## 1. Introduction

[2] Earth radiation budget observations are important because the climate machine is a heat engine, for which absorbed solar radiation (ASR) is the heat source and outgoing longwave radiation (OLR) is the heat sink. One application of Earth radiation budget measurements is comparison with model results. Numerical models incorporate our understanding of the processes that determine our weather and climate. Comparison of model results with measurements validates the processes of the model and may identify limits of the descriptions. The model must describe the transport of energy and moisture correctly in order to compute the correct distribution of OLR. Also, the model must accurately describe the clouds to determine the correct distribution of both ASR and OLR. The processes take place on a wide range of time and space scales, so it is necessary to make comparisons of model results at a variety of time scales, including the seasonal cycles, comprised of the annual and semiannual cycles, etc. Validations of both the diurnal cycles and seasonal cycles of a model are needed, as the processes of importance to these cycles differ considerably. Diurnal processes are local and mostly take place in the lower layer of the atmosphere and at the surface except for deep convection. After several days the effect of a change at any point is transmitted over the Earth, so that seasonal processes are globally connected.

[3] Many studies have been made to compare Earth radiation budget measurements with model results. *Bony et al.* [1992] used harmonic analysis to compare the seasonal cycles of cloud radiative forcing in the Laboratoire de Météorologie Dynamique circulation model with Earth Radiation Budget Experiment (ERBE) results. They also examined variations of zonal means of radiation fluxes in the time domain. *Kiehl et al.* [1998] compared the Earth's radiation budget as simulated by the NCAR Community Climate Model 3 with ERBE data in the time domain for selected regions. *Yang et al.* [1999] presented time variations of zonal means of TOA radiation to compare ERBE and NCEP/NCAR model monthly mean results. Many other comparisons have been performed between models and ERBE data for cloud radiative forcing. *Harrison et al.* [1990] and *Cullather et al.* [1997] used four months for the seasonal description of cloud radiative forcing. Others used summer and winter months for the comparison [*Barker et al.*, 1994; *Chen and Roeckner*, 1996; *Lin and Zhang*, 2004; *Cess et al.*, 1997]. *Potter and Cess* [2004] compared cloud radiative forcing results of ERBE with 19 models for regions during DJF. *Taylor et al.* [2011] used CERES data to show variations of zonal means through the seasonal cycle and to compare with the NCAR Community Climate System Model version 3 results in a study of radiation feedbacks.

[4] This paper presents a method for quantitatively comparing the seasonal cycles of two global data sets in the time domain by use of principal component analysis. To demonstrate the technique, a data set based on satellite observations from the CERES (Clouds and the Earth's Radiant Energy System) instruments [*Barkstrom*, 1990; *Wielicki et al.*, 1996; *Smith et al.*, 2011] is compared with model results from the Goddard Earth Observing System (GEOS) Atmospheric General Circulation Model Version 5 (GEOS-5). Monthly mean maps of ASR and OLR from the model and from CERES for the period March 2000 through August 2007 are used. These two data sets (based on satellite observations and model results) include parameters ASR and OLR that vary in time and space. The purpose of the model is to simulate numerically the dynamic processes that govern the ASR and OLR, so that the time response is a fundamental aspect of the model results and of the CERES observations. The quantitative comparison of the two data sets must contrast the time response observed with that computed by the model. The most efficient description of the time variation is obtained by use of principal component analysis (PCA). For a general discussion of PCA, please see *Wilks* [1995].

[5] *Mlynczak et al.* [2011] examined the seasonal cycles of Earth radiation measured by CERES with PCA and found that the annual cycle of ASR accounts for more than 95% of the overall variance of the seasonal cycles, which include the annual cycle, the semi-annual cycle, out-of-phase annual cycle, and higher-frequency terms. The use of principal components permits the reduction of the twelve monthly mean maps to a single map and is a major simplification for attempting to understand the time and space variability of the radiation fields. The method presented here can be applied to several data sets in order to compare them quantitatively and objectively and has application to the Coupled Model Intercomparison Project [*Potter et al.*, 2011].

[6] In this paper, the two data sets are described then the comparison method is applied to them. The method begins with the comparison of the annual mean maps of ASR and OLR. Next the annual mean is subtracted from the monthly mean maps to give the seasonal cycles of ASR and OLR. The time variations of these cycles are described in terms of principal components (PCs), and the spatial distributions are described by the corresponding empirical orthogonal components (EOFs). Measures are defined for the differences between the annual cycles of the two data sets. Inner products of the PCs and EOFs provide measures of the agreement or disagreement of the two data sets.