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We developed recursive procedure, which allows estimation of the part of solar energy accumulated in the Earth´s crust and estimation of the half-time of the heat radiation/accumulation parameter. This kind of parameter can show time during which one half of the accumulated energy is released back to space. The theoretical relationships were verified by the long-term pedology measurements. When we used the Wolf´s numbers as a proxy-solar irradiance parameter for the last 11000 years, we were able to estimate the half-time of the heat parameter of the continental crust. The most probable value of this parameter t1/2 is 270 years, which means that the amount of energy in the whole crust is now at its maximum, because of the anomalously high solar activity starting after the Little Ice Age. We estimated future accumulated solar energy in the crust based on three scenarios of solar activity. All of the three results show a small increase in accumulated energy until 2060 and after that a smaller or higher drop in accumulated energy, and therefore a decrease in the global surface temperature.
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Calculation of solar energy, accumulated in the continental rocks
Pavel Kalenda1, Ivo Wandrol2, Karel Frydrýšek3, Vítězslav Kremlík4
1Pavel Kalenda, CoalExp, Pražmo 129, 73904 (Corresponding author –
2Ivo Wandrol, Silesian University in Opava, Na Rybníčku 1, 746 01 Opava
3Karel Frydrýšek, VŠB-TU, Ostrava, 17 listopadu 15, 708 33 Ostrava-Poruba
4Vítězslav Kremlík, 547 01 Náchod, Czech Republic
Keywords: temperature; heat; accumulation; solar activity; climate changes
(Received 17 July. Accepted 18 August 2018 - NCGT, Vol. 6, No.3, 347-380. Erratum 30 June 2020 - NCGT
Journal Vol.8 No.2)
Two errors were found in this paper, published in the NCGT in 2018. Both eliminated each other and then the
data analysis and results of the paper remained unchanged. Changes are highlighted by yellow.
We developed recursive procedure, which allows estimation of the part of solar energy accumulated in the
Earth´s crust and estimation of the half-time of the heat radiation/accumulation parameter. This kind of
parameter can show time during which one half of the accumulated energy is released back to space. The
theoretical relationships were verified by the long-term pedology measurements.
When we used the Wolf´s numbers as a proxy-solar irradiance parameter for the last 11000 years, we were
able to estimate the half-time of the heat parameter of the continental crust. The most probable value of this
parameter t1/2 is 270 years, which means that the amount of energy in the whole crust is now at its maximum,
because of the anomalously high solar activity starting after the Little Ice Age.
We estimated future accumulated solar energy in the crust based on three scenarios of solar activity. All of the
three results show a small increase in accumulated energy until 2060 and after that a smaller or higher drop in
accumulated energy, and therefore a decrease in the global surface temperature.
Key points of this manuscript:
1. The recursive procedure of temperature changes was developed.
2. The fluids were verified as the key factor for energy transportation.
3. The variations of accumulated solar energy in the crust correlate with climate.
Keywords: solar irradiation, heat accumulation, recursive calculation, OLR, climate, scenario
(Received 17 July. Accepted 17 August)
1. Introduction
The surface temperature of the Earth is determined by the solar irradiance, by the Earth´s albedo, by
the properties of the atmosphere, by the residual heat of the Earth emitted from the depths, but also by
the physical properties of the continental crust rocks, which can accumulate some part of solar energy
for some time and release it later to the space again. The climate models suppose that the solar
irradiance is almost constant (so called solar constant = 1 360,8 ± 0,5 W/m2 (Kopp and Lean, 2011)),
and it varies only during 11-year-long cycles of about 0,1% (Lee et al. 1995). Much more important
should be the annual variations of the solar irradiance due to the eccentricity of the Earth´s orbit. The
Milankowich theory (1930) of the alternations of hot climate periods and ice ages is based on these
changes of the Earth´s orbit and variations of the obliquity of the rotation axis. But the periods of such
changes are much longer than 11 years tens of thousands of years. The Milankowich theory is now
well developed with the help of non-lineal models and we are able to estimate the reversal points of
climate changes (Paillard, 2013).
Because the Sun is not a star with constant radiation and except of the 11-year-long solar cycle there
are much longer cycles, these variations in radiation should be detectable in the global surface
temperatures on the Earth. If the Earth were completely covered by the ocean, which has a big thermal
capacity and relatively short heat exchange periods (only several months), then the whole extra-energy
from the Sun would be released to the space in a short time and only short variations of global
temperature (and climate) would be observed. As the big part of the Earth´s surface is created by
continental rocks, part of incoming solar energy is accumulated in the crust and the back release only
depends on the physical properties of the rock of the continental crust.
The pedology uses the information of the accumulation properties of soil and near-surface sediments
for soil preparation and growing plants (Bedrna, 1989; Kutílek, 1990; Klabzuba, 2001; Hora, 2011).
Temperature measurements in the boreholes were used for paleoclimatological analyses (Čermák,
1971; Čermák et al., 2003; Majorowicz et al., 2006).
In this paper we will focus on derivation of recursive formulas which we will use to calculate
temperature at any depth depending on changes of the surface temperature (solar activity).
In the third chapter, we will calculate part of the solar energy accumulated in the continental crust
during the last 11000 years (Solanki et al., 2004), and we will evaluate the “half-life of the heat”
parameter for the accumulation/release of the energy in the continental crust as a whole. At the end,
we will estimate the global temperature development based on three scenarios of solar activity.
2. Recursive relations for temperature changes at the depth below the surface
Let us have a material cube of infinitesimal small dimensions at the depth h below the surface (half-
space), which is thermally bonded with the surrounding material (see Fig. 1).
Fig. 1. Scheme of the penetration of heat from the surface to the depth and its radiation from the cube in the
depth h.
Changes in temperature inside the cube will depend firstly on the initial state of the temperature field
in the half-space, and on the temperature changes on the surface, which will be the same for the whole
surface of the half-space.
We adopt the following conventions for the next derivations:
. . . mean temperature at the depth
 . . . temperature at the depth in time t
 . . . time step = const
according to Majorowicz et al. (2006)
the formal beginning of the process
Then we can describe the changes in temperature inside the cube by the equation
where the function determines how the temperature in the monitored cube at the depth h is spread in
time to its surroundings, and the function determines the changes in temperature  at the depth h
depending on the temperature  on the surface in the time .
2.1. Equation for heat irradiation ( )
If the temperature at the depth in the material cube is different from the temperature in the
surrounding, then the temperature changes inside the cube  are proportional to the
temperature difference between the cube and its surrounding, multiplied by the material constant .
The index h further marks the fact that the considered cube is at the depth h. This dependence is
known as Newton's law of cooling. It can be written as
 material parameter - must be determined by measurement;
 mean temperature in the cube must be determined by long-term
The solution of linear differential equations of the first order with constant coefficients /2/ using the
method of variation of constants is:
 ,
 
where  is the initial temperature at the depth h. We can suppose that for one step of iteration
,  , and then we can write
where the function  could be formally written as
After the substitution /5/ into /4/ we obtain
We can modify /6/ into
2.2. Relationships for the heat sources on the surface ( )
The Earth´s crust can be thought of as a half-space. The Fourier-Kirchhoff heat equation can be used
for the evaluation of the temperature distribution from the surface to the depths on condition that the
half-space is homogeneous and isotropic medium, which does not contain any heat source.
Berger´s model of thermoelasticity (Berger, 1975; Kalenda, et al., 2012; Frydrýšek et al., 2012)
considers elastic half-space with defined horizontal coordinates and , and with the vertical
coordinate (depth) . The model is designed as a 2-D model with the axes , , because all of the
variables are symmetric with respect to the horizontal axis . The additive surface temperature is
determined by the harmonic wave with the amplitude, the angular speedand
the wave number 
We can solve the equation for determination of the thermal field at the depth h. The x-coordinate can
be neglected due to symmetry of the thermal field (  ) and for clarity, and the variable can be
changed to. Then the thermal field can be described by the equation (see also Mareš et al., 1990)
Carslaw and Jaeger (1959) derived in Chapter II (p. 50) a simplified solution of the equation for the
linear heat flow. This equation can be then simplified for conducting heat from the surface as
whereis the scalar function, which describes the temperature distribution between
borders of the stick or layer. The function  can be written in the form
 
 
 
 .
 
where  are constants. After the substitution into /10/ we obtain
If  is true according to /12/, then the function /11/ is the solution of /10/ and we can write
The function   could be formally written as . If we sign  
 then /13/ could be written as
2.3. Total temperature changes at the depth h at the time t
The function at the depth according to the equation /7/ will have a form
The function will have a form according to the equation /14/. Then the relationship /1/ can be
rewritten for the time  in the form
where  and  are material constants, which depend on the specific place and time
increment only. They should be evaluated by the measurement.
The relationships derived above show that when the material characteristics of the environment do not
change, or changes are very slow (from the calculation point of view), then the temperature changes at
the depth depend only on the temperature changes on the surface.
Based on Figure 1 and the equation /16/ it is evident that for the time, the temperature in the
monitored cube at the depth will change. The heat from the cube will transfer to the surroundings if
the temperature in the cube is higher than the average temperature in the surroundings, while part of
the heat difference from the surface will go to the depth. For the calculation, it is necessary to
determine the value of the coefficients  and through the measurement of temperatures for a
reasonably long period in time steps.
2.4. Half-life of the heat radiation/accumulation parameter
We can define the half-life of the heat
, which is the equivalent of radioisotopes, as the
time during which one half of the heat from the cube at the depth will be radiated. From the equation
/15/ follows
 . /17/
Using equation /16/ we can recalculate the surface temperature at any depth or conversely find
parameters and/or, which are consistent with the measured temperatures at these depths. We can
estimate from the parameters and the time
, which is necessary for the release of one half of
the accumulated energy back into the atmosphere.
2.5. Verification of theoretical equations by pedology measurements
 
  
  
 
 
The temperature profile from the surface of the depth of soil has been monitored since 1961 at the
meteorological and climatological station Ljubljana-Bežigrad (46 ° 04'59 "N14 ° 31'59" E, 285 m
a.s.l) and there is an almost complete database of daily temperatures at the depths of 2 cm, 5 cm, 10
cm, 20 cm, 30 cm, 50 cm and 100 cm (Ljubljana Bežigrad, 2013). A sample of these pedological
temperature measurements in years 2011 and 2012 is shown in Figure 2.
Fig. 2. The temperature records in the depths of 2 up to 100 cm in Ljubljana-Bežigrad.
As seen in Figure 2, the diurnal temperature curve smoothed with the depth and extremes showed the
phase shift (delay) with respect to extremes of temperatures on the surface. This is consistent with the
function of temperature changes in the vicinity of the surface for a homogeneous isotropic medium
(relation /9/ or Mareš a kol., 1990).
Fig. 3 - Comparison of the temperature development in the depth of 2 cm (turquoise) and 100 cm (red) and
recalculated temperatures from the depth of 2 cm to the depth of 100 cm (black). Residuals between measured
and recalculated temperatures at a depth of 100 cm are blue.
Figure 3 illustrates the recalculated temperature from the depth of 2 cm to the depth of 100 cm using a
recursive relation /16/ and the least squares method for the residues of two parameters and. It
can be seen that although the temperature at the depth of 2 cm has a phase shift from the temperature
measured at the depth of 100 cm (correlation r = 0.88), after conversion it exhibits a high correlation (r
= 0.997) where both curves only shifted by the absolute value of 3.75 ° C, which is probably due
to a local geothermal gradient or a paleoclimate development. All recalculated temperatures
from the depth of 2 cm to the depths of 10 cm up to 100 cm show a high degree of correlation with the
correlation coefficient greater than 0.995 with the measured temperatures at these depths (see Table
Table 1 The results of the recalculation of the temperature curves from the depth of 2 cm into the greater
depths. Coefficients and according to the equation /16/ for transferring heat from a depth of 2 cm below
the surface to a depth,
half-live time of heat at a given depth or heat transfer from the surface to this depth,
r with 2 cm the correlation coefficient between temperature curve at a given depth and the temperature curve
in the depth of 2 cm (without recalculation),
r projection - the correlation coefficient between recalculated temperature from the depth of 2 cm to a given
depth and the measured temperature at the same depth,
shift (°C) - means temperature difference between the measured and calculated curve temperatures for the same
depth and the smallest residuals.
Table 1 shows that the heat penetrates the depth of 5 cm very rapidly, in a matter of hours, and half of
the heat is radiated (or arrives from the surface) in about 9 hours. The heat from the surface reaches to
the depth of 20 cm in 2 days and to the depth of 100 cm in almost 17 days. This is in conformity with
the equation /9/ and other measurements in boreholes (Mareš a kol., 1990; Čermák, 1971).
3. The accumulation of solar energy in the continental crust
3.1. Energy budget
According to the Energy budget made by NASA (Smil, 2000), 51% of solar irradiance is accumulated
in oceans and continents. The rest of energy is or reflected back to the space either is absorbed by
clouds or air. A similar model, which is extended by the greenhouse effect, can be found in the 5th
Assessment Report of IPCC (2013) or in the paper by Trenberth et al. (2009). The largest part of the
energy is accumulated in the oceans because of the large heat capacity of water compared to the rocks,
and due to the faster heat transport in the ocean, allowing the heat flow orders of magnitude larger than
in solids. That is why all the climate models foresee a large accumulation of heat in the oceans, which
can be accumulated in a few months, but, on the other hand, may be released during the same period.
Most models assume that the oceans do not serve as long-term heat storage, because a substantial
portion of the heat can be released back to the atmosphere after a few months, years, or a decade
(Yulaeva and Wallace, 1994, Trenberth et al., 2014; Kumar and Hoerling, 2003; McLean et al., 2009).
Therefore climate models consider that after the period of 30 years all of the energy exchange is stable
and "settled”.
In the previous chapters, we analysed the transfer and accumulation of heat in the rock mass, and we
derived the recursive procedure, when we are able to reconstruct the temperature (heat) development
at a specific depth from the temperature variations on the surface, for common rocks of continental
crust. Just as we are able to estimate the "half-life of heat" parameter at a different place and at various
depths below the surface, we can estimate this parameter for the Earth's crust as a whole. This is based
on the consideration that the global temperatures at the surface reflect both short-term variations of
energy, coming from the sun, medium-term (several months) release of energy stored in the oceans,
and the long-term accumulation of energy throughout the Earth's crust. Therefore, we can try to
estimate the Outgoing Longwave Radiation (OLR) from the rocks of the continental crust, and the
most likely "half-life of heat" parameter of the continental crust as a whole.
3.2. Solar activity
To reconstruct the temperature curve at depth h, we need to know the long-time development of the
temperature at the surface, according to the relationship /1/ labelled as  which is measured
with the step  and the mean value of temperature at the depth h
. As direct temperature
measurements are known only at a few places on the Earth for about the last 500 years (Letfus, 1993),
and the Total Solar Irradiance (TSI) is only directly measured in the period of space flights (from
about 1980) (PMOD_WRC 2015; Fröhlich, 2006), we must find a proxy parameter that is proportional
to either global temperatures or the TSI, and it is known for a period of at least 10 times longer than
the supposed "half-life of heat” release parameter of the continental crust.
Therefore, we need the data series from at least several thousand years, and consistent over the whole
period. Such data series appears to be the proxy solar activity (Wolf numbers) that can be
reconstructed by several independent methods, and which is independent on the global temperature,
and even on other climate parameters, such as the concentration of GHG or flow in the oceans and
atmosphere. Wolf numbers can be reconstructed using at least two different methods (Usoskin, 2013):
Helio-modulation of cosmic rays, which modulates isotopes 1) 14C, and/or 2) 10Be. Usoskin et al.
(2002) or Solanki et al. (2004) reconstructed solar activity proxies (decade-averaged modulation
potential) based on the concentration 10Be, and comparison with the observed Wolf numbers in
historical times (Usoskin, 2013). For our purposes, we took a series of 11,000 Year Sunspot Number
Reconstruction by Solanki et al. (2004), which is available on the NOAA server.
3.3. Climate variations
The difference between the long-period component of OLR and the mean value of the surface
temperatures must be the same as the difference of the heat released at the depth h according to the
relation /7/. In other words, climatic variations should also reflect among others a long-term
accumulation of heat in the rocks. We can take, as a representative of the long-period component
OLR, directly the global temperature (or its differences from the mean temperature), or another
parameter, which contains global temperatures directly or indirectly, such as the water levels of the
world ocean or the glaciation area.
Comparing the two curves, i.e., which is represented in this case by the proxy of the solar activity,
converted to the depth h according to the relationship /14/, and the measured global temperatures or
the level of the world ocean, we should be able to estimate the parameter according to the
relationship /7/, for which we obtain the biggest correlation coefficient. Then we can calculate the
“half-life of the heat”
parameter according to the relationship /17/.
For our purposes, we chose as a climatic series the directly reconstructed global temperatures
“Glcru_eiv_composite” by Mann et al. (2008), which are available on the NOAA server. The
reconstructed temperatures with the time step of one year were recalculated into two series by
averaging - in a series of time increments of 10 years and the second series of time increments of 10
years, but with averaging window of 50 years. “Glcru_eiv_composite” series has been available since
500 AD, i.e. for the last 1500 years.
3.4. Results of analyses
For the conversion of energy from the Earth's surface to the depth h, it is necessary to know two
parameters: and . For the analysis of the correlation between the radiated heat from the depth h
to the surface and surface temperatures, it is not necessary to know the parameter , since it only
moves the absolute level of temperature at the depth h compared to the surface of the constant value.
Therefore the correlation coefficient is not dependent on it. We used therefore coefficient = 1. On
the other hand, the coefficient has a real physical meaning and shows how quickly the heat
accumulates in the Earth's crust, and/or how quickly it is radiated back to the surface. We calculated
for different coefficients the correlation coefficient between the two time series: 1) Of the
reconstructed surface temperature by Mann et al. (2008) and 2) volume of the heat release from the
depth h to the surface (OLR) according to /1/ (see Fig. 4).
Fig. 4 Correlation coefficient between reconstructed global temperature CRU_composite (Mann et al., 2008) and
released heat from the crust for various half-life of heat as a parameter.
It is evident that the correlation coefficient between the smoothed temperatures within the window of
50 years is higher than for the temperature smoothed within a 10-year window, and reaches the
maximum r = 0.86, indicating a statistical dependence between the two rows at a significance level of
15%. The higher correlation coefficient for the longer window shows that the values of the proxy-
Wolf numbers in increments of 10 years are physically smoothed, and that the samples did not allow
obtaining a higher accuracy either in amplitude or time. Therefore, the smoother curve of the
reconstructed temperatures in the 50-year window corresponds better with the primarily smoothed
curve of the proxy-Wolf numbers. The resulting curve of heat stored in the continental crust (in
relative units) for the maximum correlation coefficient (i.e. for
years) together with the
reconstructed temperature curve, is shown in Figure 5.
Fig. 5 Comparison between accumulated heat from solar activity and reconstructed global temperature in 50-year
time window (according to Mann et al., 2008).
We can also compare the same curve of the accumulated heat in the continental crust, with the global
sea level; reconstructed by Jevrejeva et al. (2009) (see Fig. 6).
Fig. 6 Comparison between accumulated heat from solar activity and reconstructed global sea level (Jevrejeva et.
al 2009 Fig. 3b).
Correspondence between the reconstructed global ocean level and the accumulated heat in the Earth's
crust appears to be better than for the reconstructed temperatures by Mann et al. (2008), because the
first derivative of the two curves matches more. Visible differences are only in time of the ocean level
drops after the biggest explosions of volcanoes, especially Samalas, Kuwae and Tambora, which is, of
course, a matter of the model used for the reconstruction of the global ocean level.
3.5. Discussion
The temperature variations on the surface are transmitted into the depths very slowly due to the low
heat conductivity of rocks (Čermák, 1971; Čermák et al., 2003). Heat is transferred faster by help of
fluids. Thus, we can estimate that the whole continental crust plays crucial role during the
accumulation of heat and its radiation back into space. Fluids play a significant role in this process.
The heat transfer from surface to depths can be made not only by sharing or by convection of fluids,
but also by other mechanisms, such as the thermoelastic wave with ratcheting (Kalenda et al., 2012).
The interaction between planets, the Sun, atmosphere, hydrosphere, and geosphere is well known
(Pulinets and Ouzounov, 2011; Mörner ed., 2015). For example, the variations of seismic activity have
the same periodicity as the Sun or the whole Solar System. There are periods of the Schwabe cycle
(≈11 years), the Hale cycle (≈22 years), and the Van (Jose) cycle (≈179 years) (Jose, 1965; Kalenda et
al., 2012). The solar activity reflects relative positions of the planets, and thus the movement of the
Sun around the Solar System barycenter (Charvátová, 1990). There is a close link between the
orogeny and cool climatic periods (Kalenda et al., 2012). It is therefore not surprising that many
authors have found similar periods of planets in the Solar System and climate changes. These links
were described in the entire issue of the PRP journal (Mörner 2015). For one of shortest periods we
can point to a period of 60 years, which shows the binding activity of the sun and the giant planets of
the Solar System (Scafetta, 2010, 2011 and 2012). This period is observable both at the global sea
level (Jevrejeva et al., 2009), and from the PDO and AMO climatic parameters (Klyashtorin, 2001;
Akasofu, 2009). Most importantly, the 60-year period is also marked at the aurora borealis, which
obviously does not have any connection with the climate on the Earth, but it reflects the solar wind
variations, and thus the variations of solar activity (Křivský and Pejml, 1988). Therefore, we modeled
60-year oscillations on the curve of the accumulated heat at the depths, although this period cannot be
seen on proxy data the Wolf numbers.
As we can estimate the future solar activity according to the gravitational influence of a planet
(Kalenda and Málek, 2008), we can suggest three possible scenarios for the development of solar
activity in the next 80 years Table 2.
Table 2 The estimations of average Wolf´s numbers in 10-year window
In scenario A, we assume that solar activity between the years 1622-1658 corresponds to solar activity
between the years 1980-2016. The average monthly number of sunspots will be at its maximum in the
following years: 2029 (20), 2041 (16), 2051 (10), 2062 (26), 2074 (26), 2085 (53) and 2096 (68).
In scenario B, we use the prediction of the future solar activity according to R.J. Salvador (2013) with
maxima: 2029 (27), 2038 (16), 2048 (40), 2058 (49), 2069 (49), 2079 (40) a 2093 (26), which we
smooth in a 10-year time window by the coefficient 1.7 to be comparable with the Wolf´s number
according to Solanki et al. (2004) (see Table 2).
In scenario C, we assume that the solar activity is the same as now, i.e. the Wolf´s numbers are 40 for
the whole period until 2100. The result for scenario C can be seen in Figs. 5 and 6 (the real data of
solar activity is used until 2015). We can see a so called “hiatus” between 2000 and 2030, which is
confirmed on real data now. The global temperature should rise between 2030 and 2060, but less than
between 1970 and 2000. Since 2060 we suppose the next “hiatus” of global temperatures. Moreover,
we suppose at least one volcano eruption with the VEI at least 5 (Kalenda and Neumann 2012), which
can drop the global temperature by about 0.5°C and more.
We make a projection to 2100 of the accumulated heat in the crust according to all three scenarios for
the development of solar activity, together with developments of global temperatures by Mann et al.
(2008) (see Fig. 7).
Fig. 7 The development of global temperatures according to scenarios of solar activity A, B and C until 2100
(relative units). Green real global temperatures according to Mann et al. (2008).
The current observed "hiatus" in temperatures between 1998 and 2015 corresponds fully to all three
scenarios of developments in global temperatures, because solar activity has been decreasing generally
since 1995. This "hiatus" is only assumed by 1 of 102 scenarios of the IPCC (Christy, 2015). The
period 2020 - 2040 will prove or disprove our hypothesis, based on the accumulation of heat in the
rocks of the continental crust and its release back into space after some time.
4. Conclusion
If we admit that part of the incident energy from the Sun accumulates in the rocks of the continental
crust, we can estimate, based on the solar activity and a climatological parameter containing heat or
temperature, what the material parameters of these rocks are. The greatest correlation coefficient
between the number of the proxy-Wolf numbers (Solanki et al., 2004) and global temperature
anomalies in the window of 50 years in the increments of 10 years (Mann et al., 2008) has been
detected for the "half-life of heat" parameter
= 270 years. For this parameter, the correlation
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a sign of the fact that there is a link between them.
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(Jevrejeva et al. 2009). The first derivative of both curves also corresponds, which is a sign of one
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shown that the rate of global temperatures increase will slow down (conservative scenario C), or will
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not in any case exceed 1.5 ° C, even if people emit CO2 into the atmosphere in the same way as
recently. The modern temperature maximum seems to be the result of accumulated energy in the
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... Tak, jako je v denním rytmu pozorováno zpoždění maximálních teplot za maximálním osvitem (pravé poledne) o několik desítek minut s tím, jak je nutno prohřát přípovrchové vrstvy atmosféry, tak v ročním rytmu je pozorováno zpoždění maximálních letních teplot za letním slunovratem o více než měsíc s tím, jak je nutno prohřát přípovrchové vrstvy oceánů. Obdobně pak platí, že pro dlouhodobé klimatické periody se opožďuje pozorované maximum teplot za maximem zářivosti Slunce o desítky až první stovky let s tím, jak pomalu se nahřívá přípovrchová vrstva kontinentnální kůry (Kalenda et al. 2018). Na datech z vrtu Vostok (Petit et al. 1999) i na proxydatech sluneční aktivity za posledních cca 1000 let (Usoskin et al. 2006) je možno ukázat, že dnešní tzv. ...
... Na datech z vrtu Vostok (Petit et al. 1999) i na proxydatech sluneční aktivity za posledních cca 1000 let (Usoskin et al. 2006) je možno ukázat, že dnešní tzv. antropogenní globální oteplování (AGW) je možno z 85 % vysvětlit nejvyšší sluneční aktivitou od konce Malé doby ledové do roku 1958, kdy dosáhla svého maxima, za posledních cca 600 let (Steinhilber et al. 2009) a poločasem akumulace energie v kůře 270 let (Kalenda et al. 2018). Tedy fyzikálními ději zcela jistě neantropogenními. ...
... Závisí proto nejen na příkonu slunečního záření a vyzařování do vesmíru, ale také na akumulaci tepla v atmosféře, oceánech a kontinentech. Povrchová teplota není proto bezprostředně časově svázána se sluneční aktivitou, ale s jejím časovým integrálem (Kalenda et al. 2018). ...
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Pohyb vody a tepla na Zemi představuje z fyzikálního hlediska chaotický systém, jehož chování je v detailu nepředpověditelné. Avšak v mnohaletých řadách lze vypozorovat, že dochází ke kvazicyklickým změnám rozložení povrchové teploty a srážek. Tyto změny se nazývají klimatické cykly. Jedním z významných vlivů, které cykly způsobuje, je proměnná sluneční aktivita, která má za následek změny slunečního osvitu Země. Ta ovlivňuje povrchovou teplotu Země, proudění atmosféry a oceánů, a konečně změny skupenství vody. Záření, vycházející ze Slunce, je Zemí zachycováno jenom velmi nepatrně. Země zachytí přibližně jednu dvoumiliardtinu, tj. 1,8⋅10 17 W z celkového výkonu Slunce. 3,85⋅10 26 W. V době minima sluneční aktivity byl změřen tok slunečního záření 1361 W/m 2 (Kopp, Lean 2011). Sluneční irradiace je tok sluneční energie procházející plochou 1 m², kolmou na směr paprsků, za 1 s ve střední vzdálenosti Země od Slunce (1 AU) měřený mimo zemskou atmosféru.
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Static vertical pendulums have been installed in mines and caves in Central Europe since 2007. The two dimensional optical measurement of tilt of rock mass and continuous full digital on-line evaluation of results makes possible to detect small tilt of the surroundings with resolution of tens of nanoradians or deformation of the surroundings in the horizontal plane with resolution of hundereds nanometers. The paper will describe the measurement device, measurement method, observed effects and theirs evaluation. The two years experience of measurement shows that it is possible to find the main direction of stress in the surroundings of the pendulum and its development in time. The noise level and anomalous deformation development shows the value of relative stress in the surroundings of the pendulum. The correlation of de-formation between distant stations shows existence of stress variations that they are not of local origin. The stress field has wider than regional character and effects of very far origin can be observed. The great changes in stress orientation and in stress state were observed before the biggest earthquakes on the Eurasian lithosphere plate.
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Climate change from increased greenhouse gases arises from a global energy imbalance at the top of the atmosphere (TOA). TOA measurements of radiation from space can track changes over time but lack absolute accuracy. An inventory of energy storage changes shows that over 90% of the imbalance is manifested as a rise in ocean heat content (OHC). Data from the Ocean Reanalysis System, version 4 (ORAS4), and other OHC-estimated rates of change are used to compare with model-based estimates of TOA energy imbalance [from the Community Climate System Model, version 4 (CCSM4)] and with TOA satellite measurements for the year 2000 onward. Most ocean-only OHC analyses extend to only 700-m depth, have large discrepancies among the rates of change of OHC, and do not resolve interannual variability adequately to capture ENSO and volcanic eruption effects, all aspects that are improved with assimilation of multivariate data. ORAS4 rates of change of OHC quantitatively agree with the radiative forcing estimates of impacts of the three major volcanic eruptions since 1960 (Mt. Agung, 1963; El Chichon, 1982; and Mt. Pinatubo, 1991). The natural variability of the energy imbalance is substantial from month to month, associated with cloud and weather variations, and interannually mainly associated with ENSO, while the sun affects 15% of the climate change signal on decadal time scales. All estimates (OHC and TOA) show that over the past decade the energy imbalance ranges between about 0.5 and 1 W m(-2). By using the full-depth ocean, there is a better overall accounting for energy, but discrepancies remain at interannual time scales between OHC- and TOA-based estimates, notably in 2008/09.
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This paper shows how the probabilistic SBRA (Simulation-Based Reliability Assessment) Method (i.e. Monte Carlo approach) is applied to the model of the behaviour of the lithosphere of the Earth. The method extends our initial work where we created the geomechanical model of the lithosphere. The basic idea was about the genesis of thermoelastic waves due to thermal expansion of the rock mass and the ratcheting mechanisms. SBRA method applied in this problem is a new and innovative trend for modelling in mechanics.
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We analysed three "independent" data sets of three volcanoes (Katla and Hekla on Iceland and Pichincha in Equator) and global seismicity for the time span of the last 500 years. The statistical analysis of volcano eruptions and global seismic activity show that these processes are not independent and random, but they are the consequence of one global process with the prevailing periods of approximately 43, 53 and 63 years. This process will have its maximum between 2007 and 2020. The large earthquakes precede the volcanic activity on a global scale. The Chile earthquake triggered the Eyjafjallajökull volcano activity and the Tohoku earthquake triggered the activity of volcanoes Etna (for only one week), Grímsvötn on Iceland (for only one week) and El Hiero on the Canary Islands. The seismic activity below the Katla volcano started, which means that the eruption could be expected within a period of the next couple of years.
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An update is provided on the Earth's global annual mean energy budget in the light of new observations and analyses. In 1997, Kiehl and Trenberth provided a review of past estimates and performed a number of radiative computations to better establish the role of clouds and various greenhouse gases in the overall radiative energy flows, with top-of-atmosphere(TOA) values constrained by Earth Radiation Budget Experiment values from 1985 to 1989, when the TOA values were approximately in balance. The Clouds and the Earth's Radiant Energy System (CERES) measurements from March 2000 to May 2004 are used at TOA but adjusted to an estimated imbalance from the enhanced greenhouse effect of 0.9 W m(-2). Revised estimates of surface turbulent fluxes are made based on various sources. The partitioning of solar radiation in the atmosphere is based in part on the International Satellite Cloud Climatology Project (ISCCP) FD computations that utilize the global ISCCP cloud data every 3 h, and also accounts for increased atmospheric absorption by water vapor and aerosols. Surface upward longwave radiation is adjusted to account for spatial and temporal variability. A lack of closure in the energy balance at the surface is accommodated by making modest changes to surface fluxes, with the downward longwave radiation as the main residual to ensure a balance. Values are also presented for the land and ocean domains that include a net transport of energy from ocean to land of 2.2 petawatts (PW) of which 3.2 PW is from moisture (latent energy) transport, while net dry static energy transport is from land to ocean. Evaluations of atmospheric re-analyses reveal substantial biases.
The authors have used a catalogue of auroral observations compiled from all the cataloques (or their corrections) hitherto published, sets of observations and their own supplement of hitherto uncatalogized or unknown observations of the aurorae, extracted from the most various histrocial sources found in the Czech Lands. The supplement contains 91 aurorae from Bohemia and is presented in Part I. This catalogue gives the ordinal number of the aurora, the date, the description in the original language and the English translation. The world catalogue and its elaboration with regard to long-term variations of aurorae is in Part II, and contains 3878 northern aurorae from latitudes <55°N. Part III deals with the relation between the fluctuations of the secular solar activity, in terms of occurrence of aurorae, and the fluctuations of the climate, with particular regard to Central Europe and Bohemia. -from Authors
Using many features of Ian Wilson's Tidal Torque theory, a mathematical model of the sunspot cycle has been created that reproduces changing sunspot cycle lengths and has an 85% correlation with the sunspot numbers from 1749 to 2013. The model makes a reasonable representation of the sunspot cycle for the past 1000 yr, placing all the solar minimums in their right time periods. More importantly, I believe the model can be used to forecast future solar cycles quantitatively for 30 yr and directionally for 100 yr. The forecast is for a solar minimum and quiet Sun for the next 30 to 100 yr. The model is a slowly changing chaotic system with patterns that are never repeated in exactly the same way. Inferences as to the causes of the sunspot cycle patterns can be made by looking at the model's terms and relating them to aspects of the Tidal Torque theory and, possibly, Jovian magnetic field interactions.
The rate of sea level rise and its causes are topics of active debate. Here we use a delayed response statistical model to attribute the past 1000 years of sea level variability to various natural (volcanic and solar radiative) and anthropogenic (greenhouse gases and aerosols) forcings. We show that until 1800 the main drivers of sea level change are volcanic and solar radiative forcings. For the past 200 years sea level rise is mostly associated with anthropogenic factors. Only 4 ± 1.5 cm (25% of total sea level rise) during the 20th century is attributed to natural forcings, the remaining 14 ± 1.5 cm are due to a rapid increase in CO2 and other greenhouse gases.
Remarkable among the atmospheric phenomena associated with El Niño–Southern Oscillation (ENSO) is the lag in the zonal mean tropical thermal anomalies relative to equatorial east Pacific sea surface temperatures (SSTs). For the period 1950–99, the maximum correlation between observed zonal mean tropical 200-mb heights and a Niño-3.4 (5°N–5°S, 120°–170°W) SST index occurs when the atmosphere lags by 1–3 months, consistent with numerous previous studies. Results from atmospheric general circulation model (GCM) simulations forced by the monthly SST variations of the last half-century confirm and establish the robustness of this observed lag. An additional feature of the delay in atmospheric response that involves an apparent memory or lingering of the tropical thermal anomalies several seasons beyond the Niño-3.4 SST index peak is documented in this study. It is characterized by a strong asymmetry in the strength of the zonal mean tropical 200-mb height response relative to that peak, being threefold stronger in the summer following the peak compared to the preceding summer. This occurs despite weaker Niño-3.4 SST forcing in the following summer compared to the preceding summer. The 1–3-month lag in maximum correlation is reconciled by the fact that the rainfall evolution in the tropical Pacific associated with the ENSO SST anomalies itself lags one season, with the latter acting as the immediate forcing for the 200-mb heights. This aspect of the lagged behavior in the tropical atmospheric response occurs independent of any changes in SSTs outside of the tropical east Pacific core region of SST variability related to ENSO. The lingering of the tropical atmospheric thermal signal cannot, however, be reconciled with the ENSO-related SST variability in the tropical eastern Pacific. This part of the tropical atmospheric response is instead intimately tied to the tropical ocean's lagged response to the equatorial east Pacific SST variability, including a warming of the tropical Indian and Atlantic SSTs that peak several seasons after the Niño-3.4 warming peak.