You seem to be thinking only in
terms of a linear trend.
Not exact matches
Finally, by substituting the historic
linear trend above into the IRR
term of this equation, and the industry average investment period
of 13 years into the c
term, we get the following formula, which shows that nominal R&D productivity / ROI currently stands at about 1.2 (i.e., we get only 20 % back on top
of our original R&D investment after 13 years), is declining exponentially by about 10 % per year, and will hit 1.0 (zero net return on investment) by 2020:
There have certainly been some large El Nino events over the past couple decades, and this leverages any
linear trend estimates
of the long -
term behavior (such as those shown in the recent Vecchi et al paper, which we'll be talking about more in a follow - up post to this).
The standard deviation
of the residuals from a
linear regression to annual averages 1975 - 2007 is 0.472, so we expect a range
of variation
of roughly + / - 0.94 deg.C from the long -
term trend.
It is arguably impossible to accurately detangle a multidecadal oscillation from a long -
term (probably not
linear) forced
trend in 100 years
of data.
The long
term linear trend (which is negative and has a slope
of roughly 6 days per century) indicates that on average the break up dates have been coming earlier in the season.
There have certainly been some large El Nino events over the past couple decades, and this leverages any
linear trend estimates
of the long -
term behavior (such as those shown in the recent Vecchi et al paper, which we'll be talking about more in a follow - up post to this).
Physical scientists are
of course interested in explaining those as well as the long
term, more
linear at the moment
trend.
Would this be the same J. Bob who used FFT (seriously complex stats) to «prove» that long -
term cycles in the temperature record are more significant than the
linear trend revealed by
linear regression (one
of the simplest stats there is)?
-- I'm not quite sure why you think I'm debating the validity (or lack thereof)
of short
term linear trends, as I'm clearly not.
Of course, as they point out «because rainfall is such a variable element, trend values are highly dependent on the start and end dates of the analysis» and the fact they are simply using linear interpolation it is very difficult to derive anything meaningful in terms of climate change from just one ma
Of course, as they point out «because rainfall is such a variable element,
trend values are highly dependent on the start and end dates
of the analysis» and the fact they are simply using linear interpolation it is very difficult to derive anything meaningful in terms of climate change from just one ma
of the analysis» and the fact they are simply using
linear interpolation it is very difficult to derive anything meaningful in
terms of climate change from just one ma
of climate change from just one map.
Leaving that aside, and also leaving aside the issues with fitting a 10th order polynomial to such «data» (lots
of degrees
of freedom...) what is becoming apparent to me is that there is a cyclical
trend that can be linked to physical processes such as the PDO / AMO, as well as a long -
term linear trend.
But the task at hand was to test Dan H.'s claim that the Berkeley data reinforce the characterization
of temperature change as «long -
term linear trend» or «
linear - plus - cyclic.»
Talk about short
term data — and the utter silliness
of linear trends on this.
It's stated in the text, but understanding that the absolute deviation
of the Earth's LOD from its long —
term trend refers to the absolute value
of the deviation from a
linear trend fit, whatever the sign
of the deviation.
In recent years, we also see that the annual temperature anomalies in each category have closely followed their long -
term linear trends, as shown by the final frame
of the GIF animation above:
The long -
term linear trend of the equatorial Pacific SST anomalies are incredibly flat, meaning there is little
trend.
As I understand it, your point is this: There is a long
term linear trend in the data since 1970 and the recent cessation
of a
trend is merely random fluctuation around the long
term trend.
Assuming for argument's sake that the IPCC's calculation
of the long
term trend was broadly correct, would you expect temps to rise in a more or less
linear fashion or would you expect there to be periods when temps were flat or even falling?
This is lower than the observed ice extent in 2015 (4.63 M km2) and is lower than the extent expected from persistence
of the long -
term linear trend (4.66 M km2).
It's very common in science to see a
linear trend with a cycle on top
of it; you have to be careful when interpreting such a plot to know if what you're seeing is long -
term change or short -
term.
So it seems that filtering or not
of the instrumental data in this way interacts with «something» that produces a
linear long -
term trend over the millenium.
«In response to those who complained in my recent post that
linear trends are not a good way to compare the models to observations (even though the modelers have claimed that it's the long -
term behavior
of the models we should focus on, not individual years), here are running 5 - year averages for the tropical tropospheric temperature, models versus observations...»
That doesn't seem plausible to me, and I don't think your two disjoint graphs demonstrate a pressing statistical reason to believe that has to be the case, rather than the simpler explanation that we are seeing a long
term linear warming
trend, masked by a lot
of variance.
In
terms of going back prior to 1970 to identify a
trend associated with global warming, it simply doesn't make any kind
of sense to attempt to construct a
linear trend in the time series for the last 100 years given the slight global cooling
of the 1950's and 1960's.
In fact, you can get a very good fit with actual temperature by modeling them as three functions: A 63 - year sine wave, a 0.4 C per century long -
term linear trend (e.g. recovery from the little ice age) and a new
trend starting in 1945
of an additional 0.35 C, possibly from manmade CO2.
Fit a
linear model (preferably with ARMA (1,1) noise as the noise process is autocorrelated), the
trend is the slope
of that
linear model (i.e. the coeffcient
of the
linear term of the model).
As
of now (or perhaps mor precisely, as
of last week given the ESRL problems) the CO2 - rise is sitting at that unwobbled value (0.25 ppm / yr below the long
term linear trend in CO2 - rise) but there does seem to be potential for one
of those La - Nina - caused dips in the CO2 - rise numbers perhaps in parallel with the re-aligned +8 months ENSO dip.
Two contributors forecast a September minimum below that
of 2007 at 4.0 million square kilometers and 3 contributors suggest a return to the long
term downward
linear trend for September sea ice loss (5.5 to 5.6 million square kilometers).