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Found 3 results

  1. I had some time this week, so I thought I would start a thread to discuss the question of what is the correct value of climate sensitivity for Earth with respect to the effects of CO2. For those that do not know, the definition of equilibrium climate sensitivity is the change in global average temperature in the long run due to a doubling of atmospheric CO2. This is partially a response to link to a scientific paper that estimated climate sensitivity that was linked in a post written by TimG back in July. http://www.mapleleafweb.com/forums/topic/23797-agwcc-deniers-fake-skeptics-their-mindset/?p=982902 http://www.sciencedirect.com/science/article/pii/S0304380014000404 The paper estimated transient climate response to be 1.093 °C and equilibrium climate sensitivity to be 1.99 °C. I mentioned to Tim that I thought that this was too low and did not agree with most other estimates of climate sensitivity that use other methods (though I did agree that many estimates, especially by the IPCC, were too high). I mentioned I would look at the details of the paper. If you haven't read the paper I recommend it (though you may need to pay or have access via some institution to read it). It is relatively short and uses a very simple approach to estimate climate sensitivity that relies primarily on empirical evidence and avoids making too many assumptions about the Earth's climate, which most models tend to do. Anyway, I looked into the paper and I saw a number of flaws in the methodology that could lead to an underestimation of climate sensitivity according to the empirical data. I'll discuss them and calculate a first-order correction to the estimates given in the paper. I was going to post this months ago but things got in the way. Anyway, what I find is that after first order corrections, the transient climate response is approximately 1.98 °C and the equilibrium climate sensitivity is 3.60 °C. Edit: Btw, if you can't access the paper, the methodology in the paper is basically: Look at global temperature record since 1850, detrend the data to take into account 60 year and 20 year climate cycles that correspond to events such as the Pacific Decadal Oscillation and the Atlantic Multidecadal Oscillation, assume that the anthropogenic warming after WW2 has been roughly linear since CO2 concentrations have been increasing roughly exponentially while solar forcing is logarithmic, assume that the vast majority of the warming prior to 1950 was natural due to the ending of the little ice age, obtain the anthropogenic warming since 1950 by subtracting the rate of natural warming, use the CO2 data since 1959 (I think Mauna Loa data is used) to give an estimate of transient climate sensitivity, and finally use the ratio of transient climate sensitivity to equilibrium climate sensitivity determined by various IPCC models to obtain an estimate of equilibrium climate sensitivity. WARNING: the rest of this post contains math and science. If you are afraid of math and science I suggest you run away and cry in a corner. A. Logarithm of Exponential So my biggest issue with the paper by Craig Loehle is the following statement: “The log of an exponentially rising function (as CO2 is) is of course a straight line” So I'll start by establishing the validity of the premises used for the benefit of the readers. Solar forcing is an approximately logarithmic function of CO2 concentrations; as a result, global average temperature is as well. That is, Temperature = A + B*ln(CO2 concentration), where A and B are some constants. There are many different justifications for this and the idea of this logarithmic relationship can be traced back all the way to 1896 by a guy called Svante Arrhenius. I may give a theoretical justification for this approximation in a later post (for the sake of the readers), but basically the logarithmic relationship is a very good approximation that is used by the IPCC and others. The second premise is that atmospheric CO2 has been exponentially rising since WW2. This is sort of true, although the statement can be misleading. If you take annual CO2 data from the Mauna Loa observatory (available at http://cdiac.ornl.gov/ftp/trends/co2/maunaloa.co2), then while the rate of change is approximately exponential a simple exponential fit with no constant added to the data set does not work very well. In order to get a good exponential fit to the data set you have to add a constant to the exponential. For example CO 2_ppm = 270 + 38.131*exp(0.0193(year-1950)) gives a very good fit to the data set with an R-squared value of 0.9984. Interestingly, 270 ppm corresponds to the 'pre-industrial' levels of atmospheric CO2. As for the claim that the log of an exponential function is a straight line, this is only true if there is no constant term added to the exponential. That is, ln(exp(x)) = x. But ln(a + exp(x)) != x if a!= 0. And in the case of an exponential fit to the CO2 record since WW2, we have a constant, the 270 ppm. This means that the logarithm of atmospheric CO2 concentrations is not a straight line. In an extreme case where the constant is much larger than the exponential term, the logarithm of the exponential is approximately an exponential. However, in the case of the logarithm of atmospheric CO2 concentrations since WW2, we have an intermediate situation where the magnitude of the constant is comparable with the magnitude of the exponential term. Since the time period used to estimate the anthropogenic warming is 1950-2010, for the sake of the discussion I'll take a Taylor approximation around the midyear (1980) as the logarithm of atmospheric CO2 concentrations: ln(270 + 38.131*exp(0.0193(year-1950))) ≈ ln(270 + 68.04*exp(0.0193(year-1980))) ≈ ln(338.04) + 68.04*0.0193/(338.04)*(year-1980) + 0.01932*270/68.04/(1+270/68.04)2/2*(year-1980)2 + higher order terms ≈ 58.2316423 + 0.00388466(year-1980) + 0.0000299417(year-1980)2 + higher order terms Note that the magnitude of (year-1980) is at most 30 since we are talking about 1950-2010. As a result, the magnitude of the linear term is at most 0.1165398 where as the magnitude of the quadratic term is at most 0.02694753. That is, the quadratic term is at most 23% the magnitude of the linear term. I would argue that the quadratic term being up to 23% as significant as the linear term suggests that the quadratic term should not be neglected. If this is the case then the logarithm of atmospheric CO2 concentrations should at least be considered a quadratic function of time, not a linear function of time. The higher order terms diminish in magnitude rapidly and are not very significant. For the sake of simplicity and to perform a first order correction to the Craig Loehle paper, let's suppose that the natural logarithm of CO2 is an approximately quadratic function of time, ln(CO2_ppm) ≈ 58.2316423 + 0.00388466(year-1980) + 0.0000299417(year-1980)2. Note that since Craig Loehle assumes that the change in the logarithm of CO2 concentrations have been approximately linear rather than quadratic, and since the coefficient in front of the quadratic term is positive, this means that Craig Loehle's assumption should bias his estimate of transient climate response downward and as a result, the estimate of equilibrium climate sensitivity is an underestimation. B. Definition of Transient Climate Response My second issue with the Craig Loehle paper is that the paper assumes that the warming since WW2 is the result of the transient climate response and then goes on to assume that what is calculated in the paper comparable with the transient climate responses calculated by others and given in the IPCC report. I understand why this was done, but ultimately the definition of transient climate response used by the IPCC differs from what is calculated by Craig Loehle. Let's look at the IPCC's definition of transient climate response: “A measure requiring shorter integrations is the transient climate response (TCR) which is defined as the average temperature response over a twenty-year period centered at CO2 doubling in a transient simulation with CO2 increasing at 1% per year.” http://www.ipcc.ch/ipccreports/tar/wg1/345.htm That is, the transient climate response according to the IPCC is approximately the magnitude of temperature change (assuming initially being in long run equilibrium) after the natural logarithm of CO2 concentrations have been increasing about ln(1.01) ≈ 0.00995 per year for ln(2)/ln(1.01) ≈ 69.66 years. However, the global situation since WW2 is that the natural logarithm of CO2 concentrations have been increasing quadratically over time at a rate of 0.002986 per year in 1950 to a rate of 0.004783 in 2010. That is, the rate of increase of the natural logarithm of CO2 concentrations since WW2 is much less than the scenario in the definition of transient climate response used by the IPCC and time period (1950 to 2010 = 60 years) of CO2 concentration increase is less than the 69.66 years used in the definition of transient climate response used by the IPCC. To be fair, Loehle tries to correct for this by taking into account that the increase in ln(CO2_ppm) was only about 0.326 of a doubling over 54 years. However, the overall effect of the difference in definition is that Loehle underestimates the transient climate response and I will explain why this is below. In order to perform a first order correction to the transient climate response value calculated by Craig Loehle and take into account the different definition of transient climate response used by the IPCC, I'll make the following assumption: the rate of change in global temperature in a given year is proportional to the difference between the current global temperature and the long run equilibrium global temperature at the current atmospheric CO2 levels. That is, global temperature should exponentially decay towards the long run equilibrium global temperature for a given level of atmospheric CO2. This is a reasonable assumption without further a priori information and I'll appeal to the scientific principle of Occam's Razor to justify it. Suppose that global temperature is an approximately logarithmic function of atmospheric CO2 concentrations (again this is a common assumption used by the IPCC and others). Furthermore, suppose that the effect of various positive and negative feedbacks acts as a multiplier to the initial change in temperature due to changing the atmospheric CO2 concentration (again a common assumption used by the IPCC and others). Then the long run equilibrium temperature for Earth at a given atmospheric CO2 concentration is a logarithmic function of atmospheric CO2. That is, long run temperature = A + S/ln(2)*ln(CO2_ppm), where A is some constant and S is the equilibrium climate sensitivity. Now if we use the assumption that the rate of change in global temperature in a given year is proportional to the difference between the current global temperature and the long run equilibrium global temperature at the current atmospheric CO2 levels then the change in global temperature over time is: dT/dt = k*(A + S/ln(2)*ln(CO2_ppm) - T), where k is some unknown positive constant and T is the global average temperature. C. IPCC Transient Climate Response Scenario Under the IPCC scenario for transient climate response, the natural logarithm of CO2 is a linear function of time, that is ln(CO2_ppm) = B + ln(1.01)*t. If we put this into the equation from part B, we get the differential equation dT/dt = kA + kS/ln(2)*B + kS/ln(2)*ln(1.01)*t - kT. Note that since the climate is in equilibrium at t = 0 under the transient climate response scenario, 0 = kA + kS/ln(2)*B - kT0 => T0 = A + S/ln(2)*B, where T0 is the global average temperature at t = 0. Thus the differential equation can be rewritten as dT/dt = k(T0 + S/ln(2)*ln(1.01)*t - T) . To solve for the above differential equation, make the substitution V = T - T0 - S/ln(2)*ln(1.01)*t. Then dV/dt = dT/dt - S/ln(2)*ln(1.01) and the above differential equation becomes dV/dt + S/ln(2)*ln(1.01) = -kV => dV/dt = -k(V + S/k/ln(2)*ln(1.01)). Now do the substitution U = V + S/k/ln(2)*ln(1.01). Then dU/dt = dV/dt and the differential equation becomes dU/dt = -kU. The general solution to this differential equation is U = C*exp(-kt), where C is some constant. Thus V = C*exp(-kt) - S/k/ln(2)*ln(1.01) and we get: T = C*exp(-kt) - S/k/ln(2)*ln(1.01) + T0 + S/ln(2)*ln(1.01)*t. Using the fact that the Temperature is T0 at t = 0 gives: T0 = C*exp(-k0) - S/k/ln(2)*ln(1.01) + T0 + S/ln(2)*ln(1.01)*0 => 0 = C - S/k/ln(2)*ln(1.01) => C = S/k/ln(2)*ln(1.01). Thus the differential equation can be rewritten as: T = S/k/ln(2)*ln(1.01)*(exp(-kt)-1) + T0 + S/ln(2)*ln(1.01)*t. Using a quadratic Taylor approximation of exp(-kt) gives: T = S/k/ln(2)*ln(1.01)*(1-kt+k2t2/2-1) + T0 + S/ln(2)*ln(1.01)*t => T = T0 + S/2/ln(2)*ln(1.01)*k*t2. Thus under the IPCC transient climate response scenario, global temperatures should increase approximately quadratically for the first 69.66 years. In order to get the temperature change at 69.66 years, plug in t = 69.66 = ln(2)/ln(1.01). => T = T0 + S/2/ln(2)*ln(1.01)*k*(ln(2)/ln(1.01))2 => T - T0 = S/2*k*ln(2)/ln(1.01). Note however that T - T0 is approximately the transient climate response. Thus the ratio of the equilibrium climate sensitivity to the transient climate response is S/(T - T0) = 2/k*ln(1.01)/ln(2). In the paper, Craig Loehle uses the IPCC ratio between equilibrium climate sensitivity and transient climate response of 1.81761. Using this value, one can calculate k. k ≈ 2*ln(1.01)/ln(2)/1.81761 ≈ 0.01579579. The inverse of k is 63.308, which means that the difference between the current global temperature and the equilibrium global temperature at current atmospheric CO2 decays by a factor of e in approximately 63.308 years. D. 1950-2010 Scenario Under the 1950-2010 scenario, the natural logarithm of CO2 is a quadratic function of time, that is ln(CO2_ppm) = 58.2316423 + 0.00388466(t-1980) + 0.0000299417(t-1980)2. If we put this into the earlier equation, we get the differential equation dT/dt = k(A + S/ln(2)*(58.2316423 + 0.00388466(t-1980) + 0.0000299417(t-1980)2) - T). Under the assumption of Craig Loehle, the climate is in equilibrium at t = 1950, so 0 = k(A + S/ln(2)*(58.2316423 + 0.00388466(-30) + 0.0000299417(-30)2) - T1950) => A = T1950 - S/ln(2)*58.14205003, where T1950 is the global average temperature in 1950. Thus the differential equation can be rewritten as dT/dt = k(T1950 + S/ln(2)*(0.08959227 + 0.00388466(t-1980) + 0.0000299417(t-1980)2) - T) . To solve for the above differential equation, make the substitution V = -T1950 - S/ln(2)*(0.08959227 + 0.00388466(t-1980) + 0.0000299417(t-1980)2) + T. Then dV/dt = dT/dt - S/ln(2)*(0.00388466 + 0.0000598834(t-1980)) and the above differential equation becomes dV/dt + S/ln(2)*(0.00388466 + 0.0000598834(t-1980)) = -kV => dV/dt = -k(V + S/k/ln(2)*(0.00388466 + 0.0000598834(t-1980))). Now do the substitution U = V + S/k/ln(2)*(0.00388466 + 0.0000598834(t-1980)). Then dU/dt = dV/dt + S/k/ln(2)*0.0000598834 and the differential equation becomes dU/dt - S/k/ln(2)*0.0000598834 = -kU => dU/dt = -k(U - S/k2/ln(2)*0.0000598834). Now do the substitution W = U - S/ k2/ln(2)*0.0000598834. Then dW/dt = dU/dt and the differential equation becomes dW/dt = -kW. The general solution to this differential equation is W = C*exp(-k(t-1980)), where C is some constant. Thus U = C*exp(-k(t-1980)) + S/k2/ln(2)*0.0000598834, V = C*exp(-k(t-1980)) + S/k2/ln(2)*0.0000598834 - S/k/ln(2)*(0.00388466 + 0.0000598834(t-1980)) and we get: T = C*exp(-k(t-1980)) + S/k2/ln(2)*0.0000598834 - S/k/ln(2)*(0.00388466 + 0.0000598834(t-1980)) + T1950 + S/ln(2)*(0.08959227 + 0.00388466(t-1980) + 0.0000299417(t-1980)2) Using the fact that T = T1950 when t = 1950 gives: 0 = C*exp(30k) + S/k2/ln(2)*0.0000598834 - S/k/ln(2)*(0.00388466 + 0.0000598834(-30)) + S/ln(2)*(0.08959227 + 0.00388466(-30) + 0.0000299417(-30)2) = C*exp(30k) + S/k2/ln(2)*0.0000598834 - S/k/ln(2)*(0.002088158) => C = exp(-30k)*S/k/ln(2)*(0.002088158 - 0.0000598834/k) Thus the differential equation can be rewritten as: T = exp(-k(t-1950))*S/k/ln(2)*(0.002088158 - 0.0000598834/k) + S/k2/ln(2)*0.0000598834 - S/k/ln(2)*(0.00388466 + 0.0000598834(t-1980)) + T1950 + S/ln(2)*(0.08959227 + 0.00388466(t-1980) + 0.0000299417(t-1980)2) For the sake of consistency with what I did with the IPCC scenario, I will take the quadratic Taylor approximation of exp(-k(t-1950)) around t = 1950: => T ≈ (1 - k(t-1950) + k2(t-1950)2/2)*S/k/ln(2)*(0.002088158 - 0.0000598834/k) + S/k2/ln(2)*0.0000598834 - S/k/ln(2)*(0.00388466 + 0.0000598834(t-1980)) + T1950 + S/ln(2)*(0.08959227 + 0.00388466(t-1980) + 0.0000299417(t-1980)2) => T - T1950 ≈ S/ln(2)*( (1 - k(t-1950) + k2(t-1950)2/2)/k*(0.002088158 - 0.0000598834/k) + 1/k2*0.0000598834 - 1/k*(0.00388466 + 0.0000598834(t-1980)) + 0.08959227 + 0.00388466(t-1980) + 0.0000299417(t-1980)2 ) = S/ln(2)*( 0.002088158/k - 0.0000598834/k2 - 0.002088158(t-1950) + 0.0000598834/k*(t-1950) + 0.001044079*k*(t-1950)2 - 0.0000299417*(t-1950)2 + 0.0000598834/k2 - 0.00388466/k - 0.0000598834/k*(t-1980) + 0.08959227 + 0.00388466(t-1980) + 0.0000299417(t-1980)2 ) Converting the (t-1980) terms to (t-1950) terms gives: T - T1950 ≈ S/ln(2)*( 0.002088158/k - 0.0000598834/k2 - 0.002088158(t-1950) + 0.0000598834/k*(t-1950) + 0.001044079*k*(t-1950)2 - 0.0000299417*(t-1950)2 + 0.0000598834/k2 - 0.00388466/k - 0.0000598834/k*(t-1950) + 0.001796502/k + 0.08959227 + 0.00388466(t-1950) – 0.1165398 + 0.0000299417(t-1950)2 – 0.00176502*(t-1950) + 0.02694753 ) = S/ln(2)*0.001044079*k*(t-1950)2 That is, the temperature response after 1950 due the 1950-2010 scenario should be approximately quadratic and the temperature change by 2010 should be approximately S/ln(2)*3.7586844*k. Note however that Craig Loehle assumed that the change in temperature response due to increased CO2 levels from 1950 to 2010 was linear. If the actual temperature is quadratic with a positive quadratic term then Craig Loehle underestimated the amount of warming from 1950-2010 when using a linear line of best fit. Using the value k ≈ 0.01579579 that was calculated earlier using the IPCC values, one obtains T - T1950 ≈ S/ln(2)*0.0000164920526*(t-1950)2. Plotting 0.0000164920526*(t-1950)2 from 1950 to 2010 and performing a least squares line of best fit gives a line equation of -1.9393 + 0.00098952t. This means that if one accepts the premises used by Craig Loehle (that the climate was basically in equilibrium prior to WW2 and the signal decomposition approach used to obtain the anthropogenic effect is correct) then the expected anthropogenic warming from 1950-2010 should be S/ln(2)*0.098952 per century. Craig Loehle calculates ‘transient climate response’ by taking this post WW2 warming, multiplies it by 0.54 and divides it by 0.326 to take into account the fact that according to CO2 records, only a 32.6% of a doubling in the CO2 levels occurred in the 54 year period from 1959 to 2013. This means that what Craig Loehle calculates as ‘transient climate response’ is actually S/ln(2)*0.098952*0.54/0.326 ≈ 0.23647*S. This means that the ratio between the true equilibrium climate sensitivity and what Craig Loehle calculates as ‘transient climate response’ is approximately 1/0.23647 ≈ 4.22887. But Craig Loehle assumes that what is measured is the true ‘transient climate response’ and uses the IPCC ratio of 1.81761 between equilibrium climate sensitivity and transient climate response. This means that Craig Loehle is underestimating both transient climate response and equilibrium climate sensitivity by a factor of 4.22887/1.81761 ≈ 2.3266. E. Earth was not in Equilibrium in 1950 My final issue with the Craig Loehle paper is that it assumes that the Earth was in climate equilibrium in 1950. This despite the fact that atmospheric CO2 concentrations were rising prior to 1950 and by 1950 were about 308 ppm, which is significantly higher than pre-industrial levels of 270 ppm. As a result, the assumption that the Earth was basically in climate equilibrium in 1950 is questionable. Furthermore, if the Earth was in climate equilibrium in 1950 and all of the anthropogenic warming prior to 1950 is due to CO2 emissions after 1950 then as shown in part D, the temperature response should be approximately quadratic and should be approximately 0 at 1950. However, what is actually observed is that the Earth is warming at a non-zero rate even at 1950. This suggests that some of the anthropogenic warming observed from 1950 to 2010 must be due to CO2 emissions that occurred before 1950. In order to separate warming due to emissions prior to 1950 to warming due to emissions after 1950, I used the information provided on Figure 1b of the Craig Loehle paper. Theoretically, I could try to reconstruct this data set and do the entire signal decomposition, but that is very time consuming. Instead, I tried to take the data points from the jpeg image of the graph. Of course, due to human error and pixilation, my values are slightly different from the true values. In any case, a linear line of best fit to the 1950-2010 data set I tried to obtain from Figure 1b is 0.040 + 0.0064*(year-1950). This corresponds to the actual line of best fit given of Figure 1b, which is 0.054 + 0.0066*(year-1950). The differences between the two values are most likely due to error when I tried to extrapolate the values of temperature anomaly from the graph. To try to account for this, I’ll multiply my values by 1.02, which gives a line of best fit of 0.041 + 0.0066*(year-1950). This gives the same slope, though a different intercept. However, the value of the intercept won’t be relevant for the calculations that I am about to do. I’ll assume that my modified values are ‘good enough’ and move on. So the reason I needed to infer the temperature anomaly data set used by Craig Loehle for the 1950-2010 period is because his simple linear fit doesn’t give me enough degrees of freedom to separate warming due to CO2 emissions prior to 1950 with warming due to CO2 emissions after 1950. Furthermore, it was argued in part E that the temperature anomaly over this time period should be approximately quadratic not linear. From figure 1b, it does appear that the rate of anthropogenic warming is increasing over the 1950 to 2010 time period. In any case, a quadratic least squares fit to my values gives an equation of temperature anomaly = 0.078918 + 0.0027006*(year-1950) + 0.0000644*(year-1950)2. Taking the derivative of the temperature anomaly with respect to the year gives the rate of temperature increase due CO2 emissions to after removing noise. This is 0.0027006 + 0.0001288*(year-1950). Note that when the year is 1950, the rate of temperature increase is nonzero. As explained earlier, this non-zero increase must be due to CO2 emissions that occurred prior to 1950. Furthermore, in part C it was shown that the climate decays by a factor of e towards its long run equilibrium in approximately 63.308 years. The temperature response after 1950 due to CO2 emissions that occurred prior to 1950 should be approximately E*(1 – exp(-k(year-1950))), where E is some unknown constant. The derivative of this with respect to the year is E*k*exp(-k(year-1950)). Setting the year to 1950 means that the rate of increase of temperature response per year is E*k. Setting this equal to the 0.0027006 that was obtained by the quadratic fit to the temperature response data suggests that E = 0.0027006/k. For the sake of consistency, I’ll again perform a quadratic taylor approximation of the exponential to get an approximation of the temperature response due to CO2 emissions prior to 1950, which gives: temperature response = 0.0027006/k*(k(year-1950)– k2(year-1950)2/2) ≈ 0.0027006*(year-1950) – 0.0013503*k*(year-1950)2. Subtracting the temperature response due to CO2 emissions prior to 1950 from the observed temperature response gives the temperature response due to CO2 emissions after 1950. This gives: temperature response due to CO2 emissions after to 1950 = 0.078918 + 0.0027006*(year-1950) + 0.0000644*(year-1950)2 - 0.0027006*(year-1950) + 0.0013503*k*(year-1950)2 ≈ 0.078918 + 0.000085729*(year-1950)2 if we use k ≈ 0.01579579, which was calculated in part C. Thus the difference between the temperature anomaly in a given year to the temperature anomaly in 1950 that is due to emissions that occurred after 1950 is approximately 0.000085729*(year-1950)2. However, in part D, it was shown that difference between the temperature anomaly in a given year to the temperature anomaly in 1950 that is due to emissions that occurred after 1950 should be roughly S/ln(2)*0.001044079*k*(year-1950)2. Equating this with the estimate from the last paragraph gives 0.000085729 = S/ln(2)*0.001044079*k. Isolating for the equilibrium climate sensitivity gives S = 0.000085729*ln(2)/ 0.001044079/k ≈ 3.603 °C. Dividing by the 1.81761 ratio suggests that the transient climate response is approximately 1.98 °C. F. Conclusion The Craig Loehle paper suggests that the transient climate response of Earth and the equilibrium climate sensitivity of Earth are approximately 1.09 °C and 1.99 °C respectively. While the Craig Loehle paper has a number of strengths such making few assumptions about the climate of the Earth, having a relatively small confidence interval and appealing directly to empirical data, the paper makes 3 assumptions significantly skew the estimation of these parameters. The 3 assumptions are that the logarithm of atmospheric CO2 concentrations is a linear function of time since WW2, Craig Loehle’s definition of ‘transient climate response’ is the same as what is used by the IPCC, and that the Earth roughly in climate equilibrium with respect to CO2 concentrations in 1950. In this post, I try to relax the three assumptions and perform a first order correction to the calculations of Craig Loehle. Relaxing the first two of these assumptions suggests that Craig Loehle underestimates both the transient climate response and equilibrium climate sensitivity by a factor of 2.33, though this gets offset slightly after relaxing the 3rd assumption. Overall, I find that after first order corrections, the transient climate response is 1.98 °C and the equilibrium climate sensitivity is 3.60 °C. These values are 81% higher than the values calculated by Craig Loehle. The 95% confidence intervals for these values are approximately the confidence intervals calculated by Craig Loehle multiplied by 1.81. Edit: My numbers are slightly off for a reason I explain in post #18. The corrected values are 1.62°C and 2.95°C for transient climate response and equilibrium climate sensitivity respectively. Edit 2: Later on, I make the claim that 2.95 C might be an overestimate of the ECS due to the assumption of constant decay towards equilibrium. This would only hold if I took the equilibrium to mean the Earth System Sensitivity rather than the ECS. So there is no reason to expect that 2.95 C is an overestimate of the ECS. Edit 3: Actually, since the rate of change in solar irradiance from 1850-1950 is larger than from 1950-2010, the assumption of constant 'natural warming' by Loehle results in an underestimate of climate sensitivity since natural warming should have been slower during the second period. As a result, 2.95 C is an underestimate of the best estimate of equilibrium climate sensitivity (due to the uncertainty, the result should not be significantly different from 3C). Edit 4: Actually, if you take into account the fact that only about 76% of changes in greenhouse gas forcing is due to CO2 (with CH4, N2O and other gases contributing the rest) then this suggests a climate sensitivity of approximately 2.25 C.
  2. In May of 2013, for the first time in at least 3.8 million.....possibly even 16 million years, atmospheric carbon dioxide levels broke past the 400ppm mark. The Scripps Institution of Oceanography records of atmospheric carbon dioxide levels show that Jan. 1 was the first day of the new year above that concentration, followed by Jan. 3 and Jan. 7. Daily averages have continued at this level or higher through Jan. 9, though they could continue to dance up and down around that mark due to day-to-day variations caused by weather systems. But even with those fluctuations, 2015 will likely see many months above 400 ppm, possibly starting with the very first month of the year. “My guess at this point is that January 2015 will be very slightly above 400 ppm, but it's too early to tell for sure,” Ralph Keeling, the scientist in charge of the CO2 monitoring project atop Hawaii’s Mauna Loa, said in an email. Keeling’s father, Charles, began the project in 1958. The graph that shows the decades-long rise in CO2 is eponymously called the Keeling Curve. The 400 ppm mark was first passed on May 9, 2013. In 2014, it happened two months earlier, in March. The average CO2 concentrations for March, April and June 2014 were all above 400 ppm, the first time that has been recorded. The peak CO2 measurement of 2014 was just shy of 402 ppm in May. At the Mauna Loa Observatory on the Big Island of Hawaii, back in the 1950's, a young atmospheric scientist named Charles Keeling started a project to measure CO2 and keep weekly records. It was not expected to be of great importance aside from providing a basic understanding of how much gas levels varied in the atmosphere from region to region, and whether CO2 levels varied much from place to place and over time. What they discovered was that there wasn't much geographic difference from other areas measuring CO2, but they did notice a slow upward progression of rising Co2 levels from year to year....when they began, atmospheric CO2 levels were averaging around 315ppm, but what's most alarming, is that the rate of increase has been rising as the decades progress. Our planet has many positive and negative feedback effects, which alternatively, force more carbon into the atmosphere and sequester carbon back into the oceans and rock layers - especially along mountain ranges. The problem for a creature that has the capacity to move the dials and push up carbon dioxide levels, beginning with setting fires for various purposes and using wood for heating - is that high concentrations of atmospheric CO2 that had previously only occurred during periods of excessive volcanic activity, are detrimental for life as a whole and lead to cascading effects of species dieoffs, until the much slower carbon sequestration effects of rock weathering can bring CO2 levels back to levels that are idea for the majority of life in the biosphere. Over the ages, it has been noticed that, as rock analysis of ancient gas levels have become more reliable, that CO2 levels have gradually declined over time. At first, when there were no oxygen-breathing life forms and only anaerobic bacteria, the planet was rich in both carbon dioxide and methane. But, over time, the Sun has grown hotter and thrown off more energy, and flourishing of life on Earth has depended on sequestering more and more carbon. So, for most of the last 20 or more million years, atmospheric CO2 levels stayed below 300! That is an important point to keep in mind, as we break through the 400 barrier permanently. We, as a species, have never had to live on a 400ppm CO2 planet. One where sea levels are much higher, most of the world's ice is melted, except for the eastern ice sheets of the Antarctic. And, what's most important is that, in the past, the increases to Co2 caused by planetary changes, occurred at much slower rates than what we've done since the Industrial Era began 150 years ago, and carbon levels were about 280ppm. The changes, just from what we've put up there now....never mind what we are going to add over coming decades and what we can expect (1 degree C) from the latent heating effects still stored in the oceans, will take centuries or longer to realize their full effects. Yet, here we are in 2015, with no real plausible efforts being made to stop carbon production, let alone find ways to reduce CO2 levels. This is a point where I differ with Waldo - because I don't see the big green business crowd pushing their windmills and solar panels sales as any kind of permanent solution to climate change! Real change is not going to come without addressing global population level increases, and more importantly, the modern system of capitalist economics which rewards short term thinking rather than long term planning, and delivers most of the benefits to a small greedy and powerful elite at the top of the money pyramid, while everyone further down the line, works harder and harder in an effort to buy more stuff and imitate the extravagant lifestyles of our perceived betters. Dialing back consumer-driven capitalism is going to be even harder now than it was a half century ago at the beginning of the TV age! A number of recent psychology studies are finding that the same pernicious effects seen in excessive TV viewing over the years...increased narcissism and materialism, are enhanced by all of our new hand held toys - "smart" phones, laptops, Ipads etc.. The modern environmental movements look more like shallow attempts to pretend to be dealing with a problem that others defer right from the start by denying it even exists! So, is the future a struggle between global warming deniers and global warming pretenders who think having a solar panel or an electric car means they've done their part to fix Planet Earth!
  3. http://arstechnica.com/science/2013/12/billion-dollar-climate-denial-network-exposed/ Strange how conservative posters on MLW have also been so blindly in support of bad science funded by corporate dollars. On one hand, we have climate change researched by scientists. On the other hand we have climate change deniers being pushed by billions of dollars donated from corporations and ultra wealthy conservatives into conservative think tanks. ... And for some reason... conservative partisans choose to support the people with the most to lose from changing business practices...
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