Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 17 4 2010 10.5194/npg-17-329-2010 http://www.nonlin-processes-geophys.net/17/329/2010/ http://www.nonlin-processes-geophys.net/17/329/2010/npg-17-329-2010.html http://www.nonlin-processes-geophys.net/17/329/2010/npg-17-329-2010.pdf 329 337 2010-07-22 Spatio-temporal error growth in the multi-scale Lorenz'96 model S. Herrera herreras@unican.es J. Fernández M. A. Rodríguez J. M. Gutiérrez University of Cantabria, Department of Applied Mathematics, 39005 Santander, Spain Instituto de Física de Cantabria, CSIC-UC, 39005 Santander, Spain The influence of multiple spatio-temporal scales on the error growth and predictability of atmospheric flows is analyzed throughout the paper. To this aim, we consider the two-scale Lorenz'96 model and study the interplay of the slow and fast variables on the error growth dynamics. It is shown that when the coupling between slow and fast variables is weak the slow variables dominate the evolution of fluctuations whereas in the case of strong coupling the fast variables impose a non-trivial complex error growth pattern on the slow variables with two different regimes, before and after saturation of fast variables. This complex behavior is analyzed using the recently introduced Mean-Variance Logarithmic (MVL) diagram. Baker, G. and Gollub, J.: Chaotic dynamics: an introduction, Cambridge University Press, UK, 1996. Fernández, J., Primo, C., Cofino, A S., Rodríguez, M A., and Gutiérrez, J M.: MVL Spatiotemporal analysis for model intercomparison in EPS. Application to the DEMETER multi-model ensemble, Clim. Dynam., 33, 233–243, 2008. Gutiérrez, J. M., Primo, C., Rodr\'iguez, M. A., and Fernández, J.: Spatiotemporal characterization of Ensemble Prediction Systems – the Mean-Variance of Logarithms (MVL) diagram, Nonlin. Processes Geophys., 15, 109–114, doi:10.5194/npg-15-109-2008, 2008. Just, W., Kantz, H., Rodenbeck, C., and Helm, M.: Stochastic modelling: replacing fast degrees of freedom by noise, J. Phys. A, 34, 3199–3213, 2001. López, J M., Primo, C., Rodríguez, M A., and Szendro, I.: Scaling properties of growing noninfinitesimal perturbations in space-time chaos, Phys. Rev. E, 70, 056224, doi:10.1103/PhysRevE.70.056224, 2004. Lorenz, E N.: Predictability-a problem partly solved, in: Proceedings of ECMWF seminar Predictability, ECMWF Seminar Proceedings, ECMWF, Reading, UK, Seminar on Predictability, Vol I, 1–19, 1996. Lorenz, E N. and Emanuel, K.: Optimal sites for supplementary weather observations: Simulation with a small model, J. Atmos. Sci., 55, 399–414, 1998. Orrell, D.: Model Error and Predictability over Different Timescales in the Lorenz96 systems, J. Atmos. Sci., 60, p 2219, 2003. Primo, C., Szendro, I., Rodríguez, M A., and Gutiérrez, J M.: Error growth analysis in systems with spatial chaos: Coupled map lattices and global weather models, Phys. Rev. Lett., 98, 108501, doi:10.1103/PhysRevLett.98.108501, 2007. Szendro, I., Rodríguez, M A., and López, J.: On the problem of data assimilation by means of synchronization, J. Geophys. Res., 114, D20109, doi:10.1029/2009JD012411, 2009. Wilks, D S.: Effects of stochastic parameterization in the Lorenz96 system, Q. J. Roy. Meteor. Soc., 131, 389–407, 2005.