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.

EVIDENCE FOR A UNIVERSAL LAW DESCRIBING THE TEMPERATURE-TIME RELATION FOR THE EARTH’S CLIMATE STSTEM

Sunriseon28jan2014(Rev2)

EVIDENCE FOR A UNIVERSAL LAW DESCRIBING TEMPERATURE-TIME RELATION FOR THE EARTH’S CLIMATE SYSTEM

This is an updated and revised file that was posted earlier. (Sorry, I wish I could figure out how to delete old files and upload a revised file, making this post unnecessary.) 

When light, a stream of photons with energy E = hf, shines on the surface of a metal, it produces electrons with a maximum kinetic energy K, given by K = E – W = hf – W where h is the Planck constant, f is the frequency of light and W is the work function of the metal upon which light is shining. W represents the energy that must be given up to bring the electron out of the metal. This is the photoelectric law conceived by Einstein in 1905. 

Likewise, when the sun rises and shines upon the earth, the solar energy flux (also called the solar irradiance, energy per unit time per unit surface area, measured in Watts per square meter) causes the temperature T to start rising. According to the kinetic theory of gases, the temperature T of an ideal gas is directly proportional to the average kinetic energy of the atoms or molecules of the gas. Thus, the observed annual global average temperature can be taken as an accurate measure of the energy that has been transferred to the earth from the sun. 

I found something interesting about the temperature-time relationship over the last few weeks, by studying both the climate (and weather) data at various levels, at the local level of single city, at the national level of a  single country, and also at the global level. The law can be shown to be a simple linear law of the type T = A + Bt where the nonzero intercept A, in my opinion, is exactly similar to the work function conceived by Einstein to explain photoelectricity.

I have been testing the universal applicability of this law since it became obvious to me, recently, during the bitterly cold spell that we have been experiencing in the USA, which got me interested in studying the weather and/or climate data at various levels. The temperature-time data for both Detroit, MI and London, UK, for the full month of December 2013 and (the to-date) January 2014 can be shown to follow this simple law. The global average temperature data, from 1880-2013, can also be shown to obey the same law. As with the photoelectricity experiment, where the K-f graph yields a family of parallels (for different metals, each with its own work function W), the T-t graph is also a family of parallels, with a fixed slope B and a nonzero intercept A, which can be compared to Einstein’s work function. I have deduced the equations for these parallels by considering several (x, y) pairs in the datasets at various levels. It should be noted that Millikan arrives at the absolute magnitude q of the electrical charge on a single electron (in his famous oil drop experiments) and then the numerical value of the Planck constant h from the photoelectric measurements, by using exactly the method just described. He considers various (x, y) pairs in his dataset to show the constancy of q. He does the same with the K-f measurements, where K = qVo with Vo being the stopping potential measured by Millikan (for two metals lithium and sodium). 

I have uploaded a pdf file with some figures discussing these findings on my Facebook page, see the group Global Warming for the Layman, https://www.facebook.com/groups/GWforlayman/

THE HISTORICAL CLIMATE DATA FOR YAKUTSK, RUSSIA, ONE OF THE COLDEST CITIES ON EARTH

YakutskRussiahistoricaldata1

THE HISTORICAL CLIMATE DATA FOR YAKUTSK, RUSSIA, ONE OF THE COLDEST CITIES ON EARTH

This is a slightly revised version of the document posted earlier. (Sorry, wish I can figure out how to delete files that were uploaded in the earlier post, making this unnecessary!) The historical temperatures data for this city, recently featured in a Weather Channel article, is plotted in Figures 2 and 3. Classical statistical methods lead to the conclusion that the annual average temperature has been increasing. However, a more careful examination reveals the movement of the temperature data along the parallels seen in Figure 3. This means that the average annual temperature in 2013, although higher than in 196os, is actually lower than it would have been had the trend illustrated by the parallel V continued. The temperature-time data at the local level, here the coldest city on earth, thus reveals a work function (the nonzero intercept A) as with global average temperature data.

Here’s the link to the website from which the temperature data was obtained, http://www.tutiempo.net/en/Climate/Jakutsk/03-2013/249590.htm

A UNIVERSAL LAW FOR THE TEMPERATURE-TIME RELATION FOR THE EARTH’S CLIMATE SYSTEM

Sunriseon28jan2014Sunriseon28jan2014Sunriseon28jan2014Sunriseon28jan2014

In my first post here, I uploaded the photo of the sun rising this morning, at 7:55 am, on January 28, 2014 (taken with my iPad).

When light, a stream of photons with energy E = hf, shines on the surface of a metal, it produces electrons with a maximum kinetic energy K, given by K = E – W = hf – W where h is the Planck constant, f is the frequency of light and W is the work function of the metal upon which light is shining. W represents the energy that must be given up to bring the electron out of the metal. This is the photoelectric law conceived by Einstein in 1905. 

Likewise, when the sun rises and shines upon the earth, the solar energy flux (also called the solar irradiance, energy per unit time per unit surface area, measured in Watts per square meter) causes the temperature T to start rising. I found something interesting about the temperature-time relationship over the last few weeks, by studying both the climate (and weather) data at various levels, at the local level of single city, at the national level of a  single country, and also at the global level. The law can be shown to be a simple linear law of the type T = A + Bt where the nonzero intercept A, in my opinion, is exactly similar to the work function conceived by Einstein to explain photoelectricity.

I have been testing the universal applicability of this law since it became obvious to me, recently, during the bitterly cold spell that we have been experiencing in the USA, which got me interested in studying the weather and/or climate data at various levels. The temperature-time data for both Detroit, MI and London, UK, for the full month of December 2013 and (the to-date) January 2014 can be shown to follow this simple law. The global average temperature data, from 1880-2013, can also be shown to obey the same law. As with the photoelectricity experiment, where the K-f graph yields a family of parallels (for different metals, each with its own work function W), the T-t graph is also a family of parallels, with a fixed slope B and a nonzero intercept A, which can be compared to Einstein’s work function. I have deduced the equations for these parallels by considering several (x, y) pairs in the datasets at various levels. It should be noted that Millikan arrives at the absolute magnitude q of the electrical charge on a single electron (in his famous oil drop experiments) and then the numerical value of the Planck constant h from the photoelectric measurements, by using exactly the method just described. He considers various (x, y) pairs in his dataset to show the constancy of q. He does the same with the K-f measurements, where K = qVo with Vo being the stopping potential measured by Millikan (for two metals lithium and sodium). 

I have uploaded a pdf file with some figures discussing these findings on my Facebook page, see the group Global Warming for the Layman, https://www.facebook.com/groups/GWforlayman/