M. Antonovskiy, Institute of Global Climate and Ecology, Russia, (e-mail : [e-mail]),([e-mail])

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From monitoring of ??2 atmospheric concentrations
to monitoring of global climatic change

• M. Antonovskiy, Institute of Global Climate and
  Ecology, Russia, (e-mail maria.antonovsky_at_chello
  .at),(mischa50_at_mail.ru)

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Atmospheric CO2 concentration field currently
became a potential to discovery facts of global
climatic change,

• If CO2 time series is containing and how much
  information about of different indexes of Global
  Change (biota dynamics, temperature,
  precipitation and so on)?
• Indexes assess by mean of CO2 time
  seriesstability or in stability seasonal cycles
  amplitudes and min-max statistics

• Problems
• - space-temporal non-homogeneity of CO2
  concentration field
• - data non homogeneity (different
• time of observation, different
  location of the stations)
• - demand different mathematical and
  statistical approaches (Fourier analysis,
  Tukey method, multidimensional unfolding
  methods and others)

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SRES scenarios of ??2 emission into the atmosphere
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Observations of the atmospheric CO2
concentrations on Barrow station, Alaska 71
19N, 156 38W.
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Observations of the atmospheric CO2
concentrations on Mauna Loa station. Hawai 19
32N, 155 28W
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Observations of the CO2 atmospheric
concentrations on South Pole station, 89 59S,
24 48W
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General analitical form of a time series of the
monthly observations of the atmospheric CO2
concentrations.

• a0 a1?(t1 -1959)
• a2?(t1 -1959)2A(t1 ) sin(at2 ß )
• t1 slow time with one year step,
• t2 rapid time whith one month step.

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The Trends obtained by Tukey method (
see Appendex )
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Fit equation
1959-1980 y315,10,72(x-1959)0,018(x-1959)(
x-1959)
1980-2006 y338,61,37(x-1980)0,09(x-1980)(x
-1980)
1995-2006 y357,411,64(x-1995)0,014(x-1995)
(x-1995)
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Parabolic regression model comparison for average
years values from station Mauna Loa, South Pole
and Barrow.

• MLO
• 1)1959-1989 ?. ?. y338,57 0,70?(t-1980)
  0,0171?(t-1980)2
• 2)1982-2001 ?.?. y338,49 1,31?(t-1980)
  0,004?(t-1980)2
• 3)1959-2001 ?. ?. y339,57
  0,927?(t-1980) 0,01?(t-1980)2
• BRW
• 1)1974-1989 ?.?. y337,15 0,927?(t-1980)
  0,01?(t-1980)2,
• 2)1982-2001 ?.?. y339,60 1,56?(t-1980)
  -0,0005?(t-1980)2
• 3) 1974-2001 ?.?. y340,07 1,34?(t-1980)
  0,005?(t-1980)2,
• SPO
• 1)1960-1989 ?.?. y338,30 0,7?(t-1980)
  0,017?(t-1980)2
• 2)1982-2001 ?.?. y338,55 1,32?(t-1980)
  0,0034?(t-1980)2.
• 3)1960-2001 ?.?. y338,14 0,9?(t-1980)
  0,01?(t-1980)2 ,

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Analysis rate of increase atmospheric CO2
concentration at each month of the observations
at MLO and BRW station
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Months increase at MLO station
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Months increase at MLO station
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BRW station
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BRW station
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Liner regression fit yaxb for each months
observation from MLO and BRW station. Data from
MLO at period 1959-2006. Data from BRW at period
1976-2004
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MLO station ( time series 1979-2004), Result by
multidimensional unfolding, projection of time
series on the plane of second and third
principal components.
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BRW station ( time series 1979-2004), Result by
multidimensional unfolding, projection of time
series on the plane of second and third
principal components.
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TAP station ( time series 1991-2001), Result by
multidimensional unfolding, projection of time
series on the plane of second and third
principal components.
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Analysis of the dynamics of the impute of the
trend and seasonal cycle into the
time series (synthesis) by the results of
multidimensional development (the base 12).
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A conception of Airborn Fraction (AF) was
introduced by C. Keeling and B.Boolin in 1963 on
the base of the comparison of the two monitoring
time series anthropogenic emission of the CO2
into the atmosphere and observation of CO2
concentration on the MLO station. The AF
conception is the ratio of the increase of CO2
concentration to the increase of the CO2
anthropogenic emission is a stable value, and
could be assessed by constant.
The AF conception was, for example, formulated
by Bolin B., How mach CO2 will Remain in the
Atmosphere? SCOPE 29, The Greenhouse Effect,
Climatic Change and ecosystems., ed.Bert Bolin
et. ?l.,1986
?(CO2)a is an increase of the CO2 amount at
the period t1,t2, ?(CO2)ff is the
corresponding amount of the CO2,coming of the
fossil burning, and ?(CO2)bio is the amount of
the CO2, has coming for decreasing the forest
area .
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• The AF-conception could be used in two
  directions
• To test a model to what degree the model can
  restore this regularity,
• to assess the consequences of the CO2 emission
  (in problems of the projection).

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Our input on the monitoring data of
the last 45 50 years period we have shown that
this conception is affirmed, it to consider this
AF conception with the following important
addition as an increase we should take the
increase of the average value on the interval of
averaging not less than 10 years for monitoring
data of Manna Loa station.
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Parabolic conception

• On the basis of a statistical analysis of the CO2
  atmospheric concentrations time series on Manna
  Loa station we produced a conceptionon a set of
  different parameterizations of the CO2 trend the
  best by the criterion of the projection ability
  is a parablic parametrization.

This conception was formulated M.Ya.Antonovsky,
V.M.Buchstaber. An exploratory analysis of
long-term trends in atmospheric CO2, Tellus,
43B, 1991.
The theoretical base M. Ya. Antonovsky, V. M.
Buchstaber Global Analysis of the Models of the
Global Carbon Cycle. TR 95-08 (1995), Institut
fur Statistic,Operation Research and
Computerverfaren, Universitat Wien, 1-79 pp.
They have proved that in some certain CO2 profile
in the deep ocean the box-diffusion model of the
Global Carbon cycle has the parabolic
solutions/ I.I. Mohov O. I. Mohov V. K.
Petukhov R. R. Haizulin? at proceeding of RAS,
ISSN 0002-3515, 1992, vol. 28, ?1, pp. 11-26,
they found the coefficient of parabolic solution
of initial Bern model that was projected by us on
the base of statistical analysis of morning data.
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Analytical expression of the projection of a
trend of atmospheric CO2 on the interval T2,
2100 P21 314,60,58 (t-1959)0,0186
(t-1959)2 T21989 P22
314,160,93 (t-1958)0,01 (t-1958)2
T22005 (on the base
contemporaneous monitoring data) W2
291,70,0135 (t-1921,6)2
T21985 C2,CB 2746exp
0.01965 (t-1860)
T21988 C2,DOE 29024,63exp 0.02967
(t-1958) T21985 C2H,WML
341,41,081(t-1983) exp 0.02581 (t-1958)
T21983 C2,WML 341,41,081(t-1983) exp
0.02581 (t-1958) T21983 C2L,WML
341,41,081(t-1983) exp 0.02581 (t-1958)
T21983
Remark Generator of data has displayed with the
assistance of parabola if the parabola has
changed, it means that change was happened in
the work of real generator.
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Monitoring data treatment
Projection ability function
The cross shows the year trend , obtained from
the time series of monitoring observations on MLO
station. The curve 1- is the parabola constructed
on data till 1980, to which corresponds the
curve L21K24 ( L 1961-1980 K 1981-2004) . The
data of following observation are corresponding
to this parabola till 1991, when reconstruction
of the time series of the ??2 concentration was
happened. The values of the corresponding
L21K24 became rapidly growth. Parabola
constructed on the data till 1996 to which
corresponds the functional L35K10 is watching the
trend of ??2 concentration at the period from
1997 till 2005.
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• The fit of the function of the projected ability
  of the parabolic model
• a0 a1?(t-1959) a2?(t-1959)2, constructed
  by monitoring data of Mauna Loa station.
• Data of oservations y1,..,yk
• Data of projection yma(k)tm2 b(k)tmc(k)?
  yk1,.,yn, kln

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The object of investigations

• Developed Bern model
• (calibration on climatic sensitivity
• LOW,REF,HIGH)
• ISAM model

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Responses of the developed Bern model on
different scenarios of ??2 emissions into the
atmosphere (a calibration of climatic sensitivity
of REF)
?22 parabolic approximation for Mauna Loa data
From 1959 to 2005
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The investigation on parabolic fit the responses
of the developed Bern model (under the
calibration on climatic sensitivity REF). It has
looked through the responses on different
scenarios of CO2 emission into the atmosphere.
We have made the approximation of presented
responses by the best in relation to criterion of
least square parabolas and have the following
assessments of differences.
By the best way is approximated by parabola the
result of calculations on scenarios B2, And good
enough are approximated the results on
calculation on scenarios IPCC IS92A, IS92a/SAR.
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Investigation of parabolic projection ,
constructed on data of responses of developed
Bern model during 1970-2040. A comparison of a
projection and responses of the model on
interval 2050-2100 .
Conclusion The results in the Tables on pages 28
and 29 completely in accordance the data well
described by parabola, also by the best way
recovered on data till 2040 ????.
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A comparison of the results of
parabolic approximation of the responses of the
developed Bern model. (It presents the difference
between the responses of the model and the best
in the Least Square Method approximation on the
basis of parabolic type )
Conclusion A dependence of the exactness of
parabolic approximation on calibration of model
on climatic sensitivity is weak some responces
of the model well approximated by parabola, the
others does not.
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For the responces of the developed Bern model
with calibration LOW and HIGH the following
results of projection using parabolic
approximation on the data till 2040. Calibration
LOW
Calibration HIGH
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