Extended range Arctic sea ice forecast with Convolutional Long-Short Term Memory Networks


 <p>Operational Arctic sea ice forecasts are of crucial importance to commercial and scientific activities in the Arctic region. Currently, numerical climate models, including General Circulation Models (GCMs) and regional climate models, are widely used to generate the Arctic sea ice predictions at weather time-scales. However, these numerical climate models require near real-time input of weather conditions to assure the quality of the predictions and these are hard to obtain and the simulations are computationally expensive. In this study, we propose a deep learning approach to forecasts of sea ice in the Barents sea at weather time scales. To work with such spatial-temporal sequence problems, Convolutional Long Short Term Memory Networks (ConvLSTM) are useful. &#160;ConvLSTM are LSTM (Long-Short Term Memory) networks with convolutional cells embedded in the LSTM cells. This approach is unsupervised learning and it can make use of enormous amounts of historical records of weather and climate. With input fields from atmospheric (ERA-Interim) and oceanic (ORAS4) reanalysis data sets, we demonstrate that the ConvLSTM is able to learn the variability of the Arctic sea ice within historical records and effectively predict regional sea ice concentration patterns at weekly to monthly time scales. Based on the known sources of predictability, sensitivity tests with different climate fields were also performed. The influences of different predictors on the quality of predictions are evaluated. This method outperforms predictions with climatology and persistence and is promising to act as a fast and cost-efficient operational sea ice forecast system in the future.</p>



Extended range Arctic sea ice forecast with Convolutional Long-Short Term Memory Networks
Yang Liu, Laurens Bogaardt, Jisk Attema and Wilco Hazeleger Supplement to the paper

Figure S1 .
Figure S1.Mean absolute error of sea ice area in the Barents Sea between NOAA/NSIDC Passive Microwave Sea Ice Concentration data and sea ice field in ERA-Interim from 1979-2016.The unit is square kilometer.

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Figure S2.RMSE of the SIC forecast with a lead time up to 6 weeks with ConvLSTM using SIC from ERA-Interim (ConvLSTM -SIC) and NOAA/NSIDC Passive Microwave Sea Ice Concentration data (ConvLSTM -NOAA / NSIDC).

Figure S3 .
Figure S3.Learning curve of ConvLSTM with the chosen combination of hyperparameters.The loss is measured as the RMSE of normalized sea ice concentration (0-1).

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Figure S4 RMSE of the constrained forecast of SIC for the second lead week in each month with ConvLSTM using different predictors against persistence and climatology.The unit is square kilometer per grid cell.

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Figure S5 RMSE of the constrained forecast of SIC for the fourth lead week in each month with ConvLSTM using different predictors against persistence and climatology.The unit is square kilometer per grid cell.

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Figure S6 RMSE of the constrained forecast of SIC for the sixth lead week in each month with ConvLSTM using different predictors against persistence and climatology.The unit is square kilometer per grid cell.

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Figure S7 RMSE of the operational forecast of SIC for the second lead week in each month with ConvLSTM using different predictors against persistence and climatology.The unit is square kilometer per grid cell.

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Figure S8 RMSE of the operational forecast of SIC for the fourth lead week in each month with ConvLSTM using different predictors against persistence and climatology.The unit is square kilometer per grid cell.

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Figure S9 RMSE of the operational forecast of SIC for the sixth lead week in each month with ConvLSTM using different predictors against persistence and climatology.The unit is square kilometer per grid cell.

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Figure S10 Annual mean MAE of the SIC from NCEP ensemble forecast (left) and ECMWF ensemble forecast (right) for the first week against ERA-Interim between 2015 to 2016.The NCEP real-time forecast and ECMWF ensemble forecast are from sub-seasonal to seasonal prediction project (S2S archive).The unit is square kilometer per grid cell.

Figure S11 .
Figure S11.RMSE of the operational forecast of SIC with a lead time up to 6 weeks with ConvLSTM using different predictors against persistence, and climatology from 1979 to 1982.The training and testing were based on the reversed time series of reanalysis data.The unit is square kilometer per grid cell.

Figure S12 .
Figure S12.Projection of covariance map of SIC and OHC on the time series of SIC and OHC.The regression coefficients of the regressions of SIC and OHC time series on the (a, d, g) first, (b, e, h) second and (c, f, i) third SVD modes of SIC and OHC covariance map in(a, b, c) training (d, e, f) testing and (g, h,  i)  forecast data for the first week are shown as shades and contour lines.The SVD was performed on the covariance matrix of normalized SIC and OHC.

Figure S13 .
Figure S13.Projection of covariance map of SIC and Z500 on the time series of SIC and Z500.The regression coefficients of the regressions of SIC and Z500 time series on the (a, d, g) first, (b, e, h) second and (c, f, i) third SVD modes of SIC and Z500 covariance map in(a, b, c) training (d, e, f) testing and (g, h,  i)  forecast data for the first week are shown as shades and contour lines.The SVD was performed on the covariance matrix of normalized SIC and Z500.

Figure S14 .
Figure S14.Covariance map of SIC and SFlux for the (a, d, g) first, (b, e, h) second and (c, f, i) third SVD modes in (a, b, c) training (d, e, f) testing and (g, h, i) forecast data for the first week, with shades the dimensionless SIC and contour lines the dimensionless OHC.The SVD was performed on the covariance matrix of normalized SIC and SFlux.

Figure S15 .
Figure S15.Covariance map of SIC and Z850 for the (a, d, g) first, (b, e, h) second and (c, f, i) third SVD modes in (a, b, c) training (d, e, f) testing and (g, h, i) forecast data for the first week, with shades the dimensionless SIC and contour lines the dimensionless OHC.The SVD was performed on the covariance matrix of normalized SIC and Z850.

Figure S16 .
Figure S16.Annual mean RMSE of the operational forecast of SIC for the first week with ConvLSTM using SIC and OHC.The sea ice concentration is normalized (0-1).

Table S1 .
A brief summary of hyperparameter tuning of ConvLSTM Stacked layers are the number of ConvLSTM layers, the sea ice forecast with ConvLSTM is based on SIC and OHC.)

Table S2 .
RMSE of the constrained forecast of SIC with ConvLSTM using different predictors against persistence, climatology and the baseline statistical model.The standard deviation of RMSE is included.

Table S3
Baseline statistical model 79.34 81.58 77.89 67.68 55.45 33.37 16.94 14.69 11.45 20.02 30.67 59.58 . RMSE of the constrained forecast of SIC for the first week in each month with ConvLSTM using different predictors against persistence, climatology and the baseline statistical model.The unit is square kilometer per grid cell.

Table S4 .
RMSE of the operational forecast of SIC with ConvLSTM using different predictors against persistence, and climatology.The ECMWF and NCEP real-time forecasts are from sub-seasonal to seasonal prediction project (S2S archive).

Table S5 .
RMSE of the operational forecast of SIC for the first week in each month with ConvLSTM using different predictors against persistence and climatology.The unit is square kilometer per grid cell.