# Math from a real scientist

Discussion in 'Environment' started by Old Rocks, Jun 25, 2011.

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### Old RocksDiamond Member

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http://math.nist.gov/~BRust/pubs/MAMERN09/PreprintMAMERN09.pdf

1 Atmospheric CO2 and Global Temperatures
The upper plot in Figure 1 shows an optimal regression spline [11] fit c(t) to the record
of atmospheric CO2 concentrations obtained by combining atmospheric measurements at the
South Pole [5] with reconstructions from Antarctic ice cores [1, 7]. Although the latter display
larger random variations than the former, the two records are consistent in the years where they
overlap. The spline c(t) was used to model the Climatic Research Units record [4] of annual
average global surface temperature anomalies shown in the lower plot. The solid curve was
obtained by fitting the model
T(t) = T0 +  [c(t) &#8722; 277.04] + Asin 2

(t + ) ,
with free parameters T0, , A,  , and . The constant 277.04 ppmv is the preindustrial CO2
concentration estimated by averaging ice-core measurements for 1647-1764. The corresponding
temperature anomaly, estimated by the fit, was  T0 = (&#8722;0.507 ± .016)&#9702;C. The sinusoid,
with  = (71.5 ± 2.2) yr and A = (0.099 ± .012)&#9702;C, represents the oscillation discovered by
Schlesinger and Ramankutty [10]. It accounts for  8 %of the variance in the record. The baseline
T0 +  [c(t) &#8722; 277.04], with  = (0.01039± .00042) &#9702;C/ppmv, accounts for  77 % of the
variance. It indicates a linear relationship between global warming and increasing atmospheric
CO2. The total warming since 1856 has been  0.9&#9702;C, and that warming is accelerating.

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### Old RocksDiamond Member

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http://math.nist.gov/~BRust/pubs/MAMERN09/PreprintMAMERN09.pdf

2 Man-made Emissions and Atmospheric CO2 Concentrations
Annual total man-made CO2 emissions F(ti), for the years 1850-2000, are shown in the
lower plot of Figure 2. These totals are the sums of annual fossil fuel emissions [6] and emissions
due to changes in land use [3]. Taking t0 = 1850.0 gives, for any later time ti,
c(ti) = c0 + Z ti
t0

( )F( )d + S(ti) ,
where c0 = c(t0),
( ) is the fraction remaining in the atmosphere, and S(t) is a ramp function
representing the Mt. Pinatubo eruption on June 15, 1991. S(t) is 0 on [1850.0, 1991.54],
increases linearly to 1 on [1991.54, 1993.54], and remains 1 thereafter. The amplitude constant
 turns out to be negative [2].
One way to estimate
( ) is to assume a harmonic expansion of the form

(t) = A0 + B0t +
nh
Xk=1
[Ak cos (2kt/150) + Bk sin (2kt/150)] , 1850  t  2000 ,
with nh chosen so that 2nh + 4 is less than the number of observed c(ti). Substituting the
expansion into the above integral leads to linear least squares estimates for c0, , and the Ak
and Bk. Choosing nh too large produces implausibly oscillating estimates which violate the
constraints 0 
(t)  1. The estimate for nh = 2 is plotted as a smooth curve in Figure 3. The
corresponding estimate for c(t) is shown as a dashed curve in the upper plot of Figure 2.
Another approach, which seeks a vector approximation &#947;(j), is to approximate the integral
using a rectangular quadrature rule with  = 1 year. This gives a linear regression model
c(ti) = [ 1 , F(ti, j) , s ]&#63726;
&#63728;
c0
&#947;(j)

&#63737;&#63739;
+ &#491;(ti) , &#491;(ti)  N &#56256;&#56320;0,2 ,

where F(ti, j) is a matrix of columns formed from zeroes and the values F(j), s is a vector
representation of S(ti), and &#491;(ti) is a vector of measurement errors. The covariance matrix
2 was estimated by assuming constant variance for the ice core records and a different constant
variance for the atmospheric measurements. These two constants were estimated from
deviations of the measurements from optimal regression spline fits [11] to the two sets of data.
Because of gaps in the c(ti) record, the matrix [1,F(ti, j), s] has more columns than rows,
but estimation is possible because 0  &#947;(j)  1. Even so, the estimates &#710;&#947;(j) oscillate wildly
between those bounds, so it was necessary to estimate average values of
( ) on various time
subintervals of [1850, 2000]. O&#8217;Leary&#8217;s BRAKET-LS algorithm [8] was used to compute 95 %
confidence intervals for 6 nonoverlapping 25-year subintervals shown in Figure 3. The pre-1925
uncertainties are large, but the bounds give good agreement with the &#710;
(t) estimated from the
harmonic expansion. Combining the fit of the corresponding &#710;c(t) to the measurements in Figure
2 with the results in Figure 1 suggests that man-made CO2 emissions are a major contributor
to global warming.

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### whitehallPlatinum Member

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We didn't do it rock head. Let it go. Americans didn't cause tsunamis or earthquakes or drought in Africa. Now isn't the time to go on a global guilt trip when American unemployment is around 15% and we are selling our treasure to oil producing countries. Why not table the global warming thing while America gets back on it's feet with realistic energy production and fewer regulations? Thirty years ago NOAA predicted a new ice age.

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### davemanDiamond Member

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A buck says Roxy doesn't understand a damn bit of that.

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### Old RocksDiamond Member

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Care to post where NOAA predicted an immenant ice ace in 1981?

And who has been fighting anything that would free us from dependence on oil tooth and nail? It isn't the liberals.

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### Old RocksDiamond Member

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I understand every bit as much of it as does Bentwire.

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### whitehallPlatinum Member

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Don't try to be politically cute rocky. Democrats have prevented the US from being independent of foreign oil for the last several decades. Democrats blame America for the theory of global warming and we are in an economic decline while the left wing geniuses claim that a substitute for oil is ight around the corner if only America is willing to become a 3rd world Nation. There is no substitute for oil and it's a shame that ignorant left wing Americans are coerced into believing that America is the cause of the decline of civilization and the solution is to sell our treasure to China and other socialist regimes. Didn't Obama tell Brazil Oil that "America wants to be your best customer"? What kind of story are lefties trying to hand us?

• Thank You! x 1
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### skookerasbilGold Member

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A hate America story..........these people are miserable jealous assholes who are only happy if they are bringing others down to their own level of misery. Its a cognitive fcukk-up thing found in every far left jackass. Theyve set the bar real low for themselves and loath those who are succesful........spend their lives hating on successful people.............a jealousy rage. Its at the core of their make-up for those paying attention.

Fortunately for the rest of us...........their numbers are about 21% at best........and the environmental radicals who troll in here make up a far less % of our population. Basically..........a sliver. Around 10% or less.

Fear not Whitehall.........they are losing in spectacular fashion in 2011. Guys like you and me who can think on the margin. Well..............were.............

Alan West..........^^^^^^^^^^................a future President by the way.........

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### wirebenderSenior Member

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If you had a clue rocks, you would know that all that math is based on flawed assumptions regarding the basic laws of physics. Your guys never deal in the basics because if they do, it becomes clear that they need not go any further. The predictions made by the basic laws of physics, and the associated math proves that their claims have no basis. Therefore, they skip the fundamentals, make a great many assumptions and proceed as if all is well.

Tell me rocks, which fundamental law of physics predicts any of what he claims?

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### IanCGold Member

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what laws of physics were broken by finding advantageous y axis units? when you plot two different things on the same graph and make them look similar by adjusting the scale it is a very powerful tool. when people see similar things side by side they assume a correlation/causation.

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