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.

Part Six Anomalies

The IPCC, NASA NOAA and most scientists that study Climate change and Anthropogenic Climate Change use a system of measurement for Global temperatures that most of us are not familiar with called Anomalies. I’ve described this method in previous posts on my blog in this series but once more will not hurt. Basically, someone determines a Base period and then observations are measured against that base and therefore the result can be either higher or lower than the Base. The Base period should have some relevance to the subject but whether it does or not, it must be a constant or the system will not work.

NASA and NOAA work together on developing a Global temperature and when they set the system up they picked a period from 1951 through 1980. 30 years or 360 months, as their Base and when they did that they determined, obviously sometime after 1980, that the Global temperature was 14.0 degrees Celsius. Now this is important, there is no scientific reason to use that period and according to NASA it was because that is when most of the scientists at NASA and NOAA had grown up. A much better Base would have been the geological global mean estimated to be around 17.0 degrees Celsius but then all the values would be negative and that wouldn’t have looked good.

Now that they NASA and NOAA have their base they subtract it from the global temperature that they have calculated with their proprietary software. Keep in mind that there really is no Global temperature if for no other reason than the earth is a sphere and one side is always facing the sun (Hot) the source of all our energy and one side facing away from the sun (cold). Let’s do an example, for January 2015 NASA determined that the global temperature was 14.74 degrees Celsius so 14.74 minus 14.0 (the base) leaves .74 which they then multiple by 100 and that gives us an anomaly of 74. That value is published in many versions but we’re interested in a table called the Land Ocean Temperature Index LOTI and that table gives those values all the way back to January 1880. Most temperature data that comes from NASA or NOAA is in this anomaly format.

NOAA publishes the C0₂ information but they do not use this format they publish an actually value in this case CO₂ in the atmosphere as parts per million volume (ppmv), for example the value for January 2015 was 399.96 ppmv. Sometimes the v is dropped so it would be 399.96 ppm. NOAA publishes the CO₂ ppm value by month and they go back to March 1958 so there is not as much data to use in evaluations as with Global temperatures. In previous posts here, an equation was shown that will generate a curve that matches historical CO₂ levels, present CO₂ levels and CO₂ levels as shown in IPCC reports such as the latest AR5.  When we get to that part of this analysis we’ll show both and then drop the NOAA portions since it is for such a short period of time.

This completes the introduction and now we get to what we are going to do that’s different from previous Climate work by others. Basically we are going to convert CO₂ levels to an anomaly using the same system that NASA uses for temperature. By doing that we’ll be comparing everything to the 1951 -1980 base period in the same kind of units. This should make any patterns or correlations more visible. We’ll start with showing the NASA Global temperature anomalies and then add on other items.

But first one other comment and that is we have had to make some adjustments in the NASA temperature data to make it more understandable. The first part is done by combining blocks of months and then taking an average. We are looking at climate changes not weather and so daily or even monthly movements do not mean anything. We picked ten years for a block for all the work here and we start with 1880 to 1899. This gives a smooth plot rather than the jagged ones that are normally seen and that makes it difficult to pick out climate from weather. Also in the case of NASA data we average 4 different current reports 2012.12, 2013.12, 2014.12 and 2015.01 the most current. This was done because of the process that NASA uses to determine the Global mean temperature creates some variation in the anomalies this averaging helps to minimize those variations. The following Chart was generated using this method. I have talked about this process in other posts here if the reader is interested.

The NASA global temperature anomalies using the method described here are shown in the blue plot on the Chart. We can see that there is a downward movement from 1880 to 1900 then an upward movement to 1940 then a downward movement to 1980 then a large upward movement to 2010. And lastly what looks like the beginning of another downward movement starting around 2010. In addition the entire series is moving up as shown by the black trend line.

There is no dispute on the patterns shown here the only issue is whether what this Chart shows is natural or manmade?

The next part of this analysis is looking at NOAA CO₂ data in the same anomaly format and as previously stated there is much less information here than with Global temperatures. The first Chart shown below is a plot in Green of the CO₂ data from NOAA and although most show this as a straight line, it is not it is a polynomial curve actually a logistic curve again as previously discussed here in Part Four. But first let’s look at just the NOAA data in anomaly format using the same base as the NASA Global temperatures, 1951 to 1980. The actual published NOAA CO₂ plots in ppm are shown in Part Four

In the next Chart we’ll add the logistic curve to the actual NOAA data blocking out the common years in the CO₂ model so you can see how the fit between the two data sets is very good. The actual NOAA is in green and the Modeled CO₂ is in light green. Again as previously stated this logistics curve shows CO₂ values that are in agreement with historical CO₂ records, present CO₂ and future projections of CO₂ as published by the IPCC in their various assessments, the most current being AR5.

For the rest of this analysis we will use the logistic curve for CO₂ and show it as a green plot labeled NOAA CO₂ as there is no real difference.

The next Chart shows the NASA Global Temperature and the NOAA CO₂ anomalies combined. There does seem to be a relationship between the upward movement of CO₂ and the upward movement in global temperature especially in the period from 1970 through 2000. We’ll continue this analysis to see if this apparent relationship is real or not.

The next thing to look at now that we have past temperatures and a reasonable forecast of CO₂ is what the IPCC estimates, based on the anthropogenic theory, Global temperatures will be in the future. They make this harder than it needs to be by tying the projections to economic projections, but since none of the proposed CO₂ reductions have come to pass we’ll use the one business as usual, since it is the most likely. The next Chart shows just the past NASA Global Temperatures and the IPCC estimates of what future Global temperatures will be. Keep in mind that we are showing Anomalies not actual Global Temperatures.

There can be no dispute that the IPCC projection does appear to follow the NASA trend from 1980 through 2000. This trend would make Global temperatures about 15.75 degrees Celsius by 2050. This can be calculated by adding to the base of 14.0 degrees Celsius the y axis value of 175 for 2050 after diving it by 100 to turn it back into degrees Celsius. Also we do not see any deviations its strictly a smooth upward plot not like the actual from the past.

In the next Chart we’ll add back the NOAA CO₂ plot and we’ll see that the IPCC projection and the CO₂ projection are very close indicating that there is a very close relationship between the IPCC projection and the CO₂ projection. Since the IPCC was chartered to show what the 1980 to 2000 trends would do IF THE RELATIONSHIP SHOWN THERE WAS VAILD this extension is of no surprise. This Chart is similar to the one shown in Part One that Hansen showed to Congress and is also widely used by the IPCC and NASA.

Now let’s zoom in and look at the 60 year period from 1960 through 2020 so we can see more detail; this is shown in the next Chart. There is a very clear and consistent relationship between all three measure NASA temperature, NOAA CO₂ and the IPCC temperature projections using the Anomaly system from about 1975 through 2005. This is of no surprise as the IPCC developed their Global Climate Models, GCM’s, to show this. It was the prevailing view in the environmental movement, at that time, that there was a direct link between CO₂ levels and Global temperature.

There is an obvious departure shown here between the correlation between CO2 and Global temperature. From 1880 to 1900 CO2 is below Global temperature then from 1910 to 1950 its above Global temperature; its only from 1975 to maybe 1995 the CO2 and NASA Global temperature growth rates match. That is only a 20 year out of 134 years where this is a match which is only 14.9%.

However, there is a developing problem as NASA Global temperatures are no longer following the IPCC projections even though CO₂ is going up as expected. The current deviation is almost a quarter of a degree Celsius now which can be seen in the above Chart as the blue NASA plot is below the IPCC and NOAA plots by 20 units and if we divide by 100 that is .2 degrees Celsius.

Going back to the very first Chart in this series of the Global temperatures as calculated by NASA we saw that there appeared to be a pattern of ups and downs in the temperature and based on those ups and downs another down was due, and that is exactly what we see in the above Chart; the beginning of a down period.

There are other theories about Climate Change one of which is based on variations in solar radiation which affects the Blackbody temperature and variation is the suns magnetic field which affects cloud formation and Albedo. We have also shown in Part Five that there are global movements in temperature that have been observed going back to the last Ice Age some 11,000 years ago, but especially in the past 4,000 years. Using modeling techniques and curve fitting an alternative Climate model designated PCM was developed in 2007 that has proved to be very accurate in projecting the Global temperature published in the NASA LOTI table.

This model is based on a long cycle of approximately 1000 years a short cycle of almost 70 years and a factor for CO2 using a sensitivity value under 1.0 degrees Celsius. Using the same method of looking at anomalies from the NASA base of 1951 to 1980 we have the following plot of the PCM model. We have the overall upward movement, and the cycle of ups and downs as was observed in the NASA Global temperature plot we first showed. So is this plot better than the IPCC’s plot at matching the NASA data?

In the next Chart we add the PCM model to previous one showing NASA Temperature NOAA CO₂ and the IPCC Temperature projection plots. Although we do not have a perfect match going all the way back to 1880 it is just as good for the period 1970 though 2000 as the IPCC. But more importantly it is significantly better that the IPCC from 200 to the present since is shows a slight down trend just as does the NASA data.

We’ll show one last Chart looking at the same 60 year period we used to look at the IPCC values close up. The next Chart adds the PCM model to that Chart and it’s very clear that the PCM model is significantly closer to that of the published NASA LOTI values for the entire period of NASA published Global temperatures. Although the PCM model does use a factor for CO₂ it is not slowly dependant on CO₂ for its projections; instead we have looked at past Global temperature movements and matched them with the more current CO₂ sensitivity values found in the published papers and which was also previously shown in Part Three.

A model is only as good as its projections or forecasts so based on the above Chart it is beyond dispute that the PCM model is significantly better than that of the IPCC. Further, since the PCM projects cooling and the IPCC projects warming the disparity will only get worse and worse.

The next part will be a discussion of the logic and equations used to develop the PCM Global climate model

Approximately ten or so years ago increases in Global temperatures slowed down and then actually reversed. This is fact not speculation for if you take any of the NASA LOTI releases put them in a spreadsheet and then draw a chart and add a trend line using the polynomial Order 3 option the resultant plot will turn down around 2010. The generated plot will also follow the NASA LOTI data very nicely going back to 1880, even with the data manipulation that they have resorted to, to hide the current move down in Global Temperatures.

This downturn has created an unexpected problem for those that want to change how we live in the U.S. with the UN Agenda 21 sustainable world they have already started to implement. Since the main premise was the CO2 emissions from power generation was their culprit that meant that source must be eliminated; however if the Global temperature was not going up than there was a “major” problem with their core belief which also included moving away from a free people to a system where the people were controlled, for their own good. The control of the people was required since the Warmest’s needed to reduce the people’s energy usage and the people would not support a reduced standard of living without coercion.

When NASA realized that they had a problem with CO2 going up and Global temperatures going down they resorted to manipulating the data though the “Homogenization” process they use to blend all the data collected into one Global temperature. The process they used created an upward movement in Temperatures’ that was obvious to anyone that looked and in the past on this blog I have talked about it. Because of the intentional change of data and trends that NASA has been doing I was mislead a few weeks ago when I issued my monthly report which I have done for the past year. I compared the January 2015 values to the wrong past values and although the change was in the same direction it was not to the same magnitude as I showed. For that I must apologize.

This post is using the correct data and will give the same result just to a slightly lesser degree. I have also added a forecast of what I think NASA will do with the temperatures over the next several months as they need to support the United Nations Climate Change Conference (COP21) which will be held in France at the Le Bourget site from 30 November to 11 December 2015 and the conference objective is to achieve a legally binding and universal agreement on climate, from all the nations of the world.

To achieve this they have determined that they need to show that the planet is overheating, whether it is or not, and since it is not (by satellite data) they need to show it in another form, hence the data manipulation at NASA-GISS.

This manipulation is shown in the next three Charts which all use LOTI data the first from December 1998 (Red) and the second from January 2015 (Blue) which trend lines as required in the same colors. The first is in the period January 1880 to December 1950 which is the entire temperature series up to the point that NASA uses to determine their anomaly. The anomaly is the base temperature that NASA uses to measure temperature changes from. The second Chart is the period used to determine the NASA anomaly which is from January 1951 to December 1980, 30 years. The third Chart, actually a series of Charts on the same period, is from January 1981 to the present. To support the need for a warmer present they will need to move the 1880 to 1950 data down, keep the 1951 to 1980 data constant and move the 1980 to the present data up as much as possible. If that can be shown in the following Charts then that proves what is being down since no other change would produce this effect.

Clearly, in this Chart, the past temperatures have been moved down almost a quarter of a degree C in 1880 from the 1998 red plot to the 2015 blue plot. Further the two trends almost merge at the December 1950 date since they cannot change that period since it sets the anomaly value of zero or 14.0 degrees Celsius. Random changes or adjustments would not do this.

We can see in this Chart that there is some movement in both trend lines; both are slightly below 0 in 1951 and slightly above zero in 1980. They also appear to be offsetting so we’ll check that by adding all the anomalies from this period to see if they cancel and they do. There are 360 values in that period and the 1998 series adds up to -2 and the 2015 series adds up to 4. I would be willing to bet if we looked at rounding differences the differences would be even closer to zero. So again we have proof that the manipulation of the data is not without purpose since any programmed change, with a purpose, must keep this period at or almost at zero anomalies.

This next potion, from 1981 to the present, is a bit more complex since it is showing the planned results of the NASA data manipulation so we are going to show a series of Charts. Since the 1998 red plot only goes to 1998 we can’t do a one for one comparison but we can see that for the period where the two plots are common the blue plots are above the red on the upside and the red plots are below the blue on the down side indicating that the blue plot is showing a warmer temperature and this is verified when we add the trend lines which clearly show that the blue trend is shifted up. Because NASA had to keep the 1951 to 1980 period constant the trend lines are closer together in 1981 than they are later on in 2015; this is additional prove of the manipulation

Next we get rid of the linear trend to the 2015 data and add a polynomial trend using a 3^rd order to see if it gives a better fit to the data and it does. This trend clearly shows the Global temperature peak around 2010/2011 and the down trend ever since. This is especially true if we would ignore the last couple of years where the data manipulation has started.

Sir Karl Raimund Popper (28 July 1902 – 17 September 1994) was an Austrian and British philosopher and a professor at the London School of Economics. He is considered one of the most influential philosophers of science of the 20th century, and he also wrote extensively on social and political philosophy. The following quotes of his apply to this subject.

If we are uncritical we shall always find what we want: we shall look for, and find, confirmations, and we shall look away from, and not see, whatever might be dangerous to our pet theories.

Whenever a theory appears to you as the only possible one, take this as a sign that you have neither understood the theory nor the problem which it was intended to solve.

… (S)cience is one of the very few human activities — perhaps the only one — in which errors are systematically criticized and fairly often, in time, corrected

Part Five Geological Facts

This will be a short section placed here to show what the past was until recently when all this history mysteriously disappeared. The point to these Charts is that climate has NEVER been a constant with global temperatures ranging from a low of around 12 degrees C to a high of around 22 degrees C and CO₂ ranging from under 300 ppm to as high as 7,000 ppm. We are presently at 400 ppm CO₂ with a global temperature of around 14.6 degrees C which is historically low as can be seen on the following chart going back 600 million years. It would seem that a mean temperature of 17 degrees C, as shown here, and a CO₂ level of over 1000 ppm would be more normal then what we have now so why the hysterical political movement to control CO₂?

The next chart is more current going back to the last ice age some 11,000 years ago. This chart is particularly interesting as it shows that there have been 4 cycles of cold and warm going back over 4,000 year. Based on those 4 cycles and considering the difficulty of determining exact dates and temperatures it can be said that over the past four thousand years there have been 4 cycles of about one thousand years duration with an amplitude of maybe 1.5 degrees C. And we are what would appear to be a peak of the forth cycle, indicating that we can expect a downward movement to start in the next hundred years or so. Based only on this observation It should be possible to develop a model that would be valid over this period of time and where we have human records to support these temperature changes.

However, there are also some significant temperature variations with shorter durations as shown on the next Chart. This Chart is of the Atlantic Multidecadal Oscillation or AMO where there appears to be a 60 some year cycle of under one degree C there is also a larger cycle in the pacific known as La Nina and El Niño.

The Pacific variations are not as consistent as those in the Atlantic are,but there is a greater variation as can be seen in the next chart where the La Nina and El Nino events are shown as a multivariate index called the ENSO.

The purpose to showing this four Charts is to establish that there are geological and even decadal variations in climate and none of these have anything to do with mankind or CO₂; therefore any proper theory of Climate must consider these variables as a base to work from. Only when that is done can considerations be given to things like Carbon Dioxide, which probably is only a bit player in Climate.

In the next section we’ll put this all together and show what is really happening with Global Climate and also why the Warmists and their obedient media are so wrong.