Comment on “Heat capacity, time constant, and sensitivity of Earth's climate system” by S. E. Schwartz

Abstract

[1] Schwartz [2007] recently evaluated the time constant of Earth’s climate system. However, his methodology yields to a significant underestimation of the value of t and obscures a much more interesting property of the system. Schwartz found t = 5 ± 1 years. Herein, by using an improved methodology I find that for short time scales from 0 to 2 years t is of the order of a several months and for larger time scales, at least up to 20 years, t is at least 70% larger than what Schwartz estimated. [2] Schwartz [2007] hypothesized (his equation (17)) that the climate system behaves as a first-order autoregressive process plus a linear trend. The implicit idea seems that the linear trend represents the effect of the external forcings on climate while the temperature signal, detrended of the above linear component, represents the internal variability of the same. This internal variability is assumed to be described by an AR(1) process whose autocorrelation function, r(Dt), decays as an exponential function of the lag time Dt with a given time constant t: r(Dt) = exp( Dt/t). [3] Although in physics using simple models is useful, the one suggested by Schwartz [2007], with a single time constant, is an oversimplification and, as I will prove below, it is inconsistent with the analysis. In fact, it is very well known that climate is the combination, coupling and superposition of several phenomena. Some phenomena respond quickly as the atmosphere, others as the deep ocean respond very slowly. Thus, each climate component responds with its own time constant that might range from a few months to several years or decades. [4] Given the length limitation of the temperature data herein analyzed (approximately 125 years) the analysis is limited to time scales below 20 years with a monthly resolution and I look for two time constants. The climate model I suggest is