On the application of data assimilation in the Singapore Regional Model

Abstract

One primary objective of this study is to develop and implement applicable data assimilation methods to improve the forecasting accuracy of the Singapore Regional Model. A novel hybrid data assimilation scheme is proposed, which assimilates the observed data into the numerical model in two steps: (i) predicting the model errors at the measurement stations, and (ii) distributing the predicted errors to the non-measurement stations. Specifically, three approaches are studied, the local model approach (LM), the multilayer perceptron (MLP), and the Kalman filter (KF). At the stations where observations are available, both the local model approach and the multilayer perceptron are utilized to forecast the model errors based on the patterns revealed in the phase spaces reconstructed by the past recordings. In cases of smaller prediction horizons, such as T=2, 24 hours, the local model approach outperforms the multilayer perceptron. However, due to the less competency of the local model approach in capturing the trajectories of the state vectors in the higher-dimensional phase spaces, the prediction accuracy of the local model approach decreases by a wider margin when T progresses to 48, 96 hours. Averaged over 5 different prediction horizons, both methods are able to remove more than 60% of the root mean square errors (RMSE) in the model error time series, while the multilayer perceptron performs slightly better. To extend the updating ability to the remainder of the model domain, Kalman filter and the multilayer perceptron are used to spatially distribute the predicted model errors to the non-measurement stations. When the outputs of the Singapore Regional Model at the non-measurement stations and the measurement stations are highly correlated, such as at Bukom and Raffles, both approaches exhibit remarkable potentials of distributing the predicted errors to the non-measurement stations, resulting in an error reduction of more than 50% on average. However, the performance of Kalman filter in error distribution deteriorates at a rapid pace when the correlation decreases, with only about 40% of the root mean square errors removed at Sembawang and 20% at Horsburgh. Comparatively, the multilayer perceptron is less sensitive to the correlations with a more consistent performance, which removes more than 40% of the root mean square errors at Sembawang and Horsburgh. Another major objective of this study is to analyze and predict the sea level anomalies by means of data assimilation. Sea level anomalies are extracted based on tidal analysis from both altimeter data and in-situ measurements. A reasonable fit between the altimeter sea level anomalies and the in-situ sea level anomalies can be observed, indicating the coherence and consistency of different data sources. As a demonstration of the proposed data assimilation scheme, the sea level anomalies explored in this study are the spatially and temporally interpolated DUACS sea level anomalies. At the open boundaries of the Singapore Regional Model, the sea level anomaly time series are predicted using multilayer perceptron with prediction horizon T=24 hours. Multilayer perceptron successfully captures the motion dynamics of the sea level anomalies, with more than 90% of the root mean squares (RMS, quadratic mean) removed on average. The sea level anomalies inside the model domain are then numerically modelled by imposing the sea level anomalies predicted at the open boundaries as driving force to the Singapore Regional Model. A reasonable correspondence are observed between the modelled sea level anomalies and the DUACS sea level anomalies, verifying that the internal sea level anomalies can be decently modelled through numerical simulation provided that the sea level anomalies are properly prescribed at the open boundaries.