GEOPHYSICAL RESEARCH LETTERS, ¾OL22t, NO.•2, PAGES l•09-111, JANUARY 15, 1994 Estimating thermal forcings of greenhouse gasesfrom ancient climates: The problem of statistical confounding Craig Loehle Environmental Research Division, Argonne National Laboratory, Argonne, Illinois Abstract. Data from ice cores show that CO2 and air temperature are highly correlated over the last 157,000 yr. Although this correlation can be takenas evidence that CO2 amplifies orbital forcingof temperature and is thusa strong greenhouse gas, thispaper argues thatestimating the strength of the CO2 warming effectfrom statistical evaluations of past climatesbasedon CO2 and orbital forcing is hampered by strong multiple correlations between CH4, CO2, ocean currents, ice volume (and therefore albedo), dust, and nonseasalt sulfate. To estimate the strength of the greenhouse warming effect of CO2 from historical data, these correlations andmultiple forcings should be taken intoaccount. Introduction General circulation models (GCMs) arebeingused to assess potential climate change resulting from greenhouse gas emissions. Computing the net thermal effect of a given radiative forcing is not in general simple, however, because theeffectis distributed across the globe andover thedepth of the atmosphere. Thereare also many feedbacks in theoverall system. The resulting uncertainties can be extreme, as for example for cloud and water vapor effects. This makes it unclear whichparameters should be adjusted to achieve more realistic climatesimulations. One approach to resolving these uncertainties has been the use of historical data. Past periods (say thousands or millions of yearsago) with very different climates may havesufficiently different forcing andfeedback magnitudes that the importanceof these factors can be estimated. This approach has been taken by a number of authors [Genthon et al., 1987; Hoffert and Covey, 1992; Lorius et al., 1990; Maasch and Saltzman, 1990; Pisias and Shackleton,1984] using regression, radiative balance, and GCM approaches. Given the known coupling of earth processes, we have reason to believe that the various greenhousegases and aerosols could well be coupled to each other and to factors suchas ice extent [see e.g. Loehle, 1993] in sometype of complex feedback system. If so, then levels of these various factors at different times could represent points along a single dynamic system trajectory. In such a system all the components are mutuallygoverning and in a very real sense arenotindependent factors with respect to climate. To evaluate thepossibility thatgreenhouse forcing variables have not historicallyvaried independently of each other,we analyzedice core data for the last 157,000 yr. Data were compiled for CO2 andCH4, whichare greenhouse gases, and Copyright 1994 by •he American Geophysical Union. Paper number93GL03375 0094-8534/94/93GL-03375503. O0 for sulfate, which is hypothesized to havea net cooling effect. Becausethe three variables were measured independently, their sampling dates from ice core datado not align. Dates were picked from data of Chappellaz et al. [ 1990], Legrand et al. [1988], and Barnolaet al. [1987] to spread across the 157,000-yr recordso that high, medium,and low valuesfor sulfate and CO2 werecovered aswell astheentire time period. Dates used were 147, 141.5, 140, 128, 119.5, 115, 106, 73, 66.3, 58, 30, 13, and 7 thousand years before the present (BP). Values were linearly interpolated wherethey were not available for a givendate. Note that to properlyassess these effects we cannot merely calculate a regression of say CO2vs.CI-i4 for all of the data and look at the R2 value as a measure. This is because if extremely highor low values occur rarely, thentheregression statistics will be dominated by data from the average conditions, and the R 2 value will be reduced, a problem that doesnot arise for controlled experiments. Thus, data were taken uniformly over the time interval and over the rangeof values. The results (Figure 1) show very strong correlations between the three forcing variables.If the two highvalues for sulfate resultedfrom short-term volcanic activity and are therefore anomalous,then the relations of sulfate with CO2 and CH4 are almost perfect negative linearcorrelations. The CO2-CH4correlation is also very strong. We seefrom Figure 1 that the two warmingfactors(CO2 and CH4) rise and fall roughlytogether and inversely to the cooling factor(sulfate). Dust, whichmay actto cooltheearth, also correlates positively with sulfate andnegatively with CO2 and CH4. Thus, this problem is subject to statistical confounding or colinearity. When one or more independent variables are linear combinations of others, separating their effects statistically is very difficult. Consider the following model based on the above analysis. We have CH4 = al + ]Jl CO2 (1) sulfate = (x 2 - [I 2 CO 2 (2) from our analysis. Let us try to predictthe deviations from temperatures that would be expected from solar insolation aloneby including historical datafor CO2, CH4, and sulfate, as follows: T a= Tp + •1 CO2 + •2 CH4 - •3 sulfate. (3) Here Ta is theactual temperature, and Tp is thetemperature predicted on thebasis of orbital forcing. However, because of the strong correlations (1-2), thismodel is equivalent to T a = Tp + õ1 CO2 + õ2 (ø•1 + fil CO2) - õ3 (a2 - •2 CO2 ). (4) 109