Accurate estimates of sharp features in the sea ice cover, such as leads and ridges, are critical for shipping activities, ice operations and weather forecasting. These sharp features can be difficult to preserve in data fusion and data assimilation due to the spatial correlations in the background error covariance matrices. In this article, a set of data fusion and data assimilation experiments are carried out comparing two objective functions, one with a conventional l2-norm and one that imposes an additional l1-norm on the derivative of the ice thickness state estimate. The latter is motivated by analysis of high resolution ice thickness observations derived from an airborne electromagnetic sensor demonstrating the sparsity of the ice thickness in the derivative domain. Data fusion and data assimilation experiments (using a 1 D toy sea-ice model) are carried out over a wide range of background and observation error correlation length scales. Results show the superiority of using an l1-l2 regularisation framework. For the data fusion experiments it was found when both background and observation error correlation length scales are zero, the ice thickness root mean squared error for the l1-l2 method was 0.16 m as compared to 0.20 m for the l2 method. The differences between the methods were greater when the background error correlation length scale was relatively short (approximately five times the analysis grid spacing), and were not significant for larger background error correlation length scales (e.g. 10 times the analysis grid spacing). For data assimilation experiments it was found that openings in the ice cover were captured better with the l1-l2 regularisation, with reduced errors in ice thickness, concentration and velocity. In addition, the ice thickness derivatives in the analyses were found to be more sparse when the l1-l2 method was used and are closer to the those from the true model run.
Classification of temporal data sequences is a fundamental branch of machine learning with a broad range of real world applications. Since the dimensionality of temporal data is significantly larger than static data, and its modeling and interpreting is more complicated, performing classification and clustering on temporal data is more complex as well. Hidden Markov models (HMMs) are well-known statistical models for modeling and analysis of sequence data. Besides, ensemble methods, which employ multiple models to obtain the target model, revealed good performances in the conducted experiments. All these facts are a high level of motivation to employ HMM ensembles in the task of classification and clustering of time series data. So far, no effective classification and clustering method based on HMM ensembles has been proposed. Moreover, employing the limited existing HMM ensemble methods has trouble separating models of distinct classes as a vital task. In this paper, according to previous points a new framework based on HMM ensembles for classification and clustering is proposed. In addition to its strong theoretical background by employing the Rényi entropy for ensemble learning procedure, the main contribution of the proposed method is addressing HMM-based methods problem in separating models of distinct classes by considering the inverse emission matrix of the opposite class to build an opposite model. The proposed algorithms perform more effectively compared to other methods especially other HMM ensemble-based methods. Moreover, the proposed clustering framework, which derives benefits from both similarity-based and model-based methods, together with the Rényi-based ensemble method revealed its superiority in several measurements.
Abstract. Accurate and timely forecasts of sea ice conditions are crucial for safe shipping operations in the Canadian Arctic and other ice-infested waters. Given the recent observations on the declining trend of Arctic sea ice extent over the past decades due to global warming, machine learning (ML) approaches are deployed to provide accurate short-term to long-term forecasting. This study unlike previous ML approaches in the sea-ice forecasting domain provides a daily spatial map of the probability of ice in the study domain up to 90 days of lead time. The predictions are further used to predict freeze-up/breakup dates and show their capability to capture these events within a valid time period (7 days) at specific locations of interest to communities.
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