## van Hateren 2012: May the Schwartz be with you

Figure 6. Isomorphism between resistance-capacitance circuit and two-compartment energy balance climate model. Differential equations on right can be solved to give time dependence for arbitrary applied time-dependent forcing (current). Dashed boxes enclose corresponding one-compartment systems. The figure is modified from the Reply to Comments on my 2007 paper and an in-press paper (Spring, 2012) that interprets the observed increase in GMST over the latter part of the twentieth century in terms of the two-compartment model.

Stephen E. Schwartz Home Page

http://www.ecd.bnl.gov/steve/schwartz.html

I was intrigued by a paper linked from Skeptical Science, J. H. van Hatern’s *A fractal climate response function can simulate global average temperature trends of the modern era and the past millennium* (2012). The paper can be downloaded here or viewed online.

van Hateren has extended Schwartz’ analysis of a schematic 2-box, 1-tau (e-folding time constant) ebm climate model to use multiple forcings over multiple e-folding times. This particular electronic circuit analog was brought forth in Schwartz’ 2008 reply to comments on his 2007 paper, *Heat capacity, time constant, and sensitivity of Earth’s climate system*. There were three comments: one by Knutti et al, one by Scaffeti, and one co-authored by Foster, Annan, Schmidt, and Mann.

It should be noted that Schwartz references an earlier version of this (1-box/2007 or 2-box/2008 ?) model on his web page, that of Gregory 2000. I have not been able to obtain a copy to read, confirm, cite, and link. The hazards of residing behind a paywall.

Schwartz’ website also references a work by Held 2010 *Probing the Fast and Slow Components of Global Warming by Returning Abruptly to Preindustrial Forcing*, a 1-box model, 2-tau model, although the long time scale doesn’t seem to be defined. The short tau is < 5 years.

Whew! But we aren't done yet!

Tamino discussed his response to Schwartz 2007 at Real Climate: *Climate Insensitivity* (2007).

Lucia discussed it as well at The Blackboard: *Time Constant for Climate: Greater than Schwartz Suggests!* (2007). And again: *Schwartz & Scafetta Estimate Climate Time Scale*

The 2007 1-box, 1 time constant model came up again during a WUWT Eschenbach thread via a comment by Paul_K. (2011). Eschenbach followed up that suggestion with his own take Life is Like a Black Box of Chocolates. (2011). And both were commented on by Tamino *Fake Forcing* (2011).

In addition, this topic holds Isaac Held’s interest who has blogged several times on related topics. Such as …

*3. The simplicity of the forced climate response* (2011)

*4. Transient vs equilibrium climate responses* (2011)

A comment from Tamino’s Fake Forcing post …

What kind of physical theory — even rudimentary — might make just as good a fit? There are two major flaws with Schwarz’s model. One is that his method of diagnosing the time constant is flawed. Seriously flawed — even if his model were correct his method would give the wrong result. The other major flaw is that the real climate system has more than one “time constant.”

Tamino presented a 2-box, 2-time factor model (tau = 2 and 45 years). van Hateren enters the field with model fitted to 6 time periods, each set of six scaled uniquely to three different forcings: solar, ghg, and so2/volcanic/aerosols/others.

It’s worth noting that the parameter choices for Tamino’s 2 box model violated the 2nd law of thermodynamics.

I haven’t looked at what happens with other people’s parameter choices but one needs to be careful and check the internal dynamics to make sure that parameter choices don’t translate into the possibility of net heat transfer from a cold box to a hot box. As over simplified and unrealistic as a single box model is, it can’t suffer from

this particularproblem.