EVOLUTION OF NONLINEARITY IN THE RUSSIAN PRECIPITATION-TEMPERATURE DATA

RGInfinityparadoxpost

In the attached I have discussed how nonlinearity arises as we analyze the Russian data for precipitation reported by several weather stations (184 total). This also been posted in response to a question on nonlinearity posed by Prof. Derek Abbott, which is reproduced below.

 

Question

The paradox of infinity: where does the nonlinearity come from?

The principle of linear superposition holds for the integers, eg. 3 + 4 = 7. However, when we take the integers out to infinity we now obtain nonlinear behaviour. Infinity plus any amount is still infinity, so linearity has broken down.

TOWARDS A NEW PHYSICS OF GLOBAL WARMING AND CLIMATE SCIENCE

ON A SIMPLE AVERAGE TEMPERATURE PRECIPITATION RELATION (05feb14)

TOWARDS A NEW PHYSICS OF GLOBAL WARMING AND CLIMATE SCIENCE

The term evaporation is used to describe the transformation of liquid water into its gaseous form, at ordinary temperatures, well below the boiling point. We expect evaporation rates to increase with increasing temperature. Does that mean precipitation will also follow same trend? That is, will precipitation, as observed locally, increase with increasing local average temperatures?

Precipitation is the opposite of evaporation – water coming back to the earth as rain or snow. For this, a study of the observational data reveals both types of trends, precipitation P increasing with increasing temperature T, and precipitation decreasing with increasing temperatures and also a maximum point on the graph of precipitation versus the average temperatures; all deduced empirically. The existence of a maximum point on the P-T graph implies that there is an optimum temperature for precipitation.

In this first article, I have reported the trends observed in UK, USA, Germany, Australia, Malaysia, Ecuador and Singapore. The P-T graph for all these countries reveals a negative slope. Since this article was completed, the opposite trend with the positive slope has been confirmed (prompting the note included in the appendix), quite unmistakably, with the data for China. And, both the Russia and Mongolia data show positive and negative slopes with a maximum point on the graph of temperature-precipitation graph.

So, why is there is a maximum point? Perhaps, this is analogous to the appearance of a maximum point of the blackbody radiation curve. As is well known, the attempts to explain this maximum point, theoretically, led to the birth of quantum physics.  

Following this train of thought would lead us to a new physics for global warming, or the science of climate change. In his new theory, Planck essentially describes a method of determining the average value U = UN/N of some property of interest where N is the number of microscopic entities and UN is the total value of the property of interest. In Planck’s original theory, the microscopic entities are called resonators and U is the average energy of the resonators and UN their total energy with N being a very very large integer.

A generalization of the Planck-Einstein ideas, well beyond physics, to many other branches is possible, if we recognize that Planck is trying to determine the average value of some property for a very complex system [59, 60]. This has been discussed by the present author in several articles which have been made available in non-peered publications [37, 38].