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present 2013 thus below i show the percentiles where red values indicate the observed temperature trend is running hot relative to the models 75th percentile means the observed trend is larger than 75 of the model runs over that same period and blue indicates the observed temperature trend is running cool relative to the models the list of models included can be found here in order to avoid too strongly overweighting certain models relative to others i have restricted the number of runs to include per model to a maximum of 5 the temperature observations come from the cowtan and way 2014 kriging of hadcrutv4 here is the result if we look at all trends over this period that span 15 years or more from a glance it appears that there is a good deal more blue than red here suggesting that a lot of the observed trends are running towards the cooler end of models some recent papers eg risbey et al 2014 have been looking at the hiatus and in particular 15 year trends arguing that the most recent low 15 year trend doesn t necessarily provide evidence of oversensitive cmip5 models because these models cannot be expected to simulate the exact phasing of natural variation they point out that at points in the past the observed 15 year trends have been larger than that of the models there is some support for that in the above graph as shorter trends ending around 1970 or in the 1990s tended to be towards the higher end of model runs moreover i think that anybody suggesting that the difference between observed and modeled trends during the hiatus was due solely to oversensitivity in models is misguided that being said i think if we move past the models are wrong vs models are right dichotomy and onto the adult question of are models on average too sensitive in their transient responses we can agree on the following given the apparent large contribution of internal variability to 15 year trends seeing these observed trends in both the upper and lower percentiles of modeled trends is to be expected even if models on average were too sensitive in the transient by say 35 in the case of models being too sensitive we would simply expect to see more trends in the lower percentiles than higher percentiles as above however i think a more striking picture emerges if we look at only 30 year or longer trends where some of the higher frequency variations are filtered out here we see that depending on start and end year picked the observed trends generally fluctuate between the 2nd and 50th percentiles of model runs this seems to be strong evidence that the cmip5 runs are on average running too hot otherwise one might expect the observed trends to fluctuate more evenly above and below the 50th percentile whether they are running too hot because of incorrect forcings or oversensitivity cannot be divined from the above figure but i think it provides stronger evidence that the models are running warm than the single most recent 15 year period script available here comments 8 june 13 2014 estimating ecs bias from local feedbacks and observed warming patterns example with gfdl cm3 filed under uncategorized troyca 10 45 pm 1 introduction typical energy balance methods such as otto et al 2013 or masters 2014 have been frequently used for estimating equilibrium climate sensitivity ecs over the instrumental period recently several studies have raised the possibility that these may be biased even if one were to precisely pin down the magnitude of the aerosol forcing and the current top of atmosphere toa energy imbalance in particular the net feedback or radiative restoration parameter typically represented by lambda may be different when calculated over the instrumental period vs the long term idealized co2 only simulations one could partition this into two factors 1 inhomogenous forcings certain forcings such as aerosols may be concentrated in higher latitude regions where the net feedback is smaller thereby cancelling out more of the homogenous greenhouse forcing when looking only at the globally averaged toa imbalance this was raised recently in the kummer and dessler 2014 extension of the shindell 2014 forcing enhancement from tcr to ecs although as discussed previously the enhancements in tcr and ecs are very different 2 time varying sensitivity armour et al 2013 suggest that this may result from time invariant local feedbacks with only the spatial warming pattern changing over time and triggering these local feedbacks in changing proportions over time in fact if we take the armour et al 2013 view both 1 and 2 have the same root cause the differing spatial warming pattern between the transient instrumental warming pattern case and the long term idealized 2xco2 scenarios run in the models 2 method if you will recall one of my criticisms of shindell et al 2014 was that it did not consider the observed spatial warming pattern essentially when determining forcing enhancements it relied on the gcm output for a the ratio of the localized temperature response relative to the global response essentially the relative heat capacity of each region b the spatial warming pattern in the idealized ghg scenarios c the spatial warming pattern over the historical instrumental period while a and b may need to be relied upon it seems as though one could use the information from c during the observed instrumental period rather than relying on something that gcms do poorly regional warming projections response to aerosols and horizontal heat transfer moreover an ensemble of runs from a gcm will not be able to reproduce the exact variability seen in the single realization of the instrumental period to me it seems more likely that gcms might be more correct and agree better on a and b than they would on c but even if they are not at least it is one less assumption that needs to be made regarding gcm accuracy by analogy i think there is a reasonable method for determining the bias in ecs when calculated over the instrumental period essentially for different gcms we would calculate a the zonal net feedback according to the gcm we do this by first calculating the forcing for each zone using the difference in toa imbalance for the last 25 years of the fixedsst regressions sstclim4xco2 sstclim then for each zone we calculate the difference in toa balance between the abrupt4xco2 experiment and the picontrol experiment subtract the forcing calculated in the prior step and normalize this by the local temperature increase calculated as the difference between abrupt4xco2 and the picontrol note this relies on the assumption of armour et al 2013 that the increase in surface temperature in one region primarily affects the outgoing radiative response locally rather than over some other area at the end we have an n x 1 column vector a with n being the number of zones b the spatial warming pattern over the idealized scenario from the gcm that we will use as a baseline for example if one were interested in how inhomogenous forcings may create a bias in energy balance estimates over the instrumental period one might use the historicalghg or abrupt4xco2 scenario over a time period similar to the length of the historical period if on the other hand one wanted to figure out the combined effect of those inhomogenous forcings time varying sensitivity one would use the spatial warming pattern of a run that had achieved radiative equilibrium after a doubling of co2 regardless we calculate an n x 1 column vector b which consists of each of zone s temperature change normalized by the global temperature change c the observed spatial warming pattern similar to the step above we calculate an n x 1 column vector c which consists of each zone s observed temperature change over the instrumental period normalized by the total global temperature change finally we can then calculate what the expected bias in net feedback calculated over the instrumental period will be according to each model using the following equation eq 1 where the function weight simply multiplies each element in the vector by its area fraction of the globe 3 example with gfdl cm3 first here is the fixed sst forcing calculation one thing of interest here is that the global forcing actually comes out to 7 2 w m 2 for 4xco2 which is more in line with the typical value of 3 7 w m 2 for a doubling of co2 and well above what is calculated in andrews et al 2012 using the regression technique however a look at figure 1 from andrews et al 2012 highlights why as you can see there is one point with a net imbalance above the intercept at 6 w m 2 which andrews et al 2012 takes as the forcing clearly since the regression is affected greatly by the larger t points and there is significant curvature the regression method in this case underestimates the forcing moving on here is the calculation of the zonal net feedbacks interestingly this seems to differ from the local feedbacks of the ccsm4 model used in armour et al 2013 however the primary difference seems to be the peak response at 60 degrees that does not appear to be present in that ccsm4 model next up here are the normalized temperature responses for the different scenarios in gfdl cm3 along with the observations from cowtan and way 2014 what is obvious in the gfdl cm3 historical pattern is the dip in temperatures between 30 and 60 degrees in the northern hemisphere which seems a pretty clear indication of the aerosol response in that model in the observed historical record this dip appears to be absent and overall the observed warming pattern seems much more similar to the historicalghg and abrupt4xco2 scenarios than the historical scenario apart from the lack of arctic warming finally if one where to calculate the feedback bias relative to the abrupt4xco2 scenario we find the following ratios this essentially isolates the expected forcing enhancement bias as it is baselined against the idealized 4xco2 run in this case the above ratios are 0 95 histghg 1 13 historical and 1 06 observed this suggests that if one used the historicalghg runs to estimate ecs there might be a slight overestimate relative to the co2 only run as gfdl cm3 includes the inhomogenous ozone forcing in their histghg runs were one to trust the relative strength of zonal feedbacks in gfdl cm3 it suggests about a 6 underestimate of ecs from energy balance methods over the instrumental period due to the inhomogenous aerosol forcings however ideally one could use this method with a variety of gcms to identify the expected bias among a wider array of models moreover if one were interested in the bias of effective sensitivity efs relative to ecs one would ideally get a longer run of gfdl cm3 with a doubling or quadrupling of co2 and see how the warming pattern ended up after it reached equilibrium unfortunately i am not aware of any such output currently available for this model final note in my calculations i initially performed the analysis using land and ocean zonal feedbacks and temperatures separately rather than combined into one for gfdl cm3 this did not seem to make much difference and i did not readily have available separately gridded land and ocean temperatures from observations however i seem to recall that the response was substantially different between land and ocean in armour et al 2013 so perhaps it a more wide ranging survey of gcms it would be better to separate these out again does anybody else think this a promising method for leveraging historical observations in estimating the potential bias in energy balance estimates code and data scripts and intermediate data for this post gfdl data portal cowtan and way 2014 data page comments 9 may 9 2014 on forcing enhancement efficacy and kummer and dessler 2014 filed under uncategorized troyca 10 11 pm a paper by kummer and dessler 2014 kd14 has recently been accepted by grl with the primary claim being that observational estimates of ecs over the 20th century can be reconciled with the higher ecs of cmip5 models by accounting for the forcing efficacy mentioned in shindell 2014 thus an efficacy for aerosols and ozone of 1 33 would resolve the fundamental disagreement between estimates of climate sensitivity based on the 20th century observational record and those based on climate models the paleoclimate record and interannual variations however i think there is some fundamental confusion with respect to how the forcing enhancement should be applied within kd14 which i will focus on specifically for this post ignoring what i believe to be other issues in the actual energy balance calculations for the mean time while i have noted previously that the spatial warming pattern appears to indicate a value of e the shindell enhancement near unity i would submit that even if it was significantly greater than 1 0 it has been applied in a way within kd14 that likely substantially exaggerates its effect on 20th century ecs calculations here are the issues that i see 1 ecs calculations are unaffected by the effective heat capacity whereas tcr calculations are not first let s take a look at the shindell 2014 definition for the forcing enhancement which kd14 refers to as forcing efficacy which is the ratio of the inhomogenous forcing tcr to that of the homogenous forcing tcr eq 1 tcr is calculated by dividing the temperature change by the forcing without consideration of the toa energy imbalance at the time of the calculation this is often normalized to transient change for a doubling of co2 by multiplying by f_2xco2 3 7 w m 2 but i will leave it simply in the units of k w m 2 for this post eq 2 and if we consider the simple one box temperature response to an imposed forcing at time t we have eq 3 where f is the imposed forcing change lambda is the strength of radiative restoration the increase in outgoing flux per unit of surface warming and c is the effective heat capacity of the system as can be seen by working back from equation 3 to 1 tcr and hence e will be affected by both the difference in c the heat capacity and lambda radiative restoration between the homogenous and inhomogeneous forcings on the other hand the equilibrium response t infinity to a forcing does not depend on c only lambda if we go back to the simple energy balance equation for the top of the atmosphere toa re arranging eq 1 in kd14 to solve for lambda with n representing this net toa imbalance we have eq 4 which can then be inverted and multiplied by f_2xco2 to find the ecs in terms of a co2 doubling what should be quite clear from this determination of ecs is that one can dampen the transient temperature response by increasing the value of c without it affecting the estimate of ecs after all if the temperature response is heavily damped in the first 50 years for a forcing due for example to the bulk of that forcing being concentrated in an area with deep oceans then it is true that the value for t will be lower than it might be for a scenario with less ocean damping but the toa imbalance n will be lar...
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