A guest post by Nic Lewis
Introduction and Summary
In a recently published paper (REA16),[1] Mark Richardson et al. claim that recent observation-based energy budget estimates of the Earth’s transient climate response (TCR) are biased substantially low, with the true value some 24% higher. This claim is based purely on simulations by CMIP5 climate models. As I shall show, observational evidence points to any bias actually being small. Moreover, the related claims made by Kyle Armour, in an accompanying “news & views” opinion piece,[2] fall apart upon examination.
The main claim in REA16 is that, in models, surface air-temperature warming over 1861-2009 is 24% greater than would be recorded by HadCRUT4 because it preferentially samples slower-warming regions and water warms less than air. About 15 percentage points of this excess result from masking to HadCRUT4v4 geographical coverage. The remaining 9 percentage points are due to HadCRUT4 blending air and sea surface temperature (SST) data, and arise partly from water warming less than air over the open ocean and partly from changes in sea ice redistributing air and water measurements.
REA16 infer an observation-based best estimate for TCR from 1.66°C, 24% higher than the value of 1.34°C if based on HadCRUT4v4.. Since the scaling factor used is based purely on simulations by CMIP5 models, rather than on observations, the estimate is only valid if those simulations realistically reproduce the spatiotemporal pattern of actual warming for both SST and near-surface air temperature (tas), and changes in sea-ice cover. It is clear that they fail to do so. For instance, the models simulate fast warming, and retreating sea-ice, in the sparsely observed southern high latitudes. The available evidence indicates that, on the contrary, warming in this region has been slower than average, pointing to the bias due to sparse observations over it being in the opposite direction to that estimated from model simulations. Nor is there good observational evidence that air over the open ocean warms faster than SST. Therefore, the REA16 model-based bias figure cannot be regarded as realistic for observation-based TCR estimates.
It should also be noted that the 1.66°C TCR estimate ignores the fact that the method used overestimates canonical CMIP5 model TCRs (those per AR5 WG1 Table 9.5) by ~5% (Supplementary Information, page 4). Including this scaling factor along with the temperature measurement scaling factor reduces the estimate to 1.57°C (Supplementary Table 11).
Relevant details of and peculiarities in REA16
REA16 focus on energy-budget TCR estimates using the ratio of the changes in global temperature and in forcing, measuring both changes as the difference between the mean over an early baseline period and the mean over a recent final period. They refer to this variously as the difference method and as the Otto et al.[3] method; it was introduced over a decade earlier by Gregory et al.[4] and copied by both Otto et al. (2013) and Lewis and Curry (2015).[5] The primary baseline and final periods used by REA16 are 1861–80 and 2000–09, almost matching those used in the best-constrained Otto et al. estimate. Lewis and Curry, taking longer 1859–82 base and 1995-2011 final periods, obtained the same 1.33°C best estimate for TCR as Otto et al., using the same HadCRUT4v2 global temperature dataset.
REA16 estimate the TCR of each CMIP5 model by comparing its global warming with forcing estimated in the same way as in Otto et al., using model-specific data where available and multimodel mean forcing otherwise. The method is somewhat circular, since forcing for each model is calculated each year as the product of its estimated climate feedback parameter and its simulated global warming, adjusted by the change in its radiative imbalance (heat uptake). Each model’s climate feedback parameter is derived by regressing the model’s radiative imbalance response against its global temperature response over the 150 years following an abrupt quadrupling of CO2 concentration.
In model historical simulations the weighted average period from when each forcing increment arose to 2000–09 is only ~30 years, not 150 years. Accordingly, the forcing estimation method relies upon a model exhibiting a fairly linear climate response, and hence having a climate feedback parameter (and an effective climate sensitivity) that does not vary with time (in addition to having a temperature response that is proportional to forcing). In this context, the statement in REA16 that they do not calculate equilibrium climate sensitivity (ECS) “to avoid the assumption of linear climate response” is peculiar: they have already made this assumption in deriving model forcings.
Although REA16 is based on simulations by all CMIP5 models for which relevant data are available, the weighting given to each model in determining the median estimates that are given varies over a range of ten to one. That is because, unlike for most IPCC model-based estimates, each available model-simulation – rather than each model – is given an equal weighting. Whilst only one simulation is included for most models, almost 60% of the simulations that determine the median estimates come from the 25% of models with four or more simulation runs.
REA16 do not appear to state the estimated median TCR applicable to the 84 historical-RCP8.5 CMIP5 simulations used. Dividing the primary periods tas-only difference method figure of 1.98°C per Supplementary Table 6 by 1.05 to allow for the stated overestimation by the difference method implies a median estimate for true TCR of 1.89°C. Back-calculating TCR from the difference method bias values in Supplementary Table 5 instead gives an estimate of 1.90°C. The figures are rather higher than the median TCR of 1.80°C that I calculate to apply to the subset of 68 simulations by models for which the canonical TCR is known.
There seem to be inconsistencies in REA16 between different estimates of the bias resulting from use of the difference method and blended air and SST temperature data. The top RH panel of Supplementary Figure 4 shows that the median TCR estimate when doing so, with 2000–09 as the final decade is ~2.00°C. This is a 5% overestimate of the apparent actual value of ~1.90°C rather than (as stated in Supplementary Table 5) an underestimate of 8%. Moreover, contrary to Supplementary Figure 4, Supplementary Table 6 gives a median TCR estimate in this case of 1.81°C, implying an underestimate of 4%, not 8%. Something appears to be wrong here.
REA16 also claim that energy budget TCR estimates are sensitive to analysis period(s), particularly when using a trend method. However, Supplementary Figure 4 shows that the chosen difference method provides stable estimation of model TCRs provided that the final decade has, like the 1861–80 base period, low volcanic forcing. That is, for decades ending in the late 2000s on. As discussed in some detail in LC15, sensitivity estimation using an energy budget difference method is sensitive to variations between the base and final periods in volcanic forcing, due to its very low apparent efficacy, so periods with matching volcanism should be used. The sensitivity, shown in Supplementary Table 6, of TCR estimation using the difference method to choice of base period when using a 2000–09 final period is explicable primarily by poor matching of volcanic forcing when base periods other than 1861–80 are used. Good matching of the mean state of the Atlantic Multidecadal Oscillation (AMO) between the base and final period is also necessary for reliable observational estimation of TCR.
The effect of blending air and SST data
I question whether using SST as a proxy for tas over the open ocean has caused any downward bias in estimation of TCR in the real climate system, or even (to any significant extent) in CMIP5 models.
The paper REA16 primarily cite to support faster warming of tas over open water than SST,[6] which is also model-based, attributes this effect to the thermal inertia of the ocean causing a lag in ocean warming. This argument appears to be unsound. Another paper,[7] which they also cite, instead derives an equilibrium air – sea surface warming differential from a theoretical model based on an assumed relative humidity height profile, with thermal inertia playing no role. This is a better argument. However, it depends on the assumed relative humidity profile being realistic, which it may not be. The first paper cited notes (caveating that observational uncertainties are considerable) that models do not match observed changes in subtropical relative humidity or in global precipitation.
For CMIP5 models, REA16 states that the tas vs SST warming differential is about 9% on the RCP8.5 scenario and is broadly consistent between models historically and over the 21st century. However, the differential I calculate is far smaller than that. I compared the increases in tas and ‘ts‘ between the means for first two decades of the RCP8.5 simulation (2006–25) and the last two decades of the 21st century, using ensemble mean data for each of the 36 CMIP5 models for which data was available. CMIP5 variable ‘ts‘ is surface temperature, stated to be SST for the open ocean and skin temperature elsewhere. The excess of the global mean increase in tas over that in ts, averaged across all models, was only 2%. Whilst ts is not quite the same as tas over land and sea ice, there is little indication from a latitudinal analysis that the comparison is biased by any differences in their behaviour over land and sea ice. Consistent with this, Figures 2 and S2 of Cowtan et al. 2015[8] (which use respectively tas and ts over land and sea ice) show very similar changes over time (save in the case of one model). Accordingly, I conclude that the stated 9% differential greatly overstates the mean difference in model warming between tas and blended air-sea temperatures. To a large extent that is because the 9% figure also includes an effect, when anomaly temperatures are used, from changes in sea ice extent. However, Figure 2 of Cowtan et al 2015 shows, based on essentially the same set of CMIP5 RCP8.5 simulations as REA16 and excluding sea-ice related effects, a mean differential of ~5% (range 1% – 7%), over double the 2% I estimate.
So, models exhibit a range of behaviours. What do observations show? Unfortunately, there is limited evidence as to whether and to what extent differential air-sea surface warming occurs in the real climate system. However, in the deep tropics, where the theoretical effects on the surface energy budget of temperature-driven changes in evaporation and water vapour are particularly strong, there is a near quarter century record of both SST and tas from the Tropical Atmosphere Ocean array of fixed buoys in the Pacific ocean. With averages over the full array extent based on a minimum of 40% valid data points, SAT and SST data are available for 1993-2015. The trend increase in SST over that period is 0.078°C/decade, considerably higher than the 0.047°C/decade for tas, not lower. If the required minimum is reduced to 20%, trends can be calculated over 1992-2015, for which they are 0.029°C/decade for SST, and 1.5% higher at 0.030°C/decade for tas. This evidence, although limited both spatially and temporally, does not suggest that tas increases faster than SST.
The effect of sea ice changes
The separation in REA16 of the effect of masking from that of sea ice changes on blending air and water temperature changes is somewhat artificial, since HadCRUT4 has limited coverage in areas where sea ice occurs. However, I will follow the REA16 approach. Their model-based estimate of the effect of sea ice changes appears to be ~4%, the difference between the 9 percentage points bias due to blending and the 5 percentage points (per Cowtan et al. 2015) due purely to the use of SST rather than tas for the open ocean. Changes in sea ice make a difference only when temperatures are measured as anomalies relative to a reference period, however I can find no mention in REA16 of what reference period is used.
CMIP5 models have generally simulated decreases in sea ice extent since 1900, accelerating over recent decades, around both poles (AR5 WG1 Figure 9.42). In reality, Antarctic sea ice extent has increased, not decreased, over the satellite era. Its behaviour prior to 1979 is unknown. On the other hand, since ~2005 Arctic sea ice has declined more rapidly than per mean CMIP5 projections. Differences in air temperatures above affected sea ice in the two regions, and the use of widely varying model weightings in REA16, complicate the picture. It is difficult to tell to what extent REA16’s implicit 4 percentage point estimate is biased. Nevertheless, based on sea ice data from 1979 on and unrealistically high long term warming by CMIP5 models in high southern latitudes (as discussed below), it seems to me likely to be an overestimate for changes between the baseline 1861–80 and final 2000–09 periods used in REA16.
The effect of masking to HadCRUT4 coverage
I turn now to the claims about incomplete, and changing, data coverage biasing down HadCRUT4 warming by 15 percentage points. The reduction in global warming from masking to HadCRUT4 coverage is based on fast CMIP5 model historical period warming in southern high latitudes as well as northern; see REA16 Supplementary Fig. 6, LH panel and Supplementary Table 8. But this is the opposite of what has happened; high southern latitudes have warmed more slowly than average, over the period for which data are available.
Based on HadCRUT4 data with a minimum of 20% grid cells with data, warming over 60S–90S averaged 0.05°C/decade from 1934 to 2015. The trend is similar using a 10% or 25% minimum; higher minima result in no pre-WW2 data. This trend is much lower than the 0.08°C/decade global mean trend over the period. For the larger 50S–90S region a trend over 1880–2015 can be calculated, at 0.03°C/decade, if a minimum of 15% of valid data points is accepted. Again, this is much lower than the global mean trend of 0.065°C/decade over the same period. An infilled spatial plot of warming since 1960 per BEST (http://berkeleyearth.org/wp-content/uploads/2015/03/land-and-ocean-trend-comparison-map-large.png) likewise shows slower than average warming in southern high latitudes. And UAH (v6.0beta5) and RSS (v03_3) lower-troposphere datasets show very low warming south of 60S over 1979–2015: respectively 0.01 and –0.02°C/decade.
It follows that the real effect of masking to HadCRUT4 coverage over the historical period is, in the southern extra-tropics, almost certainly the opposite of that simulated by CMIP5 models. Therefore, in the real world the global effect of masking is likely to be far smaller than the ~15% bias claimed by REA15.
In an article earlier this year updating the Lewis and Curry results,[9] I addressed the key claims about the effects of masking to HadCRUT4 coverage made in Cowtan et al. 2015 and repeated in REA16, writing:
“It has been claimed (apparently based on HadCRUT4v1) that incomplete coverage of high-latitude zones in the HadCRUT4 dataset biases down its estimate of recent rates of increase in GMST [Cowtan and Way 2014].[10] Representation in the Arctic has improved in subsequent versions of HadCRUT4. Even for HadCRUT4v2, used in [Lewis and Curry], the increase in GMST over the period concerned actually exceeds the area-weighted average of increases for ten separate latitude zones, so underweighting of high-latitude zones does not seem to cause a downwards bias. The issue appears to relate more to interpolation over sea ice than to coverage over land and open ocean in high latitudes.
The possibility of coverage bias in HadCRUT4 has since been independently examined by ECMWF using their well-regarded ERA-Interim reanalysis dataset. They found no reduction in that dataset’s 1979-2014 trend in 2 m near-surface air temperature when the globally-complete coverage was reduced to match that of HadCRUT4v4.[11] Since the ERA-interim reanalysis combines observations from multiple sources and of multiple atmospheric variables, based on a model that is well-proven for weather forecasting, it should in principle provide a more reliable infilling of areas where surface data [are] very sparse, such as high-latitude zones, than mechanistic methods such as kriging. Moreover, during the early decades of the HadCRUT4 record (which includes the 1859-1882 base period) data [were] sparse over much of the globe, and global infilling may introduce significant errors.”
Thus, the claim by Cowtan and Way (2014) that the ERA-interim analysis shows a rapidly increasing cold bias in HadCRUT4 after 1998 does not apply to HadCRUT4v4 over the longer post 1978 period. Focussing first on this period, the performance of the ERA-Interim and six other reanalyses in the Arctic was examined by Lindsay et al.[12] Although the accuracy of reanalyses in the fast warming but sparsely observed Arctic region has been questioned, the authors found that ERA-interim had a very high correlation with monthly temperature anomalies at 449 Arctic land stations. They reckoned ERA-interim to be the most accurate reanalysis for surface air temperature both in absolute terms and as to (post 1979) trend.
Lindsay et al. found GISTEMP to have a higher post-1978 trend in the Arctic than ERA-interim, but GISTEMP uses a crude interpolation and extrapolation based infilling method. Moreover, the ERA-interim version used by ECMWF to investigate possible coverage bias differs from the main dataset. It incorporates a homogeneity adjustment to its post 2001 SST data that significantly increases its temperature trend over that of the main ERA-interim reanalysis. Taking account of that might well eliminate the Arctic trend shortfall compared with GISTEMP. Certainly, over 1979-2015 both the adjusted ERA-interim and HadCRUT4v4 datasets showed a slightly higher trend in global temperature (of respectively 0.166 and 0.165 °C/decade) than did GISTEMP (0.162°C/decade).
Another recent study, Dodd et al,[13] stated that “ERA-Interim has been found to be consistent with independent observations of Arctic [surface air temperatures] and provides realistic estimates of Arctic temperatures and temperature trends that outperform, or are comparable to, other currently available reanalyses for all areas of the Arctic so far investigated.” In her Phd thesis, Dodd also noted that “The issues arising from using drifting platforms in this study highlight the difficulty of investigating [surface air temperatures] over Arctic sea ice.” All this suggests that mechanistic infilling methods are unlikely to outperform the ERA-interim reanalysis in the Arctic, or indeed the Antarctic.
Prior to 1979, there is very little evidence as to the actual effects of incomplete observational coverage, or of blending air and SST measurement, on estimated trends in global temperature. However, there are two well known long-term surface temperature datasets that are based (on a decadal timescale upwards) on air temperature over the ocean as well as land, and which moreover infill to obtain complete or near complete global coverage: NOAAv4.01 and GISSTEMP. Cowtan et al (2015) accept that the new NOAA data set “incorporates adjustments to SSTs to match night-time marine air temperatures and so may be more comparable to model air temperatures”. GISSTEMP uses the NOAAv4.01 SST data set (ERSST4). Both NOAAv4.01 and GISSTEMP show almost identical changes in mean GMST to that per HadCRUT4v4 from 1880-1899, the first two decades they cover, to 1995-2015, the final period used in the update of Lewis and Curry. This suggests that any downwards bias in TCR estimation arising from use of HadCRUT4v4 is likely to be very small. Moreover, whilst some downwards bias in HadCRUT4v4 warming may exist, there are also possible sources of upwards bias, particularly over land, such as the effects of urbanisation and of destabilisation by greenhouse gases of the night-time boundary layer.
A way to resolve some of the uncertainties arising from poor early observational coverage
It is doubtful that any method of global infilling of temperatures based on the limited observational coverage available in the second half of the 19th century or (to a decreasing extent) during the first half of the 20th century is very reliable.
Fortunately, there is no need to use the full historical period when estimating TCR. Uncertainty regarding ocean heat uptake in the middle of the historical period, although a problem for ECS estimation, is not relevant to TCR estimation. Lewis and Curry gave an estimate of TCR based on changes from 1930–50 to 1995–2011, periods that were well matched for mean volcanic activity and AMO state, and which delineate a period over which forcing approximated a 70 years ramp. That TCR estimate was 1.33°C, the same as the primary TCR estimate using 1859–82 as the base period. Updating the final period to 1995–2015 and using HadCRUT4v4 left the estimate using the 1930–50 base period unchanged at 1.33°C. The infilling of HadCRUT4 by Cowtan and Way is prone to lesser error when using a 1930–50 base period rather than 1859–82 (or 1861–80 as in REA16), since observational coverage was less sparse during 1930–50. Accordingly, estimating TCR using an infilled temperature dataset makes more sense when the later base period is used.
So does use of the infilled Cowtan and Way dataset increase the 1930–50 to 1995–2015 TCR estimate by anything like 15%, the coverage bias for CMIP5 models reported in REA16 for the full historical period? No. The bias is an insignificant 3%, with TCR estimated at 1.37°C. Small additional biases, discussed above, from changes in sea ice and differences in warming rates of SST and air just above the open ocean (which it appears the Cowtan and Way dataset does not adjust for) might push up the bias marginally. However, ~80% of the total warming involved occurred after 1979, and as noted earlier since 1979 the trend in HadCRUT4v4 matches that in the (adjusted) ERA-interim dataset, which estimates purely surface air temperature, not a blend with SST, and has complete coverage. That suggests the bias from estimating TCR from 1930–50 to 1995–2015 using HadCRUT4v4 data is very minor, and that observation based estimates of TCR of ~1.33°C need to be revised up by, at most, a small fraction of the 24% claimed in REA16.
Claims by Kyle Armour
In an opinion piece related to REA16 in the same issue of Nature Climate Change, “Climate sensitivity on the rise”, Kyle Armour made three claims:
- That, as a result of REA16’s findings, observation-based estimates of climate sensitivity and TCR must be revised upwards by 24%.
. - That the findings in Marvel et al (2015)[14] about various other types of forcing having differing effects on global temperature from CO2 (different efficacies) call for multiplying observational estimates of climate sensitivity and TCR by a further factor of 1.30.
. - That a robust behaviour in models of apparent (effective) climate sensitivity being lower in the early years after a forcing is imposed than subsequently, rather than remaining constant, requires multiplying estimates of climate sensitivity by a further factor of ~1.25 in order to convert what they actually estimate (effective climate sensitivity) to ECS.
I will show that each of these claims is very wrong. Taking them in turn:
- REA16’s findings are purely model based and do not reflect behaviour in the real climate system. There is little evidence for any major bias when TCR is estimated using observed changes from early in the historical period to the recent past, but limited observational coverage in the early part makes it difficult to quantify bias. However, TCR can also validly be estimated from observed warming since 1930–1950, most of which occurred during the well observed post-1978 satellite era. Doing so produces an identical TCR estimate to when using the long period, and any downwards bias in the estimate appears to be very small. An adjustment factor in the range 1.01x to 1.05x, not 1.24x, appears warranted.
. - As I have pointed out elsewhere,[15] Marvel et al has a number of serious faults, only two of which have to date been corrected.[16] Nonetheless, for what it is worth, after correcting those two errors Marvel et al.’s primary (iRF) estimate of the effect on global temperature of the mix of forcings acting during the historical period is the same as if the forcing had been, as per the definition of TCR, solely due to CO2. That is, historical forcing has an estimated transient efficacy of 1.0 (actually 0.99). That would, ignoring the other problems with Marvel et al., justify a multiplicative adjustment to TCR estimates of 1.01x, not 1.30x.
. - It is not true that increasing effective sensitivity is a “robust” feature of models. In four CMIP5 models, the shortfall of climate sensitivity estimated using the first 35 years’ data following an abrupt CO2 increase (roughly corresponding to the weighted average duration of forcing increments over the historical period) compared to that estimated using the standard 150 year regression method, is negligible (2% or less) for six models; for three of those the short period estimate is actually higher. The average shortfall over all CMIP5 models for which I have data is only 7%. Moreover, there is little evidence that the principal causes of estimated ECS exceeding multidecadal effective climate sensitivity in many CMIP5 models (in particular, weakening of the Pacific Walker circulation) are occurring in the real world. So any adjustment to observational estimates of climate sensitivity on account of effective climate sensitivity being, in many models, below ECS (a) does not appear to be well supported by observations; and (b) if based on the average behaviour of CMIP5 models, should be 1.08x rather than 1.25x.
Nicholas Lewis
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References
[1] Mark Richardson, Kevin Cowtan, Ed Hawkins and Martin Stolpe. Reconciled climate response estimates from climate models and the energy budget of Earth. Nature Clim Chng (2016) doi:10.1038/nclimate3066
[2] Kyle Armour. Projection and prediction: Climate sensitivity on the rise Nature Clim Chng (2016) doi:10.1038/nclimate3079
[3] Otto, A. et al. Energy budget constraints on climate response. Nature Geosci. 6, 415-416 (2013).
[4] Gregory, J. M., Stouffer, R. J., Raper, S. C. B., Stott, P. A. & Rayner, N. A. An Observationally Based Estimate of the Climate Sensitivity. J. Clim. 15, 3117–3121 (2002).
[5] Lewis, N. & Curry, J. A. The implications for climate sensitivity of AR5 forcing and heat uptake estimates. Clim. Dynam. 45, 1009_1023 (2015).
[6] Richter, I. & Xie, S.-P. Muted precipitation increase in global warming simulations: a surface evaporation perspective. J. Geophys. Res. 113, D24118 (2008).
[7] Ramanathan, V. The role of ocean-atmosphere interactions in the CO2 climate problem. J. Atmos. Sci. 38, 918_930 (1981).
[8] Cowtan, K. et al. Robust comparison of climate models with observations using blended land air and ocean sea surface temperatures. Geophys. Res. Lett. 42, 6526–6534 (2015).
[9] https://niclewis.files.wordpress.com/2016/04/ar5_ebstudy_update_article1b.pdf
[10] Cowtan, K. & Way, R. G. Coverage bias in the HadCRUT4 temperature series and its impact on recent temperature trends. Q. J. R. Meteorol. Soc. 140, 1935_1944. (2014)
[11] See http://www.ecmwf.int/en/about/media-centre/news/2015/ecmwf-releases-global-reanalysis-data-2014-0. The data graphed in the final figure shows the same 1979-2014 trend whether or not coverage is reduced to match HadCRUT4.
[12] Lindsay, R et al. Evaluation of Seven Different Atmospheric Reanalysis Products in the Arctic. J Clim 27, 2588–2606 (2014)
[13] Dodd, MA, °C Merchant, NA Rayner and CP Morice. An Investigation into the Impact of using Various Techniques to Estimate Arctic Surface Air Temperature Anomalies. J Clim 28, 1743-1763 (2015).
[14] Kate Marvel, Gavin A. Schmidt, Ron L. Miller and Larissa S. Nazarenko, et al.: Implications for climate sensitivity from the response to individual forcings. Nature Climate Change DOI: 10.1038/NCLIMATE2888 (2015).
[15] https://climateaudit.org/2016/01/08/appraising-marvel-et-al-implications-of-forcing-efficacies-for-climate-sensitivity-estimates/
[16] https://climateaudit.org/2016/03/11/marvel-et-al-giss-did-omit-land-use-forcing/
Climate Audit 
61 Comments
Reblogged this on ClimateTheTruth.com.
Thank you Nicholas Lewis.
“They” sure love their models.
In regard to “…attributes this effect to the thermal inertia of the ocean causing a lag in ocean warming.”
Surely there must be sufficient real world data to quantify this alleged lag. And again, and again, and again, if the oceans are slow on the uptake of heat energy, where is the heat energy hiding in the meantime / maritime?
Jeff
The thermal inertia lag argument is wrong. To be fair, Richardson et al don’t themselves make it, instead proffering the sounder surface energy balance argument advanced by the second paper they cite (Ramanathan 1981). But it is odd that they first cite a paper that makes the thermal lag argument. It is, however, a minor point.
Looking forward to this fisking
Nic
Thanks for another thorough treatment. It should be known, though, that no one at the US DOE can read this, as DOE apparatchicks have blocked access to CA as well as Anthony’s site in these dying days.
Hi Nick, when I heard about Richardson’s claims of tas vs ts I remembered the nighttime sea air data set that Karl(2015) used to calibrate cooling on bucket temps against ship boiler intakes. It made me wonder if the sea air temp had an overall elevated trend as Richardson claimed why had the “consensus” resisted until now citing the historical observed data (HadNMAT2 back to 1880).
I see the tas from 25-year fixed buoys data you have the trend cited as 0.047C/dec. How could they have missed mentioning such observed data? Have you trended the HadNMAT2 2013 adjusted data or earlier prior data?
The fixed buoys data enables a proper comparison of SST and tas trends to be made, since the measurements are co-located. But the record is short, covers only a limited area, and there are problems with missing data. I wouldn’t want to rely on the 0.047 C/decade tas value or its comparison with the 0.078 C/decade SST value. FWIW, the HadNMAT2 1993-2015 tropical trend (30S-30N) is 0.083 C/decade.
Since 0.83/0.078 C/dec is a 6% increase that would raise TCR by 0.1C.
Next questions: Do the GCMs output both? Is there a consistent spread? Do they have credible skill in this area or is it tuned? why wasn’t ts used as a proxy for tas all along? Now all the IPCC impact projections have to decide which metric they were using.
Nic, thanks and I do not assume anyone should know all the answers. Also, do you know the HadNMAT trend before 2013 adjustments?
The TAS and TOS data and modeling is confusing. And I think that the change in difference is significant to climate change. What difference do Richarson et al. come out with, corresponding to their TCR estimate?
The best thing to do is to use the Karl data UNADJUSTED and compute Nics base and final period…
OPPS.. if you do that ECS WILL GO UP !!
yep thats right.. The Karl adjustments actually DECREASE the long term trend.
go ahead and calculate base and final period using karl adjusted versus un adjusted.
Think Karl was manipulating the data? fine.. take his adjustments out and you just increased ECS!
Skeptics own goal… yeah!
See how Steven Mosher defends the skeptical position.
Oops!
Maybe.
So once again you simply make a couple of assertions and then claim victory.Because one set of numbers proves everything, Everything! It’s that simple.
The idea that everything on the Alarmist side is always right and everything on the Sceptic is always wrong is obviously a stupid and mundane assumption, yet all you do is apply your “brilliance” to one side.
It’s just boring now.
Nic,
Thanks for this crearly argued post. Richard Lindzen noted some time back that is implausible the data is always wrong and the models always right; nothing in the field seems to have changed since he made that comment. I would add it is doubly implausible that errors in the data are always in the same direction…. the ‘true average warming’ is always greater that the measurements. Only continued failure of the models to accurately predict future warming over the next couple of decades will end this nonsense.
Sorry about the post above as I copied the wrong material. Please delete
Nic Lewis, in your post you have covered much of the ground I have in analyzing the Cowtan paper on ocean air (tas) versus ocean water (tos) temperature trends. I have looked at the CMIP5 RCP 4.5 model runs using annual data from various time periods and global zones and determined that in general for these models tas diverges from tos in a relationship that depends on the tas warming(cooling rate). I determined this relationship by obtaining the trends devoid of noise and periodic components by using Singular Spectrum Analysis (SSA) to decompose and reconstruct the temperature series and then looking at the correlation of the first difference (instantaneous slope) of the tas trends versus the first difference of the tas trend minus the tos trend. In general these correlations for the model runs are high and lowered from higher values primarily by various segments of consecutive years having either an offset or a different slope with the segments individually having high correlations. The tas temperature trends are thus higher than those of tos in a warming period and lower in a cooling period.
I have found that this same relationship applies when the first difference of the global land trends are correlated to the land trend minus the ocean SST trend. The trends were determined in this case also by SSA decomposition and reconstruction. Here the land temperatures warm and cool faster than the ocean sea surface temperatures. In the case of land and ocean SST I can make a comparison with the observed and there I find excellent correlations using the first differences as was done for the models and the land warms (cools) at a faster rate than the ocean SST. The ratio and difference of the observed land to ocean SST trends is larger than most of the RCP 4.5 models for the period 1970-2005. The model runs produce ratios and differences that vary over a large range.
My attempts to determine the ratios and differences between the observed ocean air versus ocean SST temperature trends to compare with the model results were limited by the sparseness of the observed data. The Cowtan paper authors comment that the observed data is too noisy to make this observed to model comparison. As you have reported, I found the same contradictory data for those ocean buoys that provided tas and tos measurements at the same locations. That data does, however, come from the lower latitudes where the lesser warming is – per the models anyway- going to result in a lesser divergence between tas and tos trends.
Interesting that the Karl (2015) paper uses night time ocean air temperatures to adjust the temperatures which are ostensibly reported as SST. If the Cowtan paper observation on models held for the observed for these trends it would call into doubt the Karl paper adjustment.
Ken
Previous comment deleted, as requested.
Ken, as you say Karl(2015) used nighttime sea air temps to correct SST after he found that the bucket method had still continued by many ships beyond WWII when they were supposed to all have had transitioned to the engine intake method of temp measurement. Are you saying that Karl by using the night air temps as a calibration bridge to normalize bucket temp readings from WWII to the 2000s inadvertently transferred the tas trend into the tos? This would be a significant error. Could you determine for certain Karl did not use a correction to the correction to preserve the tos trend?
This adjustment was Karl’s most significant in eradicating “the pause.”
ERSST4 transformed as tos trend into a tas trend, over timescales of greater than a decade. The 2000-14 period is too short for this transformation to be fully effective, and anyway it may not have made much difference over that period, so Karl’s statement is not inconsistent with this transformation having been effected. There is no further correcting affecting tos vs tas after the phased adjustment of tos to tas using night air temperatures. Look at the equations in the Huang et al J Climate 2015 Part 1 ERSST paper – I think it is openly accessible.
I read Karl as shifting warming from the 20th century to the 21st by cooling a 60-yr interval prior to the 2000-2014 interval (Argo buoy era). Regardless if this was kosher using tas to normalize would have increased the trend if Richardson is correct. They both can’t be right. I know this is small potatoes. Each it seems is contributing a small shovel full. But after a while it’s a pile.
niclewis,
I sent Judith Curry (your coauthor) a link to my discussion about the climate models using the wrong dynamical equations with no response. Has she been so intimidated by the warmers that she is no longer willing to speak out?
Her website has resorted to topics in the news rather than critical discussions of global warming.
Jerry
While the Karl (2015) paper includes very little detail on how the ERSST.V4 temperature were adjusted the Huang (2014) paper linked below does explain these adjustments in good detail and including the use of ocean night time air temperatures (HadNMAT2) to adjust the ship temperatures for the entire period and not just to 1941 as was done in ERSST.V3. The Karl authors were more interested in attempting to make points about the recent warming hiatus or slowdown and merely quantifying the changes that lessen the slowdown without writing directly about the methods used in the changes – and quite frankly the large number of rather subjective choices applied to these methods.
Actually Huang does recognize and talk about the difference in trends derived for a climate model between tas and tos using the GFLD CM2.1 model and there the authors report trend differences from 1875 to 2000 where the ocean air temperature trends are higher than the ocean surface temperature trends on the order of what the Cowtan paper found for several CMIP5 models. While Cowtan judges this difference to be important, it appears the Huang paper minimizes it. Huang is evidently willing to base a judgment on the observed phenomena by using a climate model.
In my view the adjustments used in ERSST.V4 are rather complex and in some cases difficult to interpret and follow. I know the end product in the ERSST.V4 looks very much like it is heavily adjusted by HadNMAT2. At first glance it is difficult to see why this should be since the ERSST.V4 is derived from buoy and ship data and the buoy data was weighted 6.8 times the ship data. The only connecting relationship is that 0.12 degrees were added to the buoy data after calculating that 0.12 degrees was the mean difference between collocated ship and buoy data. That ship data should be the data adjusted by the HadNMAT, I think, and that would make a connection between HadNMAT2 and buoy data adjustments.
Click to access ERSST.V4.P1.JCLI-D-14-00006.1.pdf
Ken
Good point; I had forgotten that Huang discussed the tos vs tas issue. Both the ships and the buoys measure tos (albeit at different depths), and both sets of data are adjusted to match HadNMAT2 on a smoothed basis. I agree that it seems illogical to adjust the buoy data and then claim that ERSST4 is a measure of SST. It is IMO clearly a measure of NMAT on all but sub-bidecadal timescales.
Ken, should you or I write Karl and ask for the detailed methodology for Karl 2015 and if he took precautions not to contaminate tos trend with tas? If he replies no but all the front line climate scientists (who matter) already knew this (same argument made for Mike’s Nature Trick), can we then ask Richardson et al if they knew tas trend was just interpreted into GISTEMP?
I have already talked to Karl and Cowtan about this point. While Karl and his authors were willing to talk to me about other aspects of the 2015 paper and even a pending paper they did not answer my query on using night time ocean air temperatures to adjust a temperature series that is supposed to be SST and what that meant in light of the Cowtan paper. When I noted to Cowtan that in his paper there was a comment indicating that the adjustments described in Karl (2015) using air temperature adjustment is what gave the increased trend in the 2000-2014 period and that if true there was a contradiction then in the Karl paper reporting their series as SST, he appeared to back off the comment in his paper.
I lost contact with the Karl group when we had some disagreements about their pending paper where they were going to (mis)use Empirical Mode Decomposition (EMD) for determining temperature trends. That reminds me to look for any publications where the Karl group might have used EMD.
I should have added that the detailed methodology would come from Boyin Huang and not Karl. Tom Karl while a technical guy, is an administrator and not the technical guy or gal in writing these papers.
Thanks for this analysis. Very interesting.
Energy balance climate sensitivity estimates are likely biased high due to the failure to account for the natural millennium cycle that is so obvious in the climate record, and the urban heat island effect.
Dr. Richard Lindzen writes, “Lewis does not take account of natural variability, and, I suspect, his estimates are high.”
Using the Steven’s aerosol forcing estimates, you estimate TCR = 1.21 °C and ECS = 1.45 °C.
The millennium scale natural warming over the 1.33 centuries between the midpoints of your two periods is 0.11 °C. Accounting for this natural warming, the TCR is reduced to 1.02 °C.
Numerous studies show the HadCRUT4 is contaminated by the effects of urban development. Using estimates from McKitrick & Michaels 2007, the UHIE correction over the period 1980 to 2008 is 0.10 °C. This reduces the TCR to 0.85 °C [0.55-1.30 °C at 5-95% CI], and ECS is 1.02 °C [0.60-1.75 °C at 5-95% CI].
The IGW on the Social Cost of Carbon estimates ECS = 3.0 [1.70-7.15 °C at 5-95% CI]. The IWG high estimate at 95% CI of 7.15 °C is a factor of 4.1 too high! Most of the damages occurs at the high end of the range.
The FUND integrated assessment model (the ONLY model that includes benefits of warming and CO2 fertilization) gives a net social benefit of CO2 emissions of US$16.6/tCO2 [21.3-4.3 US$/tCO2 at 5-95% CI]. CO2 emissions are net beneficial.
See http://www.friendsofscience.org/index.php?id=2205
Natural variability could work in either direction. Mainstream climate scientists tend to suggest that it has, over recent decades, reduced rather than increased the observed trend. I disagree, but personally I’m not convinced that there is a clear millenial cycle either.
McGregor(2015) supplemental the OCEANS2K study, in table S7 says that the oceans SST cooled 0.41C/1000yrs from (801-1800 CE) and 0.31C from (1-2000 CE). Doubling that to get the gross drop for 2K equals 0.62C drop. Looking at the chart plot one can see most of the drop was between 1100-1700CE.
That’s a chaotic walk-down averaging out to 0.1C/100yrs. That certainly supports a 0.165C rise in the 165yrs from 1850-2015 by average natural variation. There may be no cycle but there certainly is variation. My wonder is what happens if the half of the ocean below 2000m, which the consensus assumes is stable and stagnant, gets disrupted and how often that might happen.
Nic,
Did you see the Ljungqvist reconstruction in the document at the link I provided, figure 2? Or see graph at
The Ljungqvist paper’s abstract says “Our temperature reconstruction
agrees well with the reconstructions by Moberg et al. (2005)and Mann et al. (2008) with regard to the amplitude of the variability as well as the timing of warm and cold periods, except for the period c. AD 300–800, despite significant differences in both data coverage and methodology.” It seems this cycle is well established in the literature.
ken, mpainter, the point is regarding plausibility of multi-centennial variability. The models assume none but the consensus literature agrees this is wrong.
I agree that putting high confidence into any one reconstruction is foolish but I think it would also be so to dismiss that they all show 100+ wavelength signals (unless they are specifically weighted to filter out variability like MBH98/99).
Ron, those box and whisker plots indicate to me that the uncertainty of these data is huge for what appears to be 200 year intervals and would render statements about trending temperatures very uncertain. I do not recall how this reconstruction was performed but it looks like it could be simply white/red noise.
No competent scientist would pay much regard to such a plot. The most generous characterization allowable is that it’s inconclusive.
Sorry about the string with my reply being just above.
Hi Ron, a few thoughts.
It’s okay to put confidence in one chart if the confidence is merited. But the McGregor chart is the average of apparent noise, with the average put in 200 year bins. Quite strange, very unconvincing. In a word, dubious.
I have no doubt that there has been centennial climate fluctuation during the Quaternary, and this includes the Holocene.
Armour’s article is behind a paywall, which means my imagination can run wild trying to figure this out:
“That [there is] a robust behaviour in models of apparent (effective) climate sensitivity being lower in the early years after a forcing is imposed.”
This sounds like someone was noodling around with residuals from a temporal comparison of GCM hindcasts and estimates of historical forcings, noticed a few inconsistencies, and then decided the real world had some splaining to do. I suppose that if one persists in trying to press the rumpled fabric of history against the lumpy corpus of AGW theory, the fit will eventually look better.
Matt
Armour’s article is freely viewable at http://www.nature.com/articles/nclimate3079.epdf?author_access_token=LNQKgwEONy5YVJSvlubB29RgN0jAjWel9jnR3ZoTv0PPTNF_sOIeFx9myJ_U10XLsj8_p1lqjx0RRDTJbTTc78eupvudlmNtEiNXnWHNhr4crt8ZuOmLA66TNpMu_PUg
Thanks Nic. Didn’t get me much farther though, I still hit a paywall trying to figure out where the conclusion came from. I was able to peek at a few of the figures in Armour’s paper (reference 8) and I really liked the title of Figure 3:
“The impact of uncertainty in feedbacks patterns on uncertainty in temperature-response patterns in the moist energy balance model.”
Matt, Armour’s 2013 paper (ref 8) is freely available from the PDF link at http://journals.ametsoc.org/doi/abs/10.1175/JCLI-D-12-00544.1. Journal of Climate remove their paywall on 1 January falling over two years after a paper is published.
Nick, I understand that marine air temp is taken at night to avoid radiant day heat reflecting from the ship, but there was not much information I could find to see if the time of observation had a protocol and whether it was consistently followed. This got me thinking about the same question for bucket and intake temperature measurements of the sea surface. As we know, there is a diurnal (day/night) temperature, and observation protocol changes, as known occurred during the world wars. Biases for changes in time of observation should have been foreseeable back then; after all, they had scientists too. It would have taken little effort in each transition of protocol to simply recording both ways for a while to re-calibrate. To believe this was not done and that we have to guess and change the data to erase the global warming pause seems a far stretch from what people think of as science. One can see the roots of Karl(2015) in Thompson(2008) who apparently was heralding in the adjustments to HadSST2:
For Hadley on NOAA not to have thought in the early 2000s to do controlled experimentation when transitioning from buckets and intakes to buoys is unconscionable. That they made the correction by statistical inference rather than controlled experimentation is even more outrageous.
It turns out that actual controlled experiments have subsequently been done of insulated v uninsulated buckets by Matthews and Matthews(2013) which says in part:
I have more questions than ever for Dr. Karl.
Nic, one other consideration of nighttime air temps is that the diurnal temperature range has been documented to have narrowed 0.066C/decade from 1950-2004 according to Vose(2005) Almost all of this rise is in nighttime temperature. Therefore is one is using nighttime temperatures to calculate the mean temperature there is about a 0.03/decade warming bias.
So if Karl used the night air temp any interval of length he would have introduced the diurnal trend as well as the tas trend into tos. But, in thinking more I see no reason for him to have used more than a short interval of tas as normalizing reference bridging buckets to intakes; and if he used the same correction in reverse (to uncorrect when he found the transition only partially occurred) I think he would be fine.
Ron,
Interesting point. However, the evidence you cite is only for land temperatures, which are not reelvant here.
Nic, I am thinking if tas is recorded only at night and ~62% of the warming trend is in the evening sea air trend, this would erase even the 6% difference [6%- 12%/2] in trend of tas vs. tos.
If tos is recorded also at night this could have biased the warming trend of the whole tos (SST) index.
Is there a specific time of for measuring tos?
Is there any way to know of infer the diurnal temperature range trend of the tos or tas?
I meant if 62% of the warming trend is..
Ron, you should make clear in your comments that Karl (2015) merely used the ERSST v4 data and methodology from the work of the paper I linked above with lead author Boyin Huang. Karl’s paper was aimed strictly at attempting to refute the warming hiatus i.e. zero trend. Using the New Karl, or better described as the ERSST v4, temperature series does indeed make the hiatus go away but not the significant slowdown in warming from the period 1976-1999 to the period 2000-2014. I pointed this out in communications with the Karl authors by applying Singular Spectrum Analysis to obtaining non linear trends. They wanted to do another paper wherein they could refute my concept of warming slowdown by using Empirical Mode Decomposition (EMD) and linear regression to obtain trends. When I objected to their application of EMD and showed the authors that they were incorrectly applying the method from both the literature sources I cited and examples I eventually received no replies.
The effect of night time versus day time and the issues of diurnal changes in the ocean can be evaluated by using minimum and maximum model data. That does not mean it will translate to observed temperatures but at least gives another input. As I recall when I did that exercise the differences were small but I can go back and look.
The Boyin Huang paper gives a very detailed look at all the decisions that go into adjusting the ocean temperature series and show that many of the adjustment parameters are subjective in nature. These decisions make the adjusted ocean temperature series and trends in my view more uncertain and potentially arbitrary than those for the land – and the ocean outweighs the land by a factor of 70/30. That subject is probably better to discuss at Mosher’s threads at the Blackboard. Also it is important to note that the 2000-2014 trend period being higher is unique to the ERSST v4 series among all the better known temperature data sets.
It should also be made clear that the Cowtan paper and the more recent ones on the model tas to tos differences are strictly related to models temperatures and not observed temperatures due to the lack of reliable observed ocean air temperatures. As a result the most those papers can do is attempt to quantify the effects on measurements such as model TCR and model trends using air temperatures for land and ocean and comparisons with the observed using blended temperatures. Those papers can and do throw into the comparison mix other adjustments outside the tas and tos difference and those adjustments must be defended and criticized on their own merits.
Ron, on the 2.WW compansation: The ERSSTv4 makes the step change worse than v3b:
???
“Nor is there good observational evidence that air over the open ocean warms faster than SST.”
Perhaps niclewic is on thin ice here. I have done some eye-balling on temperatures since 1980, and the difference seems clear. From wood for trees. Ocean surface temperatures increase 0,44 deg C, total global increase 0,55 deg C, land air increase 0,9 deg C, low troposphere (RSS and UAH) 0,44 deg C. I think you would get much of the same impression of the differences with a different timespan.
For me it is important to get this so right as possible, and I think it is wise to let the data speak. When it comes to the estimates of TCR, I think it starts in the wrong end. I would like to know more about natural variations first. And what interest me more is how climate warming sets itself through in the climate system. I would ask you to say something about that before you ask me to believe in the strength of forsings and sensitivity.
It should be low troposphere temperature increase of 0,45 deg C, as the raw estimate of mean for RSS and UAH.
Nobodysknowledge, Land air temps have a different trend than sea air temps because the sea’s greater heat capacity.
.
This latest attack on the observational record was predictable. The sea air is the least documented temperature so it is most easily manipulated to find some more warming.
.
I agree with you that natural variability is an important context, as are the continued official adjustments to cool the past.
New flash guys
The Karl adjustments
LOWER THE ECS
If you take Karl’s Series Raw versus Adjusted, and calculate Lewis’ Base and Final Periods
The Karl ADJUSTMENTS LOWER ECS
Just stop it with claiming people are manipulating the data.
Ron, here are the ocean tas mean (TMean) and tas minimum (as a proxy for night time air temperature) (TMin) temperature trends for the indicated time periods using the mean of the RCP 4.5 series. The trends were determined using the Singular Spectrum Analysis. The trends listed are the temperature changes for the entire period. The ratios listed are for the TMin/TMean
1861-2100: TMin = 2.383, TMean = 2.293, Ratio = 1.04
1861-2005: TMin = 0.929, TMean = 0.885, Ratio = 1.05
1976-2014: TMin = 0.773, TMean = 0.746, Ratio = 1.04
1999-2014: TMin = 0.297, TMean = 0.289, Ratio = 1.03
The differences, while small, are not insignificant and should have been discussed in detail in the Boyin Huang paper. What is commented in that paper is: “The model SAT is used since the model bias is assumed to be the same during daytime and nighttime.” Remember that the paper used only a single model and did not bother to look at all the model data that are readily available.
Come on, Steven, just because it lowers ECS does not make it correct. And by the way to what adjustments are you referring here. Karl works with temperature series but does not necessarily adjust the series. My complaint with a number of climate science papers is that the analyses published are found to be incomplete and not manipulated. Unfortunately incompleteness can be just as misleading as manipulation – although more forgivable.
Great work Ken, this looks like tas is 5% biased high by the DTR. So this would tend to support tas and tos being roughly equivalent. Nic is right; Richardson’s claim that tas is 9% higher than tos is not born out be observation.
(Can Richardson’s models be wrong?)
CRU adjusted from HADNMAT to HADNMAT2 just 3 years ago. I think it would be too soon for them to try to kludge it again so Richardson et al will have to bide his time or think of something else.
Steven Mosher, good to see you but I think you did not read that Karl(2015)’s legitimacy was an aside not the discussion point.
The reason Karl was brought in was because it reminded us that he used tas (HADNMAT2) to calibrate tos according to his paper. If the two were equivalent my thought was then that Richardson’s claim that they are not would be wrong, and if Richardson was correct that might have implications on Karl(2015).
As another aside I would be curious as to how Karl’s warming of the trend lowered EfCS exactly.
Nic, is this right that using Ken’s analysis of Boyin Huang paper that 5% of Hadley nighttime marine temp record is due to a higher Tmin trend? So subtracting 5% from the HADNMAT 6% higher trend would leave it 1% higher than tos (SST). This seems like too important a piece of knowledge to be overlooked by so many. Where did we go wrong?
Steven, BTW, Karl(2015) has no affect on HADCRUT, which is the relevant ECS parameter in this post.
Ken
Thanks – a useful analysis. It makes the non-divergence between HadMAT2 and HadCRUT4 trends over the industrial period appear even more at variance with model simulations.
Ken
Do you know what the various trends are when computed using linear regression (OLS) rather than SSA? I would be interested to know how close they are, and why they differ.
Steve..
everyone manipulates data..
you know this.
the data that satellites collect is transformed through manipulation into temperatures…
BEST manipulates data.
your snark is meaningless.
“Nor is there good observational evidence that air over the open ocean warms faster than SST.”
I have reconsidered, and think that Nic Lewis has a good point.
HadMAT1 (ocean air temperatures) and HadSST (ocean water temperatures) seem to follow each other very close through a timescale from 1870 to 2000.
After a paper from N A Rayner et. al 2003 http://badc.nerc.ac.uk/data/hadisst/HadISST_paper.pdf
One of the incontrovertible principles of climate is that SST determines air temperature. AGW seeks to turn that principle upside down. Some of the less doctrinaire of AGW proponents have backed off the claim that air temperature determines water temperature.
Nic, I made an error in the dates I used for the reported periods for SSA trend and I have corrected that error below. Again the trends are for the change in temperature over the entire period. The ratios for the SSA trends remain the same and are matched by those using linear regression. I would expect there to be differences in trends between using SSA and linear regression and primarily because SSA is not limited to a linear trend and in my mind nor should it be.
SSA Trends:
1861-2100: TMin = 2.383, TMean = 2.293, Ratio = 1.04
1861-2005: TMin = 0.929, TMean = 0.885, Ratio = 1.05
1976-2014: TMin = 0.724, TMean = 0.698, Ratio = 1.04
1999-2014: TMin = 0.331, TMean = 0.321, Ratio = 1.03
Linear regression Trends
1861-2100: TMin = 2.764, TMean = 2.661, Ratio = 1.04
1861-2005: TMin = 0.705, TMean = 0.670, Ratio = 1.05
1976-2014: TMin = 0.790, TMean = 0.760, Ratio = 1.04
1999-2014: TMin = 0.313, TMean = 0.303, Ratio = 1.03
Thanks, Ken
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