# Earth Cubed

## The Concept

Should a climate model attempt to predict the weather or is weather far too complex a process to include in a climate model. If we neglect the weather will we miss important cycles such as El Niño and La Niña? There is a temptation in modeling to try to include as many factors as possible to hopefully simulate reality.

However, increasing the complexity of the model increases the potential for error and ads degrees of freedom which are often tuned to fit data rather then taken from fundamental measurement of physics. It is my hope that this blog and the corresponding project

https://sourceforge.net/projects/earthcubed/ (not approved yet):

will succeed by attempting the avoid the complexities inherent in small time step transient models. Instead of focusing on short term transients (i.e. weather) the focus will be more on the global energy balance. This is not to say the model will be simple. The earth will be represented with three special dimensions and two temporal dimensions.

The first temporal dimensions will be the time of day, the seconded temporal dimension will be the day. The first temporal dimension is used to express the steady state solutions.  The second temporal dimension will only be used if dynamic simulations are to be preformed.

The special coordinate system will be built based upon a cube. That is the earths surface will initially be divided up into six curved faces and each division will intersect at right angles.

Further refinement will be done by subdividing each face into grids both vertically and horizontally. The vertical grid will be scaled based on the air density and the horizontal grid will be chosen to make the three dimensional partitions roughly cubical.

With this method the space of the atmosphere will be recursively divided up into a uniformly spaced coordinate grid which will locally behave like a Cartesian coordinate system but globally it will be curved around a cube.

March 1, 2009 - Posted by | Computer Science and Modeling

1. Hey S, what kind of resolution does this subdivision yield? A JPL and MIT collaboration is using a cubic model of the earth for modeling-ocean atmosphere interactions on climate.

Their model is higher resolution and improves model accuracy, though they benefit from supercomputers at NASA. The model has three states, the atmosphere, the physical ocean, and the biological ocean.

What is it you hope your model can address? Specifically, which complexities would it avoid, and how would it improve model results?

Comment by Paul Tonita | August 8, 2009 | Reply

• Interesting. I should look at their work. I wasn’t aware if anyone else was using the same coordinate system. I want the resolution to scale based upon the number of computers running the same model. Therefore, if there is only one computer running the model the resolution, should be low, but if there are many then the resolution should be high.

I really don’t have much concrete yet. As mentioned above, I was thinking of using Microsoft access for each model but I am now considering making this one of many alternatives. I will implement, Microsoft access components but I will use Java to glue them together using comconect.

https://earthcubed.wordpress.com/2009/08/06/i-decided-to-use-com-connect/

If one person runs the model the Access database should include points from places everywhere on the earth. If multiple people run the model I want each separate component (e.g. An access database) to cover a separate region of the earth.

The JPL-MIT model sounds like it may be a very good model. I recently found out that ocean atmospheric dynamics could be the dominate process driving temperature trends. This is because the instrumental recorded contains sudden changes in trend lines. This suggests hysteresis. Ocean atmosphere dynamics have been shown to be a possible source of this hysteresis.

“Abstract

Energy balance climate models of Budyko type lead to reaction–diffusion equations with slow diffusion and memory on the 2-sphere. The reaction part exhibits a jump discontinuity (at the snow line). Here we introduce a Babuška–Duhem hysteresis in order to account for a frequent repetition of sudden and fast warming followed by much slower cooling as observed from paleoclimate proxy data. Existence of global solutions and of a trajectory attractor will be established for the resulting system of a parabolic differential inclusion and an ode. ”

As for model simplifications, I was hoping that finding equilibrium solutions, would be enough to simplify the model. I am learning because there is hysteresis in the system we cannot count on the earth being near equilibrium.

“The primary reason for this is the long equilibration time of the climatecryosphere system (Fig. 3), which has at least the same order of magnitude (or longer) as the dominant periodicities of the orbital forcing, i.e. 20,000 and 40,000 yrs. This is why the upper branch of stability probably cannot be reached during a glacial cycle. At the
same time, the lower branch (interglacial state) is achieved after each or at least some terminations, and the system stays in the interglacial state for several thousand to several tens of thousands of years.”
http://www.pik-potsdam.de/members/calov/publications-1/pre-prints/calov_and_ganopolski_2005.pdf

However, it still may be able to find equilibrium solutions if we can separate the slow and fast dynamics. The slow dynamics, could be held constant, and then an equilibrium solution for the fast dynamics could be found for the value at which we hold the slow dynamics constant. Someone also showed me another climate model that was designed to be simple.

“As the complexity of general circulation models has been and still is growing considerably, it is not surprising that, for both education and research, models simpler than those comprehensive GCMs at the cutting edge of the development, are becoming more and more attractive. These medium complexity models do not simply enhance the climate model hierarchy. They support understanding atmospheric or climate phenomena by simplifying the system gradually to reveal
the key mechanisms. They also provide an ideal tool kit for students to be educated and to teach themselves, gaining practice in model building or modeling. Our aim is to provide such a model of intermediate complexity for the university environment: the PlanetSimulator. It
can be used for training the next GCM developers, to support scientists to understand climate processes, and to do fundamental research.”

Perhaps it may hold some keys as to possible simplifications.

Comment by s243a | August 10, 2009 | Reply

2. “I recently found out that ocean atmospheric dynamics could be the dominate process driving temperature trends.”

Coupled models are where it’s at. Have you checked out the CMIP stuff?

There’s a recent analysis in Science that is relevant to the ocean-atmosphere interactions. The Science Daily coverage is here.

It’s a neat idea you’ve got there. I’ll be checking back to see how things are shaping up.

Comment by Paul Tonita | August 12, 2009 | Reply

3. I’m posting the following paper here for future refference:

http://climate.lzu.edu.cn/~jhuang/publications/pdf/(87)Huang&North96.pdf

The paper uses a fairly simple model. The paper uses Fourier series, to find the temporal spectral solution. I’ve seen other papers use spherical harmonics to represent the spacial spectrum. Well, I chose a cubic coordinate system, I’m wondering about the possible benifits of using these types of basis functions, if for nothing else to try to find relationships between points which are distant in space and time.

Comment by s243a | August 16, 2009 | Reply