JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 98, NO. D3, PAGES 5025-5036, MARCH 20, 1993 New Parameterizations and Sensitivities for Simple Climate Models CHARLESE. GRAVES, 1 WAN-HO LEE, AND GERALD R. NORTH Climate System Research Program, College of Geosciences,Texas A&M University, College Station This paper presents a reexamination of the Earth radiation budget' parameterization of energy balance climate models in light of data collected over the last 12 years. The study consists of three parts: (1) an examination of the infrared terrestrial radiation to spaceand its relationship to the surface temperature field on time scales from 1 month to 10 years; 2) an examination of the albedo of the Earth with special attention to the seasonalcycle of snow and clouds; (3) solutions for the seasonal cycle using the new parameterizations with special attention to changes in sensitivity. While the infrared parameterization is not dramatically different from that used in the past, the albedo in the new data suggest that a stronger latitude dependence be employed. After retuning the diffusion coefficient the simulation results for the present climate generally show only a slight dependence on the new parameters. Also, the sensitivity parameter for the model is still about the same (1.25øC for a 1% increase of solar constant) for the linear models and for the nonlinear models that include a seasonal snow line albedo feedback (1.34øC). One interesting feature is that a clear-sky planet with a snow line albedo feedback has a significantly higher sensitivity (2.57øC) due to the absence of smoothing normally occurring in the presence of average cloud cover. 1. INTRODUCTION Energy balance climate models (EBMs) have been used extensively in the last two decadesfor conceptual studies of the large-scale climate [e.g., Budyko, 1968, 1969; Sellers, 1969; North et al., 1981, 1983; Hyde et al., 1989, 1990; Kim and North, 1991]. The models rely on simple formulas relating various energy fluxes to the surface temperature. Typically, the model surface temperature field T is the solution of c(e) OT ot V . D(x)VT + A + BT: QS(x, t)a[x, T(•, t)] (1) where • is a unit vector from the center of the Earth pointing to the point on the Earth being considered; t is the time; x is the sine of latitude; C(•) is the space-dependent heat capac- ity per unit area, which takes on different constant values dependent on whether the local surface is land, sea or sea ice;D(x) is a horizontal thermal diffusion coefficient, depen- dent quadratically onx2; A and B areempirical parameters relating the outgoing infrared flux to the surface temperature to be determined from data (these are part of the subject of this study); Q is the solar constant divided by 4; S(x, t) is the normalized seasonaldistribution of heat flux entering the top of the atmosphere; and a[x, T(•, t)] is the coalbedo, which may be dependent on the local temperature as well as position (also a subject of the present study). In solving the equation we require the boundary condition that the hori- zontal heat flux into the poles vanish. When the temperature dependenceof the coalbedo is held fixed, the model is linear and it is convenient to use the discrete Fourier representation since the harmonics are uncoupled. The nonlinearity stemmingfrom the temperature •Currently atDepartment of Earth and Atmospheric Sciences, St. Louis University, St. Louis, Missouri. Copyright 1993 by the American Geophysical Union. Paper number 92JD02666. 0148-0227/93/92JD-02666505.00 dependence of the albedo is sufficiently mild that even when it is included the harmonic representation is often a useful approximation. Most of the studies have concentrated on applications that exploit the ability of the linear version of the model to reproduce the ensemble average seasonal cycle in the present and altered climates [Hyde et al., 1990; Crowley and North, 1988; Short et al., 1991; Baum and Crowley, 1991]. In addition, some studies have introduced noise forcing to simulate fluctuations at frequencies away from the forced seasonal cycle and its harmonics [North and Cahalan, 1982; Leung and North, 1990; Leung and North, 1991; Kim and North, 1991]. All of these studies have relied on parameterizations derived from satellite data taken from the 1970s [cf. North and Coakley, 1979]. Nonlinearity enters the model as the snowcover (and possibly cloud) movements alter the albedo leading to a feedback which can increase climate sensitivity and even induce bifurcations with occasionally bizarre effects [e.g., Lin and North, 1990]. There are especially interesting effects near the poles that are associated with the small ice cap instability [North, 1984]. These are of special interest be- cause they might be relevant to some paleoclimatic transi- tions [e.g., Crowley and North, 1990; Suarez and Held, 1979; Watts and Hayder, 1984; Lin and North, 1990; Huang and Bowman, 1991]. An interesting feature of EBMs is that under present conditions they produce an isolated subfreezing Greenland in summer even in the absence of snow-albedo feedback. Was the glaciation of Greenland sudden? Are there sudden transitions across the Arctic Ocean that could remove the perennial ice cover there? Are there any sudden transitions that could be related to the large-scale Laurentide Continen- tal glaciations that have repeated themselves many times in phase with orbital element changes on astronomical time scales? The northern hemisphere problem is much more problematic than that in the southern. It is likely that ice-albedo feedback is not the whole story as suggested by Huang and Bowman [1991]. Deblonde and Peltier [1990] have coupled the linear EBM to a dynamical ice sheet model and while their ice sheets are very realistic, they point out 5025