## Gordian Knot of Nonsense – Part 2. A simple hypothetical temperature model

September 5, 2011I will refer to “Climate related sea-level variations over the past two millennia” (Andrew C. Kemp, Benjamin P. Horton, Jeffrey P. Donnelly, Michael E. Mann, Martin Vermeer, and Stefan Rahmstorf, PNAS, 2011) as KMVR2011.

As I noted in the previous post, the KMVR2011 model is the progeny Vermeer and Rahmstorf’s 2009 PNAS model and Rahmstorf’s 2007 Science model.

Here is the KMVR2011 model

where

Where *H* is the sea level, *T(t)* is the global temperature,* T _{oo}*,

*a*,

_{1}*a*,

_{2}*b*and

*τ*are all constants and

*T*is a to-be-determined time varying function related to

_{o}(t)*T(t)*as defined by equation

*1a*.

Now, consider a temperature evolution of the following form, where *t’ *is a constant…

Note the following points about equation* II*…

- KMVR2001 stipulate that
*a*+_{1}*a*=_{2}*a*, where*a*is defined in VR2009. - VR2009 says
5.6 ± 0.5 mm/year/K*a =**> 0*. - Therefore
*a*+_{1}*a*> 0_{2} *b*is defined in VR2009, where they claim that*b = -49 ± 10 mm/K*.- Therefore,
*b < 0* - Therefore,
*-(a*_{1}+ a_{2})/b > 0 - Since
*-(a*, then the exponential in equation II increases with increasing_{1}+ a_{2})/b > 0*t*. - So, if
*C*is chosen to be positive, then*T(t)*is increasing with increasing*t*.

Does equation *II* present a realistic temperature evolution? Figure 1 shows some simple examples compared to the GISS global temperature. Figure 1 uses * a = a_{1} + a_{2} = *5.6 ± 0.5 mm/year/K and

*b = -49 ± 10 mm/K,*but it would look the same, qualitatively, for any choice of a and b used in the KMVR2011 Monte Carlo simulations used to populate their data for their “Bayesian updating.”

What happens to the sea level rise rate, *dH(t)/dt*, when equation *II* is inserted into equation *I*?

All the terms on the right side of equation* III* are constants except *T _{0}(t)*.

*d*is the rate at which the sea level rise is increasing or decreasing. So given a time evolution in the form of equation II…

^{2}H(t)/dt^{2}

We know that *a _{2}* is greater than or equal to zero. (If

*a*, then the KMVR2011 model becomes exactly the same at the VR2009 model.) What about

_{2}= 0*dT*? (i.e. How does the equilibrium temperature change with time?)

_{0}(t)/dtConsider equation* Ia*. Notice that *T _{0}(t)* is always trying to “catch up” with T(t). That is, if

*T(t) > T*, then

_{0}(t)*T*is increasing. Conversely, if

_{0}(t)*T(t) < T*then

_{0}(t),*T*is decreasing.

_{0}(t)Since we are told that the world is now at unprecedented high temperatures compared to the last millennium, then by implication *T(t) > T _{0}(t)* for the present day. This obvious point is confirmed for the last 100 years by KMVR2011 figures 4A & 4C. Consequently,

*dT*must be increasing with time for the present day and for the entire last century.

_{0}(t)/dt## Pulling it all together

Given the KMVR2011 model described by equations *1* and *1a*, and given a temperature evolution described by equation *II* (and as illustrated by the various model temperatures in figure 1, and “Model temperature 2” in particular), then *d ^{2}H(t)/dt^{2}* is negative. That is, the sea level rise rate is guaranteed to be decreasing. This is a rather bizarre result that is a consequence solely of the design of KMVR2011’s model. It is not some math trick or mistake. KVMR2011 should have been able to anticipate this problem, since it parallels very closely a similar problem with VR2009. And I know Mr. Rahmstorf was reading my blog.

KMVR2011 would likely argue that my equation *II* cannot represent a realistic temperature scenario, and that their model can only work for realistic temperature scenarios. Figure 1, model temperature 2, above refutes such a claim. We are left with the following situation: When a simple temperature scenario with a rapidly rising temperature that is similar to the last half of the 20th century is applied to KVMR2011’s model, it yields a decreasing sea level rise rate. This point alone should be enough to raise the eyebrows of KMVR2011’s readers.

But there is much more to come.

Posted in Uncategorized **|** Tagged climate, climate change, Climate related sea-level variations over the past two millennia, Global sea level linked to global temperature, global warming, michael mann, PNAS, Rahmstorf, sea ice, sea level rise rate, temperature, Vermeer **|**

The model does not even take into account a finite supply of water. Why take it seriously at all?

by Anonymous September 16, 2011 at 6:23 pmHuh?

by tommoriarty September 16, 2011 at 8:30 pm[…] Sanity « Gordian Knot of Nonsense – Part 2. A simple hypothetical temperature model Gordian Knot of Nonsense – Part 3 September 22, […]

by Gordian Knot of Nonsense – Part 3 « Climate Sanity September 22, 2011 at 10:27 pm