-1=e^ipi

So I estimated this using 1876-2009 data and I get the following 95% confidence intervals: K1 = (-1.2 +/- 2.7) ppm per celcius K2 = (4.0 +/- 1.2)x10^-4 ppm per million tons of carbon K3 = (-1.54 +/- 1.18)x10^-2 per year K4 = (4.6 +/- 3.4) ppm per year Make of that what you wish. So I guess this model assumes that oceans respond immediately to temperature changes, but assumes that the CO2 decay effect is not negligibly small? If I were to assume that this model's assumptions are valid then it suggests a decay time of excess CO2 of ~65 years. If this is primarily due to interact with the oceans, then the fact that it is similar to the decay time of ~63 years in post #1 and the decay time of ~67 years in post #154 is interesting. My understanding is that there is a bit of uncertainty about how many millions of metric tons of carbon are needed to increase atmospheric CO2 by 1 ppm. The results of the regression I just did suggests that ~2.5 billion metric tons of carbon are needed, which agrees with the 2.6 billion metric tones I got in post #154, and also with the range of estimates in the scientific literature.

Maybe think of it as a concept similar to the centre of mass. The centre of mass in the Pluto - Charon system isn't in either Pluto nor Charon. So the vast majority of the mass of the Pluto - Charon system isn't near the centre of mass. But that doesn't mean the centre of mass of this system isn't a useful concept. Or maybe ask yourself this: What prevents the water at the bottom of the ocean from being at the same temperature as the surface of the ocean? This isn't as simple as saying colder water is heavier because then you have to explain why some water is colder than others and what prevents heat transfer from the surface to the deep ocean until isothermal conditions are reached.

Also, if the approximation that the decay rate for the Earth's carbon sink is equal to the decay rate of the Earth's temperature sink holds, then the decay rate of ~67 years is valid. Note that this does seem consistent with the decay rate I got using the IPCC information and posted in the original post (~63.3 years). Interestingly, there are many climate cycles that have this time scale as well (such as the North Atlantic Multidecadal oscillation, the oscillation in the length of the day, and perhaps solar cycles such as the Gleissburg cycle). So if we think about how the Earth responds to increases in atmospheric CO2, we can think about it on 3 different time scales. In the short run (with the decay time of ~1 year), one gets a fast response due to the direct forcing effects of CO2 and the fast feedback effects of water vapour and lapse rate. This gives the transient climate sensitivity (not to be confused with the transient climate response). In the medium run (with a decay time of 60-70 years), one gets an additional response as the oceans & permafrost warm and obtain equilibrium with the increase in surface temperatures due to the CO2. This gives the equilibrium climate sensitivity. And in the very long run (with a decay time of ~1000 years), one gets an additional response due to glaciers melting and vegetation changing (which gives the Earth system sensitivity). Of course since this timescale is less than the timescale of excess CO2 being absorbed by the oceans, the Earth system sensitivity will not get released, so the equilibrium climate sensitivity is more relevant. If this is the case, then the climate sensitivity value I got in post #92 ((1.98 +/- 0.92) Celcius) is closer to the transient climate sensitivity than the equilibrium climate sensitivity since it came with a decay time of ~3 years. If the actual decay time to the equilibrium response is ~63 years, then my value in post #92 is underestimating equilibrium climate sensitivity by a factor approximately (1 - 1/63)/(1 - 1/3) = 1.48. So this means that the results I got in post #92 actually suggest a climate sensitivity of ~3C and are therefore not in contradiction with the results I got from correcting Loehle's paper as well as the mainstream scientific opinion and the IPCC. So we are looking at a transient climate response of ~2C, and equilibrium climate sensitivity of ~3C, and an earth system sensitivity of 4-4.5C.

Now that I think about it, I think the model used in post #154 is missing one important factor. And this factor explains why I got a negative and uncertain estimate for the CO2 released by increasing the temperature of the characteristic heat sink of earth. Increasing the temperature of the characteristic heat sink does cause it to release CO2. However, if one increases atmospheric CO2 then the oceans will want to absorb some of this extra CO2 in order to get to thermodynamic equilibrium. So having unusually high CO2 levels will cause CO2 to be absorbed over time, which will reduce the rate of increase of atmospheric CO2. Since the increase in temperatures over the past century are very correlated with increase in CO2, the factor I used in the model in post #154 that describes the increase in rate of atmospheric CO2 increase due to warming the heat sink picked up the decrease in the rate of atmospheric CO2 increase due to oceans absorbing CO2, which made the estimate negative. In fact, it should be expected that the rate of CO2 being absorbed by the ocean since atmospheric CO2 concentrations are higher than normal more than offsets the rate of CO2 being released by the oceans due to the oceans warming as we can see here: http://www.skepticalscience.com/human-co2-smaller-than-natural-emissions.htm Since the oceans contain far more carbon than the atmosphere, it is reasonable to approximate the rate at which the oceans absorb CO2 due to having less 'effective CO2' than the atmosphere as being proportional to the difference between atmospheric CO2 and some 'characteristic CO2 ppm of the earth's carbon sink'. So the model (omitting volcanism and other natural causes for reasons I explained earlier) would be: dCO2/dt = E*Human_emissions(t) + C*dTs/dt + G*dCO2s/dt Where Ts is the characteristic temperature of the Earth's heat sink and CO2s is the characteristic CO2 ppm of the Earth's carbon sink. Plus there would be the two equations (that came from linear approximations): dTs/dt = D*(T(t) - Ts(t)) and dCO2s/dt = H*(CO2(t) - CO2s(t)) Despite not knowing Ts(t) and CO2s(t), I could eliminate them by taking the differential equation + the linear approximations and integrating like I did earlier. However, the problem is that I would have added 3 unknowns (G, H, CO2s(0)), but I would not have added any explanatory variables since I am already using CO2 in my regression. The regression in post #154 has 5 explanatory variables and 4 unknowns. A new regression would have 5 explanatory variables and 7 unknowns. So I would need to use a priori information to reduces the number of unknowns to 5 in order to be able to estimate it. I could assume that the Earth's temperature sink and carbon sink were in equilibrium in ~1850 (which might be reasonable). Alternatively, I could assume that the decay rate of the Earth's carbon sink and the decay rate of the Earth's temperature sink are the same (which might be the case for example if they are both driven primarily by ocean convection as opposed to diffusion). In any case, I'll think about making modifications to the model in post #154.

I want to retract an earlier claim I made about hurricanes. The reduction in the surface-tropopause temperature gradient due to global warming does not cause less frequent or less intense hurricanes. It was incorrect of me to think this is a mechanism that causes this. That said, the arguments 'higher temperatures -> more energy -> more hurricanes' or 'higher temperatures -> more water vapour -> more hurricanes' are incorrect as well. The reduction in the surface-tropopause temperature gradient is a result of the air carrying more water when it is warmer. As humid air moves adiabatically upward and cools, once it becomes saturated some of that water will condense to water droplets. That condensation process releases latent heat, which partially offsets the temperature loss of the air from moving upward. This is why wet air will have a lower lapse rate than dry air, and why warmer humid air will have a lower lapse rate than cooler humid air. The earth's troposphere is usually on the edge of adiabatic stability. As a result, the warming of the planet, which increases water vapour in air cancels out the reduction in the surface-tropopause temperature gradient; that is, a parcel of air moving from surface to tropopause at the edge of adiabatic stability will have exactly the same temperature as tropopause air once it reaches to tropopause, so no work to run a heat engine can be done. In order for hurricanes to form, you need adiabatic instability, which can occur if the air is on the edge of adiabatic instability and then the air near the surface is warmed slightly by the sun. Since the atmosphere is relatively transparent to sunlight, the effect of the sun will be to warm the surface more than the upper troposphere. The reason why hurricanes generally form during the summer is because there is more sunlight to warm the surface faster than the tropopause and the tropopause does not have an equilibrium temperature profile for that level of sunlight. So the extra sunlight creates adiabatic instability, which causes hurricanes. This is also why you have hurricanes form in the tropics: because the tropics have the most direct sunlight so therefore the most adiabatic instability due to the sun warming the surface more than the tropopause. Even if the waters around Britain increased to 27 C (temperatures good for hurricanes to form in the tropics today), you still wouldn't get hurricanes forming at that latitude because the sun wouldn't be strong/direct enough to create the adiabatic instability necessary. However, since global warming causes an increase in water vapour, there will be more cloud cover and the upper troposphere will be more opaque to longwave radiation from the Earth. As a result, the sun will have less ability to warm the surface more than the upper troposphere and therefore there will be less adiabatic instability. As a result, expecting less intense and less frequent hurricanes still make sense, but not due to the simplistic 'reduction in surface-tropopause heat gradient makes the heat engine less effective' argument that I gave earlier. The reduction in the polar-equatorial temperature gradient is still relevant with respect to reducing the efficiency of various climate phenomena such as tornadoes for example.

Actually, I take that back. By the definition I am using, the characteristic temperature of the heat sink is equal to the surface temperature when the Earth is in equilibrium. So at the end of the little ice age when surface temperatures were ~13-14C the heat sink temperature was equal to surface temperature.

Okay, so I simplified the model by removing the decay and the constant term on the justification that natural variation does not contribute significantly (on the time scale of a century) to changes in CO2 levels other than through planetary heating. So basically the simplified model only has two mechanisms by which CO2 levels can change; human emissions and emissions due to ocean heating and permafrost melting. So the model is: dCO2/dt = (D*CO2(0) – CD*Ts(0)) - D*CO2(t) + E*Human + DE*Integral(0 to t; Human*dt) + CD*T. Which means I can estimate this by performing the regression: dCO2/dt = β0 + β1*CO2(t) + β2*Human + β3*Integral(0 to t; Human*dt) + β4*T + error with the restriction β3/β2 = -β1. So I use the data from 1876 to 2009 to perform the Gauss-Newton estimation and these are my 95% confidence intervals for C, D, E and Ts(1876): C: -81 +/- 181 D: 0.015 +/- 0.012 E: 0.00038 +/- 0.00011 Ts(1876): 14.14 +/- 0.030 C is the CO2 emitted in ppm due to increasing the characteristic heat sink by 1 celcius. It's negative and very uncertain. Maybe I need to use an empirical value for E to better estimate this. D is in (year)^-1, and suggests that the decay time of the characteristic heat sink is ~67 years. E is in ppm per million metric tones. It suggests that about 2.6 billion metric tonnes of carbon is needed to increase atmospheric CO2 by 1 ppm. This seems to be consistent with numbers I see online (which suggests 2-3 billion metric tons). Ts(1876) corresponds to the characteristic heat sink temperature in celcius for 1876. (note that I am assuming here that global temperatures are the hadcrut4 temperature anomaly data + 14C, so if that assumption is off slightly then this estimate is off by the same amount).

Maybe. But you have to remember that there is far more ocean than ice, and that ice has a larger heat capacity. Are you saying that the justification of approximately 0 C is due to the enthalpy of fusion of ice? The other thing that is relevant here is that the ocean response is faster than the glacier response and ocean heating would be more relevant to CO2 increase than glaciers. Because I don't know the characteristic temperature of the heat sink (which corresponds to changes in CO2 released from the ocean). So I use the fact that the rate of change of temperature should be proportional to the temperature difference between the surface and the heat sink, then integrate, to get around this. Well the issue here is that it takes longer for the ocean to warm than the surface. Maybe it takes on the order of decades/centuries to catch up. And the warming of the oceans is where you are going to get most of the CO2 emissions due to temperature increase. So by including the other factors it might be possible to estimate the time scale of decay for the oceans, as well as how strong this feedback response is. But I can try your model and present the results. For the sake of discussion.

Okay, so I ran the unrestricted model: dCO2/dt = β0 + β1*CO2(t) + β2*Human_emissions(t) + β3*Integral(0 to t; Human_emissions(t)*dt) + β4*t + β5*Integral(0 to t;CO2(t)*dt)) + β6*T(t) + error Over the 1876-2009 period, nothing is very statistically significant. This maybe because the ice core CO2 data acts differently from the Mauna Loa CO2 data. If I do the same thing but over the 1959-2009 period (so only Mauna Loa data) things improve but the β1 and β5 are not very significant, which makes my estimates in the restricted model not significant. I think this suggests that either there is no excess CO2 decay effect (which wouldn't make sense because then equilibrium wouldn't be reached) or that the CO2 decay effect is too small and the time period is too short a period to measure this CO2 decay effect (more likely, since my understanding is this would be on the order of hundreds or thousands of years). In that case, perhaps I should drop the CO2 decay effect from the model on the basis that 50-100 years is too short a period for it to be significant. I could always measure it using ice core data that covers hundreds or thousands of years.

I feel so dumb right now. I made a very basic mistake back in post #94. I mixed up T(t) - Ts(t) with Ts(t) - Ts(0). Rather than substituting, I should add (1) with D*(3). Then I get: dCO2/dt - (dCO2/dt)_human - (dCO2/dt)_volcano - A - B*CO2(t) + D*CO2(t) - D*CO2(0) - D*Integral(0 to t; (dCO2/dt)_human*dt) - D*Integral(0 to t;(dCO2/dt)_volcano*dt) - ADt - BD*Integral(0 to t;CO2(t)*dt)= C*D*(T(t) - Ts(0)) If I replace change in atmospheric CO2 due to human emissions with E times human emissions and I remove the volcanic emissions by sticking it into the constant term (see my last post that suggests that volcanic CO2 eruptions are roughly constant with time) then I get: dCO2/dt - E*human_emissions(t) - A - B*CO2(t) + D*CO2(t) - D*CO2(0) - ED*Integral(0 to t; human_emissions(t)*dt) - ADt - BD*Integral(0 to t;CO2(t)*dt)= C*D*(T(t) - Ts(0)) Isolating for dCO2/dt gives: dCO2/dt = (A + D*CO2(0) - CD*Ts(0)) + (B - D)*CO2(t) + E*human_emissions(t) + ED*Integral(0 to t; human_emissions(t)*dt) + ADt + BD*Integral(0 to t;CO2(t)*dt) + CD*T(t) There are 7 dependant variables, but only 6 unknown parameters (A, B, C, D, E and Ts(0)). So I can can estimate this by performing a regression with 1 restriction. For example: dCO2/dt = β0 + β1*CO2(t) + β2*Human_emissions(t) + β3*Integral(0 to t; Human_emissions(t)*dt) + β4*t + β5*Integral(0 to t;CO2(t)*dt)) + β6*T(t) + error where the restriction is β1 = β5β2/β3 – β3/β2. Of course this restriction is non-linear. So I'll have to derive things and write the code to do the Gauss-Newton estimation. Also, with this regression, I can get an estimate of C, which means that I can calculate the characteristic heat sink temperature. So forget what I said earlier about not being able to calculate it. Edit: this error was also why I was getting nonsense earlier.

Because I am trying to account for non-ocean/permafrost emissions to get ocean/permafrost emissions to be able to estimate some useful parameters. The reason I am interested in these parameters is because my earlier regression that had change in temperature as the dependent variable and yielded a climate sensitivity of ~2 had a very low time scale of decay. So I need to figure out a good way to relax the assumption of constant decay rate towards equilibrium for temperature in order to get a better estimate of climate sensitivity. The regression could also help explain other things, such as temperature changes due to changes in the Length of the Day generally lag by ~6 years. Anyway, I've tried some simpler regressions. I regressed a constant, CO2, human emissions, and volcanic emissions on changes in CO2. The residual seems to behave very differently prior to 1958 compared to after it. This probably is a result of the fact that I use Mauna Loa CO2 data after 1959, where as before then I have to use ice-core data. The ice core data is less accurate, and was smoothed by 5 years, which means it is unlikely to show any spikes in CO2 output that might be due to volcanic activity. Using only the 1959-2009 period, volcanism isn't statistically significant and has a negative effect. From removing volcanism from the equation and looking at the residual, I see no correlation between the residual and volcanic activity. Perhaps I need to use monthly data instead, but I don't have monthly CO2 output data (though I could interpolate and then add dummies to count for seasonal effects). One possibility is that the volcanic aerosols decrease temperature, which causes a reduction in CO2 output which hides the CO2 output that is due to volcanism. But when I add temperature to the regression, the residual doesn't look much different. Another possibility is that the CO2 emission data is 'corrupted' and already includes volcanic emissions. So I looked at the residual of both change in CO2 and change in Human emission output after removing the exponential trend. But neither of the residuals resemble volcanic activity. I tried changing things such as using volcanic aerosol data directly, but I seem to get the same result. As far as I can tell, volcanism cannot significantly explain the variation in changes in atmospheric CO2 over time. Or at least this is true for large volcanic eruptions such as Krakatoa and Pinotubo. Maybe the vast majority of volcanic CO2 comes from flood volcanoes or from undersea rifts and this CO2 output is relatively constant since minor eruptions are far more frequent. From my understanding of volcanism, this could very well be the case since the volcanoes that create the massive and infrequent erruptions are rarer and they tend to release a higher stratospheric aerosol to CO2 ratio (thus the majority of the volcanic CO2 may not show up in the aerosol data). If that is the case, then perhaps I should just treat volcanic CO2 emissions as a constant and remove the volcanic aerosol proxy from the regression because it doesn't seem to explain anything.

It's in one of your ten commandments. Thou shall keep the sabbath holy. And 'thou shall not kill' is a mistranslation. It is closer to 'though shall not murder'. The bible commands people to kill those that work on the sabbath It doesn't count as murder of course because the person was violating the sabbath. Numbers 15:32.

What about people like David Cameron who claim that the killing of Lee Rigby had 'nothing to do with Islam' and that ISIS are not even 'muslim'. Harper has made similar concepts? More like on the right you have religious apologists that don't want to associate anything bad with religion and on the left you have cultural relativists who think criticizing any religion that isn't christianity is racist. I don't think this is a left-right issue, because the mainstream position across the political spectrum is to hide from reality. The people that do challenge this come from all sorts of political positions (Bill Maher to Tarek Fatah to Geert Wilders), but all of them are in the minority. More like the cities of Toronto and New York would be twittering about how they need to stop the non-existent 'counter attacks' and politicians from Obama to David Cameron to Harper would be going on about how it has nothing to do with Islam or Islamism even if the shooter was yelling allahu ackbar while killing people and released a video online clearly explaining their motive. All of the progressives would give themselves a pat on the back for not being 'racist'.

No. That's your Ben Affleck-like / 'progressivism' mental delusion making you interpret reality that way. More like the motives are unknown. There is no manifesto. No video explaining the motives. No people witnessing him decry his motives during the attack. All I have seen are some facebook comments describing that he was a vocal atheist that disliked religion. But of course the media has instantly jumped on this as the explanation. Furthermore, according to the media, the attack was due to racism because apparently 'atheists' and 'muslims' classify as races now. There is no doctrine of atheism to justify killing in the name of atheism. There are atheists of all races, genders, sexual orientations, etc. As for your claim that the vast majority of atheists are while males, I want to see evidence to back it up. This seems like a ploy to associate atheism with whiteness and maleness and thereby discredit atheism via guilt by association since white males are the most demonized group in western society today. I have a question for you. If this is the case, then could these neurological differences help explain some of the 'gender wage gap'? Or would that violate the doctrine of progressivism? I think you are confusing misogyny with advocation for gender equality (example: Karen Straughan).

And I'll dispute the claim of the feds and the RCMP. I'm with Tom Mulcair on this one, the attack on parliament hill does not classify as terrorism. That doesn't imply what the motive was. It's not like he made a video or released a manifesto explaining the justification for his action (unlike say Anders Brevik or Zehaf-Bibeau).

That attack was clearly motivated by Islamism. Though I wouldn't classify it as terrorism. As for mentally ill, that is questionable unless you want to consider all religion as a mental illness. Out of curiosity, where are you getting your information about the guy's motive? I cannot find that much information about it online.

I have to go to sleep because I have work tomorrow. But I might be way overthinking things. Maybe I should just regress change in CO2 on a constant, CO2, Human emissions and Volcano emissions and then just look at the residual.

I'll do the unrestricted regression for comparison (there are definitely no mistakes with that). dCO2/dt = H + I*CO2(t) + J*CO2_emissions + K*Volcanic_Aerosols + L*Integral(0 to t; CO2_emissions*dt) + M*Integral(0 to t; Volcanic_Aerosols*dt) + N*t + O*Integral(0 to t;CO2(t)*dt)) + error. The 95% confidence intervals of H, I, J, K, L, M, N and O are (4.28 +/- 3.64), (-1.39 +/- 1.34)x10^-2, (7.49 +/- 12.00)x10^-4, (9.21 +/- 5.11)x10^-1, (-1.52 +/- 6.15)x10^-4, (-2.39 +/- 3.14), (-4.74 +/- 3.69)x10^-2, and (1.18 +/- 21.32)x10^-4. Basically nothing is statistically significant for the unrestricted model. The issue might be that I don't have enough data to estimate my parameters. Maybe I should use monthly data or use a longer time period.

Okay, after fixing the mistake in the code the 95% confidence intervals for the coefficients A, B, D, E, and F are: (262233 +/- 3588895), (-829 +/- 12326), (3.16 +/- 153.66)x10^-4, (46.22 +/- 1.37) and (-15601554 +/- 0.1). So Human emissions and Volcanic emissions are significant. Not sure why the volcanic parameter is negative, maybe cause of the 6 month lag I used. Also, My method of error estimation is generally an overestimation for non-linear estimations. I could do f-tests to determine more accurate values. I'll have to go through my code when I have more time to make sure everything is done properly. I'm skeptical of my results. Edit: These results are nonsense. See post #149. @ Bonam - if I multiply the mean of volcanic emissions (in the arbitrary units) by the estimate of F I get -1 x 10^-5. Where as if I multiply human emissions in 2008 by the estimate of E I get 4 x 10^-5. So that's only a factor of 4 difference.

@ Bonam: I just realized I mixed up two numbers when I made my last post. The magnitudes of E and F should be 10.8 and -15601623 respectively. Actually, looking at my code again, I forgot a squared. Which means my error estimates are all off. I'll correct this, just give me a minute. No. And nether do the vast majority of scientists. The consensus on cellular respiration is pretty well established.

Not necessarily. Again the units I used for the volcanic emission data is somewhat arbitrary so that has to be taken into account. Though I can check this question for you. Just give me a minute.

A few things. Obviously if you are trying to explain changes in temperature over time you want to use the aerosol data directly. But if I am trying to explain CO2 emissions over time I need a proxy for volcanic CO2 emissions. Since aerosols decay much more quickly that CO2, I have to perform the sharpening to get a decent proxy of volcanic CO2 emissions. This is done so that the unexplained variability in my data is lower so that I can get good estimates of the parameters that I am interested in. There are a few things the regression explaining changes in CO2 over time can help answer. For one, it can help answer 'where the heat is going?' and help make predictions about how temperatures will change in the future. Also, it can help answer how much additional CO2 will be released (via ocean warming and permafrost melting) due to an increase in temperatures. Yeah, that 200 million tons / year value is fairly well known. However, it is an average and there is quite a bit of uncertainty on that value. Also, I need volcanic emissions for each year since 1876 to do my time series analysis. All I need is something that is proportional to volcanic emissions, since the regression scales it for me to explain the data. Also, using CO2 data directly can cause issues of reverse causality which is something you usually want to avoid when doing regressions. I do this for human emissions as well despite the fact that Human CO2 emissions are far more well known and it is fairly well known how many metric tonnes of CO2 correspond to how many ppm of CO2. I am basically assuming that I do not know what these values are because I don't want to make assumptions that may skew my results and cause me to underestimate my uncertainty. That's actually one of the problems of GCMs and some of the more pure physics approaches to estimating these interactions. Often they underestimate their uncertainty because they don't take into account the uncertainty on all the scaling parameters that they obtain from the scientific literature. It's not a term that is used. I was just using known words to describe a concept that I did not have a word for. Basically, you can think of the oceans + glaciers + permafrost as a 'heat sink'. They don't necessarily warm as fast as the surface. Changes in forcing (due to changes in solar irradiance, CO2, etc.) cause the surface to warm, which then warms the heat sink. If you think of this heat sink as having a single temperature, call it the characteristic temperature, then the rate of heat transfer from the surface to the heat sink is going to be proportional to the temperature difference. Just think of the characteristic temperature as a useful concept for explaining and predicting heat transfer.

Okay, so I went through with the non-linear regression of the change in CO2 on a constant, CO2, Human emissions, Volcanic emissions, the integral of Human emissions, the integral of Volcanic emissions, time, and the integral of atmospheric CO2. I used the data from 1876 to 2009. Basically I did the regression dCO2/dt = (A - D*CO2(0)) + (B + D)*CO2(t) + E*CO2_emissions + F*Volcanic_Aerosols + E*D*Integral(0 to t; CO2_emissions*dt) + F*D*Integral(0 to t; Volcanic_Aerosols*dt) - (AD)*t - (BD)*Integral(0 to t;CO2(t)*dt)) The 95% confidence intervals for the coefficients A, B, D, E, and F are: (262233 +/- 10191481), (-874 +/- 361), (2.98 +/- 0.0000018)x10^-4, (0.141 +/- 0.000025) and (1.95 +/- 0.000011)x10^-3. Though I will point out that I got the error message 'Matrix is close to singular or badly scaled' when doing the Gauss-Newton method. Only the constant is not statistically significant, which isn't that relevant. E and F are highly significant, which suggests that both volcanism and human emissions are significant at explaining changes in CO2 concentrations over time. Most relevant is the estimate of D, which if you invert it suggests that the characteristic temperature of Earth's heat sink has a decay time of 3355 years. Edit: sorry I made a mistake in my code. These parameters are nonsense. Please do not trust them.

I want to correct a claim that I made in my last post. (2.04 +/- 0.42) years for Volcanic Aerosol decay time is incorrect. I should have performed the transformation k -> -ln(1-k) on the inverse of the decay time, so the actual decay time is (1.48 +/- 0.31). I'll explain my method to get this value because it is relatively simple. I am using two data sets. One is optical aerosol depth at 550 nm (550 nm corresponds to the peak frequency of the sun. i.e. yellow light). http://data.giss.nasa.gov/modelforce/strataer/tau.line_2012.12.txt The second is a list of the list of largest eruptions in recent history. http://en.wikipedia.org/wiki/List_of_large_volcanic_eruptions_of_the_20th_century I look at the period 1876-2009 because that is the period during which all my data sets overlap. The basic idea is that aerosols in the atmosphere will decay at a particular rate, but new aerosols will be released via volcanoes. My differential equation is dA(t)/dt = C + B(t) - k*A(t), where t is time, A is the amount of volcanic aerosols, k is the decay rate of Aerosols, C is the volcanic emissions from weak volcanic eruptions and B is the volcanic emissions from strong volcanic eruptions. The reason I separate weak volcanic eruptions from strong volcanic eruptions is because weak volcanic eruptions are relatively frequent (so the emissions are roughly constant) so most of the variability will be due to the few major eruptions (I use the 88 eruptions of Volcanic Explosivity greater than 3). To represent the magnitude of emissions from strong volcanic eruptions, I define a variable, call it J, which for a given year is equal to the number of volcanic erruptions of Volcanic Explosivity 4, plus 10 times the number of volcanic erruptions of Volcanic Explosivity 5, plus 100 times the number of volcanic erruptions of Volcanic Explosivity 6 (I do this because the Volcanic Explosivity Index is logarithmic with a base of 10). Then I can just estimate k by regressing dA(t)/dt = C + D*J(t) - k*A(t) + error, where D is a constant. Then I can get volcanic emissions since C + B(t) = dA(t)/dt + k*A(t) This gives a much 'sharper' function than the original volcanic aerosol data. But with the current value I get a few years where there are negative volcanic emissions; this is most likely due to the fact that I am lagging the change in aerosols by 6 months relative to aerosols to avoid reverse causality and also due to error. If I want to ensure that all emission values are positive, I would have to drop the decay time to 1.02 years. Also, the claim I made in my last post that the literature suggests decay times of 3 years is inaccurate. Rather the 3 years corresponds to roughly the time it takes to get back to roughly background levels (http://link.springer.com/article/10.1007/BF02839287). So a decay time of 1.02 years isn't inconsistent because the decay time corresponds to the time it takes for excess aerosols to shrink to 1/e = 36.8% of the original value (and (1/e)^(3/1.02) is approximately 5%). The scientific method does not tell people what to do.

I find the double standard that the politicians and media have quite interesting. Muslims kill atheists while yelling Allahu Akbar. -> Media tells us it has nothing to do with Islam. An atheist kills 3 muslims. -> Media tells us it is a hate crime that is motivated by hatred of Islam.