Extending the Square Root Method to Account for Additive Forecast Noise in Ensemble Methods

Patrick Nima Raanes Nansen Environmental and Remote Sensing Center, Bergen, Norway, and Mathematical Institute, University of Oxford, Oxford, United Kingdom

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Alberto Carrassi Nansen Environmental and Remote Sensing Center, Bergen, Norway

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Laurent Bertino Nansen Environmental and Remote Sensing Center, Bergen, Norway

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Abstract

A square root approach is considered for the problem of accounting for model noise in the forecast step of the ensemble Kalman filter (EnKF) and related algorithms. The primary aim is to replace the method of simulated, pseudo-random additive so as to eliminate the associated sampling errors. The core method is based on the analysis step of ensemble square root filters, and consists in the deterministic computation of a transform matrix. The theoretical advantages regarding dynamical consistency are surveyed, applying equally well to the square root method in the analysis step. A fundamental problem due to the limited size of the ensemble subspace is discussed, and novel solutions that complement the core method are suggested and studied. Benchmarks from twin experiments with simple, low-order dynamics indicate improved performance over standard approaches such as additive, simulated noise, and multiplicative inflation.

Corresponding author address: Patrick Nima Raanes, Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Rd., Oxford OX2 6GG, United Kingdom. E-mail: patrick.raanes@maths.ox.ac.uk

This article is included in the Sixth WMO Data Assimilation Symposium Special Collection.

Abstract

A square root approach is considered for the problem of accounting for model noise in the forecast step of the ensemble Kalman filter (EnKF) and related algorithms. The primary aim is to replace the method of simulated, pseudo-random additive so as to eliminate the associated sampling errors. The core method is based on the analysis step of ensemble square root filters, and consists in the deterministic computation of a transform matrix. The theoretical advantages regarding dynamical consistency are surveyed, applying equally well to the square root method in the analysis step. A fundamental problem due to the limited size of the ensemble subspace is discussed, and novel solutions that complement the core method are suggested and studied. Benchmarks from twin experiments with simple, low-order dynamics indicate improved performance over standard approaches such as additive, simulated noise, and multiplicative inflation.

Corresponding author address: Patrick Nima Raanes, Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Rd., Oxford OX2 6GG, United Kingdom. E-mail: patrick.raanes@maths.ox.ac.uk

This article is included in the Sixth WMO Data Assimilation Symposium Special Collection.

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