The first and second authors acknowledge support by NASA Grant NAG 5-1660 managed by Dr. Ken Bergman, section head of Climate Modeling, NASA headquarters. Thanks are due to Dr. Zhijin Li from the Supercomputer Research Institute (SCRI) at The Florida State University for many fruitful discussions during the research. We also thank an anonymous reviewer and Dr. Y. C. Sud for their comments and suggestions, which helped us much to improve the manuscript. The data used in this work were obtained from the archived dataset in DAO/NASA. All the computations were carried out on NASA’s CRAY J90. This research was also supported by Supercomputer Computations Research Institute at The Florida State University, which is partially funded through Contract DE-FC0583ER250000.
Cacuci, D. G., 1981a: Sensitivity theory for nonlinear systems. Part I: Nonlinear functional analysis approach. J. Math. Phys.,22, 2794–2802.
——, 1981b: Sensitivity theory for nonlinear systems. Part II: Extensions to additional classes of responses. J. Math. Phys.,22, 2803–2812.
——, 1988: The forward and adjoint methods of sensitivity analysis. Uncertainty Analysis, Y. Ronen, Ed., CRC Press, 71–144.
Fillion, L., and R. Errico, 1997: Variational assimilation of precipitation data using moist convective parameterization schemes: A 1D-var study. Mon. Wea. Rev.,125, 2917–2942.
Hall, M. C. G., 1986: Application of adjoint sensitivity theory to an atmospheric general circulation model. J. Atmos. Sci.,43, 2644–2651.
——, D. G. Cacuci, and M. R. Schlesinger, 1982: Sensitivity analysis of a radiative-convective model by the adjoint method. J. Atmos. Sci.,39, 2038–2050.
Molod, A., H. M. Helfand, and L. L. Takacs, 1996: The climatology of parameterized physical processes in the GEOS-1 GCM and their impact on the GEOS-1 Data Assimilation System. J. Climate,9, 764–785.
Moorthi, S., and M. J. Suarez, 1992: Relaxed Arakawa–Schubert: A parameterization of moist convection for general circulation models. Mon. Wea. Rev.,120, 978–1002.
Rabier, F., P. Courtier, and O. Talagrand, 1992: An application of adjoint models to sensitivity analysis. Beitr. Phys. Atmos.,65, 177–192.
——, E. Klinker, P. Courtier, and A. Hollingsworth, 1996: Sensitivity of forecast errors to initial conditions. Quart. J. Roy. Meteor. Soc.,122, 121–150.
Redelsperger, J. L., and F. Guichard, 1996: Detailed analysis of cloud systems observed during TOGA-COARE: Simulations forced and unforced by the large scale motions. Proc. ECMWF Workshop, New Insights and Approaches to Convective Parametrization, Reading, United Kingdom, ECMWF, 58–76.
Rinne, J., and H. Järvinnen, 1993: Estimation of the Cressman term for a barotropic model through optimization with the use of the adjoint model. Mon. Wea. Rev.,121, 826–833.
Schubert, S. D., J. Pfaendtner, and R. B. Rood, 1993: An assimilated data set for Earth science applications. Bull. Amer. Meteor. Soc.,74, 2331–2342.
Sud, Y. C., and A. Molod, 1988: The roles of dry convection, cloud-radiation feedback processes and the influence of recent improvements in the parameterization of convection in the GLA GCM. Mon. Wea. Rev.,116, 2366–2387.
Takacs, L. L., A. Molod, and T. Wang, 1994: Documentation of the Goddard Earth Observing System (GEOS) general circulation model—Version 1. NASA Tech. Memo. 104606, Vol. 1, 64 pp.
Yang, W., and I. M. Navon, 1996: Documentation of the tangent linear model and its adjoint of the adiabatic version of the NASA GEOS-1 C-grid GCM—Version 5.2. NASA Tech. Memo. 104606, Vol. 8, 61 pp.
——, ——, and R. Todling, 1997: Documentation of the tangent linear and adjoint models of the Relaxed Arakawa–Schubert moisture parameterization packages of the NASA GEOS-1 GCM—Version 5.2. NASA Tech. Memo. 104606, Vol. 11, 40 pp.
Zou, X., A. Barcilon, I. M. Navon, J. Whitaker, and D. G. Cacuci, 1993: An adjoint sensitivity study of blocking in a two-layer isentropic model. Mon. Wea. Rev.,121, 2833–2857.