Data Driven Prediction Without a Model

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Ensemble data assimilation techniques, including the Ensemble Transform Kalman Filter (ETKF), have been successfully used to improve prediction skill in numerical models for weather forecasting. However, less research has been conducted on data assimilation techniques for systems with no numerical model. In this study, we begin by applying the technique of bred vectors to a reconstructed phase space model for simple, autonomous nonlinear systems and compare the predictive capabilities of data driven bred vectors to those computed using a numerical model. Next, we show that a combination of the phase space reconstruction with ETKF yields a new technique, which we call Nearest Neighbor ETKF, for forecasting using only time series data. This technique is applied to a simple nonlinear system, the Lorenz three variable model, to demonstrate its effectiveness in forecasting noisy time series data. Finally, we use this technique to forecast field variations in the magnetosphere, which exhibit low dimensional behavior on the substorm time scale. The time series data of the magnetic field variations monitored by the network of ground-based magnetometers in the auroral region are used for forecasting at two stages. In the first stage, the auroral electrojet indices, computed from the magnetometer data, are used to reconstruct the dynamics and Nearest Neighbor ETKF yields forecasts of the index that are more skillful than persistence. In the second stage, the multivariate time series from several auroral region magnetometers is used to reconstruct the phase space of the magnetosphere-solar wind system using Multi-channel Singular Spectrum Analysis. The Nearest Neighbor ETKF is applied to ensemble forecasts made using model data, constructed from long time series of the data from each magnetometer, in addition to observations in the reconstructed phase space, constructed from magnetometer measurements concurrent with the start of the forecast. Additionally, the spreads of the ensembles constructed to forecast these times series are used as precursors to understand and predict extreme space weather events.