significant at the 5% level based on a one-sided F test. The area enclosed by thick lines is the region of the Pacific sector considered in this study.
Concluding Remarks
The present study investigated the impacts of initialization of SIT in April on Arctic sea-ice predictability and further identified the critical areas for the skilful forecasts of the September SIE. To this end, following partly Day and others (Reference Day, Hawkins and Tietsche2014b), a series of perfect model ensemble prediction experiments were conducted using climate model MIROC5.2. Ensembles with initialization of the April SIT can predict the September SIE for greater lead times than those without initialization – up to 2 years ahead. SIT correctly initialized in April leads to the skilful prediction of SIE in the first September due to the persistence of SIT (Fig. S2). We also speculate that a summer-to-summer re-emergence mechanism contributes to the prediction skill in the second September. On the other hand, the incorrect initialization of SIT in April results in errors in the SIC and thickness in the Pacific sector from July to September and consequently influences the prediction skill of the SIE in September. Our results suggest that the initialization of the SIT in the Pacific sector significantly improves the forecast accuracy of SIE by decreasing the errors in sea-ice fields from July to September.
Incorporating accurate sea-ice observations for forecast initialization is an important step in making skilful seasonal sea-ice forecasts. Production centres routinely assimilate available satellite-derived and in situ atmosphere and ocean observations and SIC. However, SIT data are not currently available from May to September each year (e.g., Tilling and others, Reference Tilling, Ridout and Shepherd2016). For other months, these data do not go back far enough to initialize a sufficient number of hindcasts to provide robust estimates of predictive skill. The present study showed the effectiveness of SIT initialization in April when the observed data are available (e.g., Ricker and others, Reference Ricker, Hendricks, Helm, Skourup and Davidson2014), as shown in previous studies (Day and others, Reference Day, Hawkins and Tietsche2014b; Yang and others, Reference Yang2016; Chen and others, Reference Chen, Liu, Song, Yang and Xu2017; Mu and others, Reference Mu2017; Blockley and Peterson, Reference Blockley and Peterson2018; Kimmritz and others, Reference Kimmritz2018). Furthermore, our results suggest that the critical region for sea-ice initialization is the Pacific sector. If the initialization of ice thickness only in a specific region of the Arctic Ocean is found to improve the regional predictability of sea ice, from the viewpoint of cost performance, it will be useful for planning observational campaigns as well as developing forecast systems.
Meanwhile, large-scale Arctic sea-ice circulations are dominated primarily by the Beaufort Gyre (BG) and the Transpolar Drift Stream (TDS) (e.g., Kwok and others, Reference Kwok, Spreen and Pang2013). Considering the sea-ice advection, the initialization of thickness is expected to be sufficient in upstream regions. However, predictions initialized in the Pacific sector (PSINIT in this study) include a substantial contribution from the BG and TDS. It is therefore unclear how initial SIT in the upstream of the BG and TDS contributes to errors in the Pacific sector via advection as well as melting processes. This point needs to be addressed in future work.
Supplementary material
The supplementary material for this article can be found at https://doi.org/10.1017/aog.2020.13.
Acknowledgements
This work was a part of the Arctic Challenge for Sustainability (ArCS) Project (Program Grant Number JPMXD1300000000). Jun Ono was supported by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Young Scientists (B) 17K12830. Numerical experiments were conducted on the Earth Simulator at the Japan Agency for Marine-Earth Science and Technology (JAMSTEC). We thank the two anonymous reviewers and scientific editor Dr David Babb for their useful comments and suggestions.
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