Part Seven Equations that define Climate

The PCM Climate model development was based on some very basic and simple principles that I think NASA, NOAA and the IPCC has either ignored or forgotten. The reason for this is they thought they knew what was causing the apparent increase in world temperatures in the 1980’s. Therefore they didn’t try to find out why but instead looked only at what the result would be if that observed pattern was caused by CO₂ and that it continued into the future. Since CO2 was not the Ultimate cause of the increase in apparent Global temperatures the results of the work were flawed and we now have policy being built to, in essence, stop Mother Nature from doing what is natural to her. Obviously this will not work and will ultimately cause great harm!

The first is that the Earth’s temperature is very stable never deviating from a mean of about 17 degrees Celsius by more than +/- 2% over the past several hundred million years; which means there are no positive feedback mechanisms.

The second is the fact that for all practical purposes the planet’s surface temperature is determined solely by the energy arriving here from the sun and how long it stays there.

The third is that water in the oceans, lakes and rivers along with what is the atmosphere acts as a thermal buffer that holds a tremendous amount of heat.

The fourth is that the energy that makes it to the surface falls on a small circle centered on a direct line from the center of the sun to the center of the earth creating a hot spot.

The fifth is that the energy from the hot spot flows north and south to the polls through both the oceans and the atmosphere.

The sixth is that the planet rotates around the sun in an elliptical orbit and the planet spins around its axis so that hot spot moves up to the tropic of cancer and down to the tropic of Capricorn creating thermal flows that are not easy to model as the land and water portions are not the same over the entire planet.

The seventh is that changes in the intensity of the solar wind will make changes in the earth’s magnetic field and that changes how high energy particles enter the atmosphere and that increases or decreases the planets cloud cover.

The eighth is that small changes in cloud cover make changes in the planets albedo and that will make changes in the amount of energy reaching the surface of the planet.

The ninth is that small changes in the energy reaching the planet’s surface makes a large change in the temperature because of the physics involved in the Stefan-Boltzmann Law.

The tenth is that the combination of: the orbital changes of the Earth, the fact that the Earth rotates every 24 hours, and there is a variable energy input from solar radiation and the solar wind create, means that what we call climate and weather is not and has never been a constant

It is my professional opinion that the physics and chemistry interactions on the planet considering all the variables, along with the external orbital variables are not model-able with present knowledge and computer power to predict global climate with sufficient precision and accurately to justify make energy or economic policy. By this I mean we have not been measuring climate at the global level long enough to know if the logic we have developed and use is correct or not. Temperatures have gone both up and down while CO₂ was going up.

However, having said that I do think that there is enough data over the past 4000 to 5000 years to make a crude model that will explain or at least get us into a ball park understanding of the thermal energy flows that seem to us as climate change. This misunderstanding is because these changes are orders of magnitude longer than a human life. In particular there is a thousand year cycle and a seventy year cycle that is observed and we know that CO₂ will have some effect on how fast the heat in the atmosphere radiates off the planet e.g. the black body temperature and the greenhouse effect which was discussed in Part Two.

Since we know that the last cold period, the little ice age, bottomed around 1600 to 1650 and we know there is a thousand year pattern and a seventy year pattern it seemed to me that it should be possible to write simple equations that would be able to show these thermal movements. The following equations will, in fact, accurately predict Global Temperatures from January 1600 to the present; with two assumptions. One is that the Global Temperature was in the general range of 13.5 degrees Celsius in 1600. Two was that CO₂ levels were in the range of 270 ppm during that same period. The developed equations are robust enough to allow for some changes in these two key variables. A model of CO₂ was already shown in part four.

The following five equations will produce a Global Temperature from a time series starting from January 1600 to which we give the value 1 and label that number as M. Each succeeding month from that date adds 1 to that number such that January 2015 is M = 4981 and that gives a CO₂ value of 399.98 ppm verses the actual of 399.96 or an error of .02 ppm which is basically no error; and a Global Temperature of 14.57 degrees Celsius verse NASA at 14.74 degrees Celsius for an error of .17 degrees Celsius using January 2015 values published in the LOTI table.

The following are the definitions of the terms used in the five equations. GT equals Global Temperature in degrees Celsius. LT equals the Global Temperature adder from the 1000 years cycle. ST equals the Global Temperature adder from the short cycle. CO₂ equals the level of CO₂ in ppm. CT equals the Global Temperature adder from the CO₂ level. Just an aside the result from using these five equations may not be exactly what my spreadsheet calculates because it uses more places in the calculation.

GT = 13.5 + LT + ST + CT

LT = SIN (( M -3500 ) * .0004974 ) * .45

ST = SIN (( M -350 ) * .0088139 ) * .14

CO₂ = 270 + 730 / ( 1 + 8.75 * EXP ( .00173 * (4612 – M )))

CT = (( 14 / ( + EXP ( -.009 * CO2 ))) -7 ) – 5.867

These five equations were developed without the use of any statistical software and were first developed using the 2003 version of Excel; since then I have upgraded to the 2007 version so I can now use the .xlsx format. I am also sure that these equations could be improved on with the use of appropriate software which I do not have. This model was developed solely by observation of the relationships found. The serious reader, if interested, may request a copy of the spreadsheet containing this model by sending me a formal request to david.pristash@gmail.com and after reviewing the request I will send the requester a copy of the spreadsheet in xlsx format or a reason why I did not

The following three Charts were made using these five equations the large variation in the NASA data can be seen in these charts and that is why I use a 12 month running average and/or the blocks of 10 years in most of my work. These Charts are identical except for the time frames shown. The red plot is actual NOAA monthly CO₂ data in ppm. The Green plot is actual monthly NASA data converted from anomalies to degrees Celsius for Global Temperature. The blue plot is the CO₂ model in ppm. The purple plot is the PCM Climate model projection of Global temperatures cased on these five equations in degrees Celsius.

The first Chart is for a 200 year period bracketing the NASA and NOAA data. The purple PCM plot is not perfect but it is very close to the green NASA plot.

This Chart goes back to 1600 which is about the time the temperatures bottomed out during the Little Ice Age and forward to 2100.

This last Chart starts at the bottom of the last ice shows the peak of the current long cycle around 2150 at 15.1 or 15.2 degrees Celsius and then continues moving down to the next tough around 2700 and then continuing with the start of the next upswing. We can see that the 2700 bottom is only about .6 or .5 degrees Celsius higher even though CO₂ has peaked at 1000 ppm.

It is my personal belief after studying the available literature that the variations is the suns electromagnetic radiation along for the particle based solar wind has an effect on the Earth’s magnetic field; and those variations allow more or less of the cosmic rays (charged particles) to enter the Earth’s atmosphere. Those particles interact with the water in the atmosphere to create droplets which then form clouds. Clouds being the main driver of the Albedo of the Earth have a significant effect on how much and how long the thermal energy stays on the atmosphere before being re-radiated out. This is, of course, the greenhouse effect which determines the earths Global Temperature.

This is not my idea but it is the one that I think is the principle cause of the short cycle and possibly of the long cycle as well.