As the author of a good chunk of the GISS code, you know that what this code fragment does is take the sum of the potential and kinetic energy of the atmosphere all over the planet at the end of each time step, and compare it to the total at the start of the time step. If they are different, the amount of the difference (“ediff” in the code) is spread evenly around the whole world as thermal energy. If ediff is negative, thermal energy worldwide is removed from each gridcell. While this is reasonable if it is only a rounding error, my questions are:

1. As near as I can tell, there is no alarm (as exists many places in the code) to stop the model if the value of ediff gets too large. Is this the case?

2. What is the mean, standard deviation, range, total energy transferred, and net energy transferred for ediff in a typical run?

3. What is the usual location of the source of the energy imbalance, geographically, elevationally?

4. What is the usual reason for the energy imbalance?

5. The conversion factors used in this code to go from energy to temperature, such as SHA (specific heat of air), kapa (ideal gas law exponent) and mb2kg (millibars to kilograms), are for dry air. However, most of the world’s air isn’t dry. How much does this bias the wet/dry areas of the planet? What is the total error of this simplification?

6. The atmosphere exchanges kinetic energy with both the ocean and the lithosphere on a variety of time scales, at a scale relevant to climate. Is this exchange taken into account in the model, or is all of the energy transferred in this manner in the real world merely converted into heat (or just ignored) in the model? (See http://www.fao.org/docrep/005/Y2787E/y2787e03b.htm#FiguraB for the effect of this energy exchange on climate.)

All the best of the New Year to you,

w,

I will paraphrase his answers, because this was on a mailing list, so I won’t quote directly. His main points were:

‘€¢ ediff is always small

‘€¢ it occurs because the temperature equation doesn’t have an implicit term for thermal dissipation (kinetic energy to heat in turbulent fluid)

‘€¢ it is monitored

‘€¢ it is a small percentage of total heat fluxes, usually around 2 W/m2, and doesn’t vary much

‘€¢ the source is probably associated with high mass (near surface) high velocity wind, but it’s hard to say because it’s small

‘€¢ any decrease in KE goes to heat, only a small amount, but it has to be accounted for

‘€¢ the difference in the wet/dry difference in the conversions didn’t amount to much

‘€¢ heat dissipated by surface friction with the lithosphere (about 1.7 W/m2) is much larger than momentum transferred to the lithosphere by the atmosphere.

‘€¢ the Length of Day (LOD) changes are small momentum exchanges, and don’t have a noticeable effect on climate.

I believe I have expressed his statements clearly, and any faults are mine, not his.

I wrote back thanking him for his answers and asking a few more questions, but he hasn’t answered, he might not have seen it. I asked why 2 W/m2 was “small” yet 3.7 W/m2 was the size of CO2 doubling of interest … seems like considering 2 W/m2 as small and not worth investigating, when looking for a 3.7 W/m^2 signal, does not bode well. It also highlights the small size of the signal of interest.

I also asked if there was any kind of real world evidence that the thermal turbulent loss was only 2 W/m2. This number seems very small to me, considering the amount of turbulence in the atmosphere and the ocean. Natural flows of any kind tend to speed up until further increase in speed is balanced by turbulent loss.

This type of turbulent speed limitation can be measured in, for example, a iron pipe connected to an elevated reservoir. Turbulence inside the pipe slows the outflow, such that the final speed is turbulence limited. This type of turbulence limitation is common in nature.

Another example is a jet of smoke. It is almost completely dissipated before it crosses the room. Once again, the distance the jet travels is limited by turbulence. How much of the kinetic energy of the jet has turned into heat? Seems like it would be larger than a few percent.

Finally I asked about his statement that LOD and climate weren’t related, given the large amount of scientific research showing correlations between the LOD and climate. A Google Scholar search on LOD and climate reveals over 2,000 references, such as

Angular momentum exchange among the solid Earth, atmosphere, and oceans: A case study of the 1982’€”1983 El Nià±o event, Dickey et al.

Trend in Atmospheric Angular Momentum in a Transient Climate Change Simulation with Greenhouse Gas and Aerosol Forcing, Huang et al.

I’m hoping he’ll answer. In the meantime, that’s as much as I know about the ediff.

w.

]]>P=A P A’+ B Q B’

Where denotes the transpose

P is the covariance of the states

Q is the covariance of the input

A is the state transition matrix

B is the state input matrix

The entire distribution can be propagated as well via ito calculus.

http://en.wikipedia.org/wiki/It%C5%8D_calculus

I’m still not sure why this “discovery” in the code deserved its own thread. I hope the audit of the code is not searching for suspicious comments.

]]>Are you sure you weren’t making brownies?

]]>Years ago I used a similarly named “fudge factor” in the process to make rice krispies.

In my case it was e (empirically) d (determined) a (arbitrary) f (fudge) f (factor).

It thus follows that ediff must equal (experimentally determined intermediate fudge factor) or some such.

It was a small chuckle. ]]>

The fluids of interest in AOLGCM models are viscous, heat-conducting fluids. The IPCC and many others in the climate-change-modeling community, always, without exception, advertise that the AOLGCM models are based on conservation of mass, momentum, and energy. That being the case, the momentum equations must contain accounting of diffusion of momentum. An equation for conservation of the sum of thermal, kinetic, and potential energy must contain accounting of the diffusion of energy and the rate of work done on the fluid by pressure and viscous forces. An equation for conservation of thermal energy must contain accounting of the diffusion of energy and irreversible viscous dissipation.

Models of fluid flows based on conservation of mass, momentum and energy and in which accounting of diffusion of momentum and energy are present are not hyperbolic. Models of fluid flows that do not account for diffusion of momentum and energy do not conserve momentum and energy. Thermal energy equations that do not account for viscous dissipation do not conserve energy.

Additionally, auxiliary differential-equation-based models that are functions of the dependent variables of the problem will also affect the classification into hyperbolic, parabolic, and elliptic. Auxiliary differential equation models can also affect the well- or ill-posedness of the overall equation system.

One reason that hyperbolicity seems to arise in these discussions is that hyperbolicity is required in order to ensure shadowing. At least that is my understanding. Shadowing seems to be invoked as a means to avoid all the adverse properties and characteristics of equation systems that exhibit chaotic responses. So far as I have been able to determine, the complete model equation systems used in AOLGCMs have not yet been classified into the usual hyperbolic, parabolic, and elliptic classes. Additionally, I have also been unable to find documentation in which the complete model equation systems, at the continuous-equation level, have been shown to have the potential to exhibit chaotic responses. All nonlinear physical phenomena and processes do not exhibit chaotic response. Nonlinearity is not a necessary and sufficient condition for chaos. Necessary, but not sufficient.

The properties of numerical solution methods used to obtain approximate solutions for the continuous equations also have profound effects on the overall problem. The numbers generated by the codes are what count. Consistency, stability, and convergence of the discrete equations must always be considered in detail in order to ensure the numbers represent accurate approximations to the continuous equations.

In many cases the properties and characteristics of the discrete equations can easily destroy those of the continuous equations. The discrete approximations to the continuous equations must preserve all the important properties and characteristics of the continuous equations. Especially, if the continuous equations have been rigorously shown to exhibit chaotic response, the discrete approximations must accurately preserve the properties and characteristics of those equations.

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