Greetings, Professor Keating,

If you look at the following image on wikipedia, you'll see the historical record of temperate and atmospheric co2 for the last four hundred thousand years:

https://en.wikipedia.org/wiki/...

If you inspect it, and compare the time evolution, you'll see that the co2 has been lagging temperature over time. That is, temperature goes up first and then co2 goes up. Temperature goes down and then co2 goes down.

You can get the data yourself from here:

http://www.ncdc.noaa.gov/paleo...

I've attached an image which plots the two of them on the same graph to make it easier to see. Time goes from right to left in my plot.

I've also taken the trouble to generate two other plots, which you can reproduce using the data available from NOAA that I linked to above.

The plots show dtemperature/dt (rate of change of temperature with time) as a function of co2 concentration minus temperature, and dCO2/dt as a function of temperature minus co2. (These variables have been brought to zero mean and unit standard deviation so they have the same units and one can be subtracted from the other.)

The two variables, temperature and co2, track each other so well that we can do linear perturbation theory. I.e. the dynamics keeps temperature and co2 close to each other, so it shrinks the value of:

abs(T - co2)

where T is temperature and co2 is atmospheric carbon dioxide concentration.

So, we write:

dT/dt = f(co2 - T) + noise

dco2/dt = g(T - co2) + noise

where f and g are functions. Now we suppose that the response is linear so:

dT/dt = k(co2 - T) + noise

dco2/dt = m(T - co2) + noise

where k and m are constants.

Now, if k is positive, then it means that temperature increases when there is excess carbon dioxide (i.e. more than usual for this temperature).

If k is not positive, then it means that, ignoring the effect of noise, temperature does not increase in response to excess atmospheric carbon dioxide.

If m is not positive, then it means that carbon dioxide does not increase when the temperature is above what it usually is at this carbon dioxide concentration.

If m is positive, it means that carbon dioxide increases when the temperature is higher than usual for this carbon dioxide concentration and decreases when the temperature is lower than usual for this carbon dioxide concentration.

Behold the graphs, or better yet, download the data from NOAA yourself and analyse it.

The result: m is positive. k isn't.

Finally, I invite you to apply the measure of Granger causality to the two time series:

https://en.wikipedia.org/wiki/...

I did this using the Granger causality tests included in the free statsmodels module for python. The result: The temperature forecasts the atmospheric carbon dioxide concentration better than the co2 concentration forecasts the temperature by a factor of 10 to the power of 40.

I have yet to encounter any evidence of comparable definiteness suggesting an influence of atmospheric carbon dioxide on global temperature, as have you.

Your math is invalid because you are subtracting nonequal units. You cannot subtract CO2 from temperature, and vice verse because they do not have the same units. For example, (400 ppm - 30 degrees C) does not make sense.

However, I understand what you are trying to do. You are trying to show the rate of temperature change as a function of rate of CO2 change. The proper math for this would be to have two functions like this:

f(dT/dt)/g(dCO2/dt), where dT/dt is the amount of temperature change over time and dCO2/dt is the amount of change in the CO2 level over time.

If you do this correctly, what you will have managed to do is to demonstrate what climate scientists have been saying for quite some time, there has been a natural trigger in the past. What we have learned (and I have covered in previous submissions) is in the past some natural trigger would occur that caused the temperature to start rising. This trigger has most often been solar activity and Milankovitch cycles. Once the temperature begins to rise in response to this naturally occurring trigger the CO2 levels begin to increase. This not only continues the temperature increase due to increased efficiency of the greenhouse effect, but also leads to additional water vapor in the atmosphere, another potent greenhouse gas. Once the natural trigger goes away, the temperature will begin to drop which will cause the atmospheric water vapor to condense out of the air and remove the CO2.

Now, look at what is going on today. Those natural triggers are not present. In fact, the natural cycle we are in would result in cooling temperatures if we were not present. We do not have a naturally occurring something increasing the temperature which would lead to CO2 being released into the atmosphere. But, we still have a sustained increase in the atmospheric CO2 levels. That increase is due to man made emissions. But, what is very interesting is the fact that the level of CO2 increase is

What this means is that we have replaced the natural triggers that led to increased CO2 levels with our own man made emissions. We are now pumping the atmosphere full of CO2 and that is having the same effect as it did in the past when some natural event caused the level to rise.

We can describe the past and present warming periods this way: Some event led to an increase in atmospheric CO2 levels, which led to an increase in global average temperature. In the past, that event was usually the Milankovitch cycles. Today, that event has been our industrialization. Either way, the science comes out the same.

You have not proven man made global warming is not real.

If you look at the following image on wikipedia, you'll see the historical record of temperate and atmospheric co2 for the last four hundred thousand years:

https://en.wikipedia.org/wiki/...

If you inspect it, and compare the time evolution, you'll see that the co2 has been lagging temperature over time. That is, temperature goes up first and then co2 goes up. Temperature goes down and then co2 goes down.

You can get the data yourself from here:

http://www.ncdc.noaa.gov/paleo...

I've attached an image which plots the two of them on the same graph to make it easier to see. Time goes from right to left in my plot.

I've also taken the trouble to generate two other plots, which you can reproduce using the data available from NOAA that I linked to above.

The plots show dtemperature/dt (rate of change of temperature with time) as a function of co2 concentration minus temperature, and dCO2/dt as a function of temperature minus co2. (These variables have been brought to zero mean and unit standard deviation so they have the same units and one can be subtracted from the other.)

The two variables, temperature and co2, track each other so well that we can do linear perturbation theory. I.e. the dynamics keeps temperature and co2 close to each other, so it shrinks the value of:

abs(T - co2)

where T is temperature and co2 is atmospheric carbon dioxide concentration.

So, we write:

dT/dt = f(co2 - T) + noise

dco2/dt = g(T - co2) + noise

where f and g are functions. Now we suppose that the response is linear so:

dT/dt = k(co2 - T) + noise

dco2/dt = m(T - co2) + noise

where k and m are constants.

Now, if k is positive, then it means that temperature increases when there is excess carbon dioxide (i.e. more than usual for this temperature).

If k is not positive, then it means that, ignoring the effect of noise, temperature does not increase in response to excess atmospheric carbon dioxide.

If m is not positive, then it means that carbon dioxide does not increase when the temperature is above what it usually is at this carbon dioxide concentration.

If m is positive, it means that carbon dioxide increases when the temperature is higher than usual for this carbon dioxide concentration and decreases when the temperature is lower than usual for this carbon dioxide concentration.

Behold the graphs, or better yet, download the data from NOAA yourself and analyse it.

The result: m is positive. k isn't.

Finally, I invite you to apply the measure of Granger causality to the two time series:

https://en.wikipedia.org/wiki/...

I did this using the Granger causality tests included in the free statsmodels module for python. The result: The temperature forecasts the atmospheric carbon dioxide concentration better than the co2 concentration forecasts the temperature by a factor of 10 to the power of 40.

I have yet to encounter any evidence of comparable definiteness suggesting an influence of atmospheric carbon dioxide on global temperature, as have you.

**Response:**Your math is invalid because you are subtracting nonequal units. You cannot subtract CO2 from temperature, and vice verse because they do not have the same units. For example, (400 ppm - 30 degrees C) does not make sense.

However, I understand what you are trying to do. You are trying to show the rate of temperature change as a function of rate of CO2 change. The proper math for this would be to have two functions like this:

f(dT/dt)/g(dCO2/dt), where dT/dt is the amount of temperature change over time and dCO2/dt is the amount of change in the CO2 level over time.

If you do this correctly, what you will have managed to do is to demonstrate what climate scientists have been saying for quite some time, there has been a natural trigger in the past. What we have learned (and I have covered in previous submissions) is in the past some natural trigger would occur that caused the temperature to start rising. This trigger has most often been solar activity and Milankovitch cycles. Once the temperature begins to rise in response to this naturally occurring trigger the CO2 levels begin to increase. This not only continues the temperature increase due to increased efficiency of the greenhouse effect, but also leads to additional water vapor in the atmosphere, another potent greenhouse gas. Once the natural trigger goes away, the temperature will begin to drop which will cause the atmospheric water vapor to condense out of the air and remove the CO2.

Now, look at what is going on today. Those natural triggers are not present. In fact, the natural cycle we are in would result in cooling temperatures if we were not present. We do not have a naturally occurring something increasing the temperature which would lead to CO2 being released into the atmosphere. But, we still have a sustained increase in the atmospheric CO2 levels. That increase is due to man made emissions. But, what is very interesting is the fact that the level of CO2 increase is

*leading*the temperature increase. In the natural cycles, it was typically*lagging*the temperature increase.What this means is that we have replaced the natural triggers that led to increased CO2 levels with our own man made emissions. We are now pumping the atmosphere full of CO2 and that is having the same effect as it did in the past when some natural event caused the level to rise.

We can describe the past and present warming periods this way: Some event led to an increase in atmospheric CO2 levels, which led to an increase in global average temperature. In the past, that event was usually the Milankovitch cycles. Today, that event has been our industrialization. Either way, the science comes out the same.

You have not proven man made global warming is not real.

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