Not Spaghetti

"Eq. 3 1/τ+ ≈ (αsCs + αoCo)/(Cs + Co)

Eq. 4 1/τ- ≈ β(1/Cs + 1/Co)

so τ- becomes very short, and the model reduces essentially to a one-box model with time-constant τ+ and response as noted above."

I think this is true because with large Beta, the ocean will quickly heat or cool the atmosphere but Lucia mentioned overlapping boxes in which case the effective beta is reduced and the effective heat capacity of the top box is increased. This can effectively narrow the temperature difference while still allowing for a top box time constant that isn't too quick.

For more information on overlapping boxes, see my post at the climate audit message boards:

Overlapping Boxes
http://www.climateaudit.org/phpBB3/viewtopic.php?f=4&t=774

With regards to beta, I think the inequalities are important. If any tuning is done maybe treat it as a constrained optimization problem (like linear programming) where the parameters are only tuned within the limits of their uncertainty. I think there would be more uncertainty in the forgings then the heat transfer coefficients, therefore I think more tuning could be done with regards to the forgings then the heat transfer coeficients.