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description= 3 posts published by troyca during May 2011;
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the (338), and (74), for (57), that (53), this (44), model (33), solar (26), period (25), volcanic (25), enso (25), with (21), warming (21), trend (21), 2011 (20), are (20), from (19), #century (18), than (18), factor (18), what (17), observations (17), mmm (16), can (16), not (15), runs (14), noise (14), tsi (14), nino3 (14), have (13), forcing (13), using (13), about (12), lower (12), get (11), may (11), 2012 (11), multi (11), between (11), our (11), one (11), more (11), response (11), 2010 (10), recent (10), has (10), mean (10), against (10), only (10), will (10), time (10), would (10), mei (10), 2014 (9), regression (9), trends (9), months (9), here (9), used (9), true (9), hadcrut (9), coefficient (9), adjusted (9), 2013 (8), tamino (8), factors (8), also (8), was (8), all (8), other (8), but (8), component (8), errors (8), error (8), these (8), results (8), sunspots (8), actual (8), sensitivity (7), two (7), 20th (7), even (7), below (7), there (7), since (7), above (7), result 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have left the area so what do our trends look like from 2000 2010 if we use this white noise model the resulting confidence interval for 2 5 97 is 0 112 0 290 c decade and the nino3 4 adjusted trend for hadcrutv3 is well outside of it at 0037 of course we have fitted nino3 4 to the 1975 2000 errors so it s no surprise that we get a smaller error there than we would expect for the 21st century projections which have not been used for training furthermore the models don t have solar and volcanic forcings for the forecast the way they did for the hindcast so that might be another source of divergence then there is the question of whether actual forcings have tracked the a1b scenario and of course there are other temperature data sets i may try this with giss still what s interesting to me is how small of a noise model would explain the errors between the mmm and the enso adjusted hadcrut observations from 1975 2000 it seems particularly surprising given the way the projections and actual observations diverge early in the 21st century comments 3 may 13 2011 sensitivities in regression analysis of the modern warming period 1979 2011 filed under uncategorized troyca 12 30 pm there are many examples in the blogosphere of regressions run against the temperature record the goal being to glean the effects of certain factors and the true warming signal or even using this method for prediction for this most recent warming period i stumbled across ones from tamino kelly o day and arthur smith which builds on tamino s analysis an interesting note is tamino s analysis resulted in an estimated warming of about 1 5 greater than that of kelly s for uah i wanted to examine closer the choices that can lead to such a difference first a few notes all code is available here as well as an excel spreadsheet highlighting the individual runs data is automatically downloaded via the internet in the code much of the stuff i grab from climate explorer http climexp knmi nl data because it is easy to work with mei k r nino3 4 sunspots tsi multi model mean i will be examining the period of january 1979 january 2011 the start date i picked because that s when the satellite indices start and the end date is the last month of tsi reported at the time of starting this analysis this differs slightly from both tamino s analysis 1975 2010 and kelly o day s 1979 feb2011 although not enough to significantly alter the trends also note that for the tsi dataset some months are missing data along the way for these i simply used an average of the two closest values to estimate for the volcanic forcing from giss recent months are missing data and i assumed 0 for those 1 first glance at results dataset raw adj_r 2 raw trend 2 factor adj_r 2 2 factor trend 3 factor adj_r 2 3 factor trend noaa 0 60 0 160 0 72 0 157 0 74 0 176 hadcrut 0 57 0 155 0 73 0 151 0 76 0 175 uha 0 34 0 140 0 68 0 126 0 70 0 145 rss 0 39 0 147 0 69 0 136 0 72 0 160 giss 0 52 0 166 0 65 0 158 0 66 0 173 the trends above are all reported in c decade and represent the supposed true warming signal with the exogenous factors removed the raw trend is just a simple linear regression against time the 2 factor uses mei volcanic and the 3 factor uses mei volcanic tsi i got similar lags to what has been reported by the aforementioned analyses near instant solar 0 1 months for tsi 3 month enso lag for surface and 5 month for satellite and somewhere between 6 9 months for volcanic forcing lag what should be immediately obvious from above is that much of the difference in the true warming trend between kelly o day s regression versus tamino s can be attributed to the addition of a solar component on the one hand adding the solar factor would seem to make the model more complete and does improve the adjusted r 2 value on the other hand the adjusted r 2 value is only modestly improved but the additional variable has a large influence on the result furthermore as i ll discuss later the regression underestimates the instantaneous volcanic forcing according to what we would theoretically expect and the solar forcing appears to be overestimated if we corrected these the trends go down slightly i also want to point out that determining the proper model can be ambiguous for instance there might be 0 01 difference in the adjusted r 2 value between the top 50 or so different runs and with a noisy thing like the temperature set using such miniscule differences to determine the best model is tricky 2 mei vs kaplan and reynolds nino3 4 one choice we have for the regression is using the multivariate enso index vs the nino3 4 region sst bob tisdale discusses a bit on the difference although he uses hadsst instead of k r at the beginning of this post a quick glance at the relevant time period and differences can be seen here basically in the first panel we can see the slight downward trend during this period this means that removing the enso activity will generally make the factor independent warming appear larger than one that does not attempt to remove enso activity or the greater the assumed enso effect over this period the more it is assumed to have masked the remaining warming the second panel highlights the differences in choosing the index since mei has a greater downward slope choosing that index will make the true warming appear larger the included spreadsheet has more details but in my 2 factor analysis volcanic and enso i compared the results using these two different enso indices nino3 4 adj_r 2 nino3 4 trend mei adj_r 2 mei trend giss 0 645 0 148 0 652 0 158 rss 0 683 0 121 0 69 0 136 uha 0 673 0 111 0 682 0 126 hadcrut 0 711 0 143 0 731 0 151 noaa 0 709 0 150 0 716 0 157 once again the trends above are all reported in c decade and represent the trend once the specified index and volcanic factors are removed as can be seen the trend is sensitive to the choice of mei vs nino3 4 particularly the satellites while correlation appears better for mei in all datasets it should be noted that the actual adj_r 2 are pretty close 3 tsi vs sunspots another choice we can make presuming we start in 1979 or later is the choice of tsi vs sunspots to use to account for the solar factor once again here is a graph of the two the first panel shows that the beginning of our period started out with higher solar activity while the most recent years have low solar activity the result of attempting to fit a linear trend therefore is one that shows a large down slope this explains why a regression that takes the solar factor into account will generally show an increased trend vs time or why a higher solar coefficient means a greater implied solar independent warming trend once again i performed comparisons of using tsi vs sunspots for that third factor the results are in the spreadsheet but it was basically a tie with the adjusted r 2 values with neither doing better in all datasets using sunspots consistently resulted in a larger estimate factor independent warming although only by a small margin 0 01 c decade for all datasets using the sd of tsi vs sd of sunspots over the period to scale a sunspot would be equivalent to about 0082 w m 2 and considering this factor the solar coefficient using sunspots was higher than its tsi equivalent hence the slightly greater estimate of underlying warming 4 the volcanic forcing for this one i only used the giss index for stratospheric optical thickness tamino uses ammann et al 2003 for his i ve inverted the thickness value because it is a negative forcing as we can see the result over this period is a positive trend meaning that the removal of this will decrease our apparent true trend this explains why using only two factors enso volcanic generally has a lower true trend than that raw calculation the removal of the volcanic decreases this trend more than the enso removal increases it 5 stefan boltzmann sense tamino mentions that the response to the solar factor is greater than s b predicts a back of the envelope calculation yields 0 19 c w m 2 from s b at current temperature rather than simply using 1365 for tsi 0 7 albedo 4 shadow area surface area 0 033 c expected immediate response per 1 w m 2 change in tsi a quick glance at the spreadsheet suggests the statistical model is estimating about 2 3 times that for surface record or satellite if we use the rough estimate for volcanic forcing based on optical thickness here we get an expected response of approximately 0 19 c w m 2 25 w m 2 tau 4 75 c tau for our coefficient for our surface datasets we re only getting about 33 50 of that and 75 of that for the satellite datasets the combination of the higher solar contribution and the lower volcanic contribution over this period results in a significantly higher estimate for the true warming trend than we would get if we used a simple physical model for these contributions 6 what do the models say i ran the same regression against the multi model mean to see its immediate response to forcings the results can be found in the spreadsheet as well since these are primarily physical models it should give the expected physical response for volcanoes and solar factors and since it neither simulates enso very well and the enso factor is not a forcing the enso coefficient should be far smaller for the same time period jans 1979 2011 we get a significantly lower value for the solar coefficient 015 than we get for the actual observations and even lower than s b however it s worth noting that the third of the period is in the 21 th century where actual historical solar and volcanic are not used if i shift to only 1979 1999 we get a solar coefficient 036 that is approximately the expected value from s b also as expected the enso component is almost non existent less than 10 of what we get for actual observations however the volcanic response is something of a surprise staying considerably lower 1 6 c tau and near the immediate response of the observations this may suggest that rather than give an immediate response to a volcanic event the multi model mean smears the cooling over a variety of lag times or even longer on the scale of several years such that it is difficult to tease out 7 another time period i tried running the regression on some other time periods such as 1900 1950 and 1910 1940 on hadcrut with the results in the spreadsheet this period seems like it would be relatively straight forward based on the graph of estimated giss model forcings i had to use sunspots and nino3 4 since those go back further in time than tsi or mei the results are also in the spreadsheet on the one hand the calculated enso factor had about the same effect as during the modern warming period on the other hand the volcanic and solar lags and coefficients were all over the place even changing signs depending on what portions of the early 20 th century were included the adj_r 2 values are significantly lower so i m not sure if the weird results are due to more noise and uncertainty specifically in the early 20 th century observations or if generally the regressions run on thirty year periods are limited in determining responses to volcanic and solar forcings going back to the multi model mean running on the 1910 1940 period gives a better correlation than against the observations with a significantly lower enso factor yet again and while the lags are a bit more variable we get a volcanic coefficient 2 5 and solar coefficient adjusted to tsi 0 022 that at least appear somewhat reasonable not surprising given that it should be using about the same physical model throughout 8 hadcrut pure statistical model vs some physical components below i show the different modeling approaches against the observations for the top red line it uses the pure statistical model with the optimized lags for the two lines below that i used the estimated theoretical values from s b substituted in for the statistical estimates only solar in one case both solar and volcanic in the other case i should note that the lags in these lower to lines have not been fitted based on the new coefficients so it might be possible to lower the rmse for those with better fit lags the standout appears to be that larger volcanic response the trouble is that if the lag is off for a few months with the high volcanic sensitivity it ends up failing spectacularly greatly increasing the error i think this is why a statistical model that assumes the lag in response to a volcanic forcing is always going to be the same will always tend to underestimate the magnitude of this response anyhow the above also demonstrates the sensitivity of the estimated true warming to assumptions about the effects of other factors it is worth pondering to what degree a statistical model over this period has the ability to accurately capture the magnitude of smaller effects such as the solar component vs noise i may look into that in a future post comments 3 may 4 2011 into the 21st century with cmip3 mmm ar 1 filed under uncategorized troyca 12 31 am code and data for this post can be downloaded here it s getting sloppy i know i m not an r guy in my last post i looked at the 20th century hindcast within the context of assuming the multi model mean represents the true forced component of our climate and the weather noise errors can be simulated using an ar 1 process with the two charts below i ve extended this to look at the first 11 years in the 21st century and also included the gisstemp and noaa calculated anomalies in addition to hadcrut as you can see the differences between the individual observational series are tiny compared to the differences between our various runs the following zooms in closer to focus on the period since 1980 although it maintains the 1900 1950 baseline one thing that stands out is that recent years have fallen increasingly below the multi model mean in all 3 observational series even landing outside the 54 pseudo runs in places on the one hand this seems unique to the 21st century suggesting the multi model mean isn t doing as good of a job of forecasting as it has in hindcasting on the other hand the degree to which current observations fall below the multi model mean is sensitive to the baseline chosen i ve used 1900 1950 for similarity to the ipcc ar4 report but a more recent baseline will lessen the difference so it s worth noting that a slight overestimate of warming by the mmm in the latter part of the 20th century hindcast has also contributed to this difference this will become more evident when looking at the histograms of trends so what if we compare the trends of the observations to our mmm ar 1 noise model each histogram below is of 1000 run of the mmm our ar 1 process using the same parameters as above the first chart is a similar to one that can be found at lucia s here except that it uses the 1000 pseudo runs instead of only the 54 runs available in the ensemble and it uses annual averages that must end in 2010 rather than going up to the current month...
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