The authors acknowledge support by the West Australian Department of Environment and Conservation under the Indian Ocean Climate Initiative Stage 3 and the Australian Climate Change Science Program of the Australian Department of Climate Change and Energy Efficiency.
Abramov, R. V., , and A. J. Majda, 2008: New approximations and tests of linear fluctuation-response for chaotic nonlinear forced-dissipative dynamical systems. J. Nonlinear Sci., 18, 303–341.
Abramov, R. V., , and A. J. Majda, 2012: Low-frequency climate response of quasigeostrophic wind-driven ocean circulation. J. Phys. Oceanogr., 42, 243–260.
Carnevale, G. F., , and J. S. Frederiksen, 1983: Viscosity renormalization based on direct-interaction closure. J. Fluid Mech., 131, 289–303.
Carnevale, G. F., , M. Falcioni, , S. Isola, , R. Purini, , and A. Vulpiani, 1991: Fluctuation-response relations in systems with chaotic behavior. Phys. Fluids, 3A, 2247–2254.
Frederiksen, J. S., 1981: Growth and vacillation cycles of disturbances in Southern Hemisphere flows. J. Atmos. Sci., 38, 1360–1375.
Frederiksen, J. S., 1998: Precursors to blocking anomalies: The tangent linear and inverse problems. J. Atmos. Sci., 55, 2419–2436.
Frederiksen, J. S., 1999: Subgrid-scale parameterizations of eddy-topographic force, eddy viscosity, and stochastic backscatter for flow over topography. J. Atmos. Sci., 56, 1481–1494.
Frederiksen, J. S., 2012a: Statistical dynamical closures and subgrid modeling for inhomogeneous QG and 3D turbulence. Entropy, 14, 32–57.
Frederiksen, J. S., , and C. S. Frederiksen, 1993: Monsoon disturbances, intraseasonal oscillations, teleconnection patterns, blocking, and storm tracks of the global atmosphere during January 1979: Linear theory. J. Atmos. Sci., 50, 1349–1372.
Frederiksen, J. S., , and A. G. Davies, 2000: The regularized DIA closure for two-dimensional turbulence. Geophys. Astrophys. Fluid Dyn., 92, 197–231.
Frederiksen, J. S., , and T. J. O'Kane, 2005: Inhomogeneous closure and statistical mechanics for Rossby wave turbulence over topography. J. Fluid Mech., 539, 137–165.
Frederiksen, J. S., , A. G. Davies, , and R. C. Bell, 1994: Closure theories with non-Gaussian restarts for truncated two-dimensional turbulence. Phys. Fluids, 6, 3153, doi:10.1063/1.868139.
Frederiksen, J. S., , T. J. O'Kane, , and M. J. Zidikheri, 2012: Stochastic subgrid parameterizations for atmospheric and oceanic flows. Phys. Scr.,85, 068202, doi:10.1088/0031-8949/85/06/068202.
Gritsun, A. S., 2001: Fluctuation-dissipation theorem on attractors of atmospheric models. J. Numer. Anal. Math. Modell., 16, 115–133.
Gritsun, A. S., 2010: Construction of response operators to small external forcings for atmospheric general circulation models with time periodic right-hand sides. Izv., Atmos. Oceanic Phys., 46, 748–756.
Gritsun, A. S., , and G. Branstator, 2007: Climate response using a three-dimensional operator based on the fluctuation–dissipation theorem. J. Atmos. Sci., 64, 2558–2575.
Gritsun, A. S., , G. Branstator, , and A. J. Majda, 2008: Climate response of linear and quadratic functionals using the fluctuation–dissipation theorem. J. Atmos. Sci., 65, 2824–2841.
Hasselmann, K., 1997: Multi-pattern fingerprint method for detection and attribution of climate change. Climate Dyn., 13, 601–611.
Hegerl, G. C., , H. von Storch, , K. Hasselmann, , B. D. Santer, , U. Cubasch, , and P. D. Jones, 1996: Detecting greenhouse-gas-induced climate change with an optimal fingerprint method. J. Climate, 9, 2281–2306.
Jin, F. F., , L. L. Pan, , and M. Watanabe, 2006a: Dynamics of synoptic eddy and low-frequency flow interaction. Part I: A linear closure. J. Atmos. Sci., 63, 1677–1694.
Jin, F. F., , L. L. Pan, , and M. Watanabe, 2006b: Dynamics of synoptic eddy and low-frequency flow interaction. Part II: A theory for low-frequency modes. J. Atmos. Sci., 63, 1695–1708.
Kiyani, K., , and W. D. McComb, 2004: Time-ordered fluctuation-dissipation relation for incompressible isotropic turbulence. Phys. Rev.,70E, 066303, doi:10.1103/PhysRevE.70.066303.
Majda, A. J., , and X. Wang, 2010: Linear response theory for statistical ensembles in complex systems with time-periodic forcing. Comm. Math. Sci., 8, 145–172.
McComb, W. D., 1990: The Physics of Fluid Turbulence. Oxford University Press, 594 pp.
McComb, W. D., , and V. Shanmugasundaram, 1984: Numerical calculation of decaying isotropic turbulence using the LET theory. J. Fluid Mech., 143, 95–123.
O'Kane, T. J., , and J. S. Frederiksen, 2004: The QDIA and regularized QDIA closures for inhomogeneous turbulence over topography. J. Fluid Mech., 504, 133–165.
Zidikheri, M. J., , and J. S. Frederiksen, 2009: Stochastic subgrid parameterizations for simulations of atmospheric baroclinic flows. J. Atmos. Sci., 66, 2844–2858.