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Bred vectors and forecast errors in the NASA coupled general ...

Bred vectors and forecast errors in the NASA coupled general ...

including the deepening thermocline in the eastern Pacific and the consistent positive zonal wind stress anomaly that prevailed in the central basin. For the next phase of our studies, we will extend the coupled bred vectors with two-sided breeding in the ensemble members for a much longer hindcast experiment period so that we can explore their impact on different starting months. Additionally, based on our results of error structure in subsurface temperature, we will explore the possibility of including the time-varying error structures derived from the BV in the background error covariance within a data assimilation scheme like OI. Appendix In this section, we briefly describe the procedures that we use to obtain the fitting parameters of a Gaussian function (Equation (1)), i.e. the fitted error variance and the correlation length. f 2 r r) = C0 exp[ − ] (1) L ( 2 The Levenberg-Marquardt algorithm is first applied to estimate these parameters and the standard deviation of the fitting points are required for nonlinear fitting. In our results, the standard deviations from both the one-month forecast error and bred vector have larger values at short ranges and smaller values near the tail. Therefore, this scheme will try to overfit the tail. In order to avoid overemphasizing the small covariances at large separations (which is dominated by sampling errors), we use the e-folding value of the 32

average of the first two fitting points to determine how many data points will be used for fitting and a corresponding length, L e , is chosen. Once (C 0 , L) are determined, we repeat the procedure by increasing the number of points used for the fitting and calculate the rms error within L e . The (C 0 , L), which has the smallest rms error, is assigned to our final result. If the e-folding range cannot be found at the last point of the data, it suggests a very large-scale linear behavior of the error covariance. We then switch to a simple linear regression form (Equation (2)) to avoid failure in fitting the nonlinear scheme: 2 r ln( f ( r)) = ln C0 − . (2) 2 L Acknowledgements We are very grateful for much technical support from NASA global modeling assimilation office support staff, especially to Sonya Miller. We also greatly appreciate many valuable discussions with Joaquim Ballabrera. The GMAO component of this work has been supported by grants from NASA Seasonal-to-Interannual Prediction Project (NASA-NAG-55825 and NASA-NAG-12418). References Alves O., M. Balmaseda, D. Anderson, and T. Stockdale, 2002: Sensitivity of dynamical seasonal forecasts to ocean initial conditions. Quart. J. Roy. Met. Soc., 103, 647-667. Cai M., E. Kalnay, and Z. Toth, 2003: Bred vectors of the Zebiak-Cane model and their 33

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