1) A model for the estimation of the wind energy in new areas, from the wind observations in neighborhood areas. By Dr Costas Kyritsis 2000

This is from a study  by the author, financed from the company Arcadia-Rokas that installs Wind-energy parks in selected areas in Greece.


Research ideas under development: astronomical meteorology, astronomical climatology.

2) Application of the solution of stochastic differential equations over finite resolutions, in the estimation of the probability  of the random formation of hurricanes (tornados, cyclones). By Dr Costas Kyritsis 2001

This paper is a direct application of the stochastic calculus on finite resolutions and the simple qualitative analysis on the solutions of random coefficient linear system of two 1st order stochastic differential equations.

3) Proof that a system of weather high pressures (anticyclones, source of good weather) and low pressures (cyclones, source of bad weather) of the earth's atmosphere, placed at the vertices of a spherical harmonic standing wave (eigenstate) with dihedral m-fold equatorial symmetry (e.g.  m= 3, m=4) and 6-fold altitude symmetry (l=6) (or at the vertices and edge midpoints of a platonic regular polyhedron also), is a stable system under bold assumptions. By Dr Costas Kyritsis 2002

In this paper, we prove that under bold assumptions about the atmospheric temperature distribution, a system of  anticyclones (downward spiral wind, or High weather pressures) and cyclones (upward spiral winds, or Low weather pressures) that has the symmetry of a , dihedral 6-fold  equinoctial symmetry (m=3 or m=4, L=6 ) (also placed at the vertices of a icosadodecahedron , and the middle of the vertices of a a icosahedrons or dodecahedron) , is a statistically stable wind-flow system, relative to the attractions and repulsions of the cyclones and anticyclones. The proof is based on a old paper by Leech, who proves that under very general force interactions this pattern among some other of other platonic solids, is indeed a stable system in balance. This pattern has a correspondence to the patterns of the general circulations of the atmosphere as in the models of Handley, Ferrel, and Bergeron with the circulation-cells and the observed High-Low zone in the atmosphere. This concept is the general concept that the atmosphere is a motor, that takes as input the energy from the sun and gives as output kinetic energy of the air (winds). Similar is the concept of the sea where the input maybe the universal attraction from the moon and other celestial bodies and the output is tides at spherical harmonics. Nevertheless to prove that under more refined assumptions about the temperature distribution, the observed system of cyclones and anticyclones, is a deviation of such a statistically stable m- gonal equatorial and l-gonal altitude, symmetry  pattern is a totally different work.  Such spherical harmonic distributions in the planet's atmosphere are only one of many other stochastic eigenstates that a functional space expansion would give for the stochastic state of the global atmosphere at each moment. Besides the spherical harmonic integer parameters m, l also the third radial spherical harmonic integer parameter n seems to occur in the atmosphere as temperature reversals (drop or increase of temperature) as a function of the height from the surface of the ground. That such spherical harmonics patterns are observed also as elasticity waves (or tidal pulsation ) at seismic activity of the earth together with that fundamental period of them (almost 1 hour), was an old (1911) work of  A.E.H. Love. The latter discovery of A.E.H. Love , in particular, may have interesting applications in earthquake statistical forecasting. It may turn out that there is a statistical preference to prior and metaseismic activity, at time intervals of almost one hour, due to the above globe's elasticity waves or tidal pulsation in spherical harmonic patterns. This line of though could be classified as Astronomical Seismology too.

4) New stochastic models for the modulation of  periodic weather phenomena and earth's atmospheric cyclones and  anticyclones random parameters, from the main influential  celestial bodies (planet's, moon's, Jupiter's,  sun's etc )  cycles. By Dr Costas Kyritsis 2003

In this paper we analyze  what are the appropriate stochastic processes, that can describe how, many weather parameters (like temperature, humidity, pressure, wind speed, cloud formation etc) and random variables of earth's atmospheric  cyclones and anticyclones , (like duration, waiting time, radius and rotational period), depend or are modulated or are triggered, in a stochastic or statistical way from various celestial  cycles. The main causal mechanism behind this effect is the modulation of the flow of the solar wind from the motions and cycles of the planetary celestial bodies. In is turn the periodically affected solar wind influences the earth's atmosphere weather phenomena (like cloud formation, wind precipitation etc). More refined causal explanations would involve the electromagnetic and gravitational field too.  Examples of such cycles are: The sun's magnetic cycle (22 years, and sunspots cycles, very close to the 12 earth years duration of Jupiter's "year"), earths orbital cycle (1 year), suns rotation period (from 26 [phenomenal 28] to 37 days), moons rotation (28 days), earths axial rotation (1 day), Jupiter's axial rotation (spin, about 10 hours), and the relatively recently discovered (1960, see keyword Helioseismology ) sun's spherical pulsation (a particular system of spherical harmonics (standing waves) with an equatorial with a strong  harmonic of 5 minutes, and 3 more pulsations, of  periods 40 minutes, 58 minutes and 160 minutes (l=2). Since the equatorial pulsation of 5 minutes as spherical harmonic creates usually a 6-fold (n=0,1,...,20, l=0,1,2,3, m=0,1,...,7) symmetry in the Sun's equator (azimuth order) , with 6-fold (not excluding  other integers  too) altitude symmetries (l=3), this combined with the rotation of the sun creates one more periodicity of period almost 4 days (26/6=4.3, or phenomenal 28/7=4) ! In addition the altitude 6-fold symmetry (l=3) in the spherical harmonic of the sun's pulsation, combined with the magnetic half cycle of 11 years, distinguishes  as special harmonics the cycles of 3.66 and 1.83 years. (If l=2 then the periods are 5.5 and 2.75 years). In these cycles we may add the spin-rotation of the planet Venus (mainly the rotation period of rotation the higher cloudy atmosphere of Venus which has period 4 days and influences more the solar wind)  and the spin-rotation of the planet Mercury. We should add also the well known 1 hour period of the elasticity tidal waves of the earth's solid surface, the 18.6 years cycle of the fluctuation of the earth's axis, the almost 30 years cycle of the shift of perihelion (almost identical to the 30 earth years duration of the Saturn's "year") , and the 25,900 years cycle of the mutation of earth's axis.  Most of these planetary or solar-system cycles influence the earth's atmosphere as we mentioned through periodic modulation of the solar wind that reaches the earth. The solar wind in its turn triggers weather phenomena, like cloud formation etc. Examples of celebrated effects of the solar wind on the earth's atmosphere is the Aurora effect on the North Pole, and similar fluctuations on the earth's magnetic field.. The stochastic processes involved in global weather phenomena have many time and space levels of description. In the functional space expansion of their stochastic states, an orthogonal base of eigenstates, that includes spherical harmonics of the planets atmosphere as well as spherical harmonics of the sun's pulsations and sun's "meteorology", or other periodicities of the local solar system (involving the planets orbit , planet's spin, and moons period, etc)  may lead to better weather forecasting. This research brings also some light to "tuning" effects in the early formation of the solar system, through the standing waves of the solar wind, like the coincidence of  the orbital rotation period with the own spin period of the moon and its coincidence furthermore with the average sun's external own spin period, or the approximate  coincidence of earth's own spin period with Mar's own spin period , and similar other approximate coincidences on the Venus, Jupiter, Saturn etc The suggested tools for such stochastic processes are those discussed in the page about statistics in the  present address pages. These tools include techniques of multi-resolution analysis, and the corresponding wavelet bases, created by the resolution levels. We may also use standard techniques like spectral analysis, (e.g. of wind speed) , search for multiple evenly spaced peaks of histograms etc. The author has verified, to his surprise, using spectral analysis on the wind speed in Greece, that even  the Helioseismology   periodicities of 160 minutes, and 58 minutes do appear in the earth wind speed too! The 6 hours sea tides (e.g. in the bridge of Chalkida in Greece) ,and other wind periodicities of 8 hours , 24 hours,  the 48 hours periodicities and the 28 days periodicities are somehow known to people that pay attention to wind and weather. The strong influence of the sun's cycles, through the radiation,  the solar wind, etc and also of the  various of earth's cycles of astronomic motion on the earth's meteorology,   could be considered as an important for the civilization new science under a name like Astronomical Meteorology.

Remark about such meteorological cycles and ecological, social, and biological cyclic phenomena: These cycles of the planets of the solar system do not only influence the earth's weather as we analyze here (e.g. spectral analysis of wind speed or multiple discrete peak features of wind speed  histograms) , but also ecological, social and biological events. It is well known that the moon's cycle (or the sun's rotation period too) is very closely related to the menstruation cycle of women. The day-night cycles is obviously firmly rooted to human and animal  biology as need for sleep, food , circadian rhythms etc. But it seems that the solar pulsation cycle of almost 3 hours might me strongly correlated with human biological cycles, like the average duration of digestion, period of cycles of sleep (1st sleep is almost 3 hours) etc. There are also solar oscillation with periods between 1hour and 5 minutes. The physics of vibrations of gaseous balls, that give the well known frequencies on all the spherical harmonics, with the interesting relations on their lowest frequencies,  do apply here (see the old works of Lamp, Love, Stokes, Rayleigh etc)   In fact the solar cycles from 11 years to 5 minutes have been discovered to be cycles of  the distant  stars too. The 11 years cycle or the 12 earth's years duration of the Jupiter's "year", seem to correspond to the year's sign of the Chinese astrology, while the sun's spin of (phenomenal) 28 days to the moon sign of the Vedic astrology which seems to be also identical with the biorhythm cycle. These cycles may correspond to the human biology , physiology and consciousness. Examples are the average duration of films and average duration of  education lectures, as constants in the human attention (corresponding the the 3, hours cycles and its submultiples). And the 5 minutes cycle might have most probably firmly rooted cycles in the human psychology , duration of sexual orgasm and libido.  Examples of it in the collective social realm, is  the wide spread average duration of songs (2.5 minutes, the half period) which is also an emotional cycle. The half-period of the 4 days cycle , in other words 2 days or 48 hours, seems to be related with the duration of the metabolism of the proteins. Old eastern philosophy seems to be oriented  to this realization too. Examples are the exercises of Tai chi. Qigong, etc and the way they believed that cosmic energy is interacting with the body and nervous system. My extensive statistical  studies prove that these cycles emerge also in social phenomena when it occurs superposition of collective activities of large numbers. Another example where the solar wind modulated by planetary cycles influences the human biology seems to be the case of the woman's pregnancy. Among all planetary cycles the Venus's "year" (orbital period around the sun) is the closest to the duration of the woman's pregnancy. The previous solar cycles supplement the discoveries of the Maurice Clotterell's cycles that range from 28 days to 18,139 years, and explain the Maya astrology, the small ice age (of 374-450 years) , the rise and fall of large civilizations, and the 7,000-7,500 (2*3740)  years cycle of the apocalypse to Saint John. All large Clotterell's cycles seem to correspond to  a larger period of reversal of the sun's magnetic poles, not of 22 years but of n*3,740 years!  The present cycles nevertheless are in time scale from the 28 days to 5 minutes, thus more interesting and tractable as far as statistical confirmation is concerned. So it might occur to some that  these sequences or threads of causalities might be a future scientific physical, biological , ecological and social explanation of many beliefs of astrologers. It is not astrology though as it has to be based on strictly measurable physical magnitudes like magnetic field, gravitational field, solar wind, atmospheric wind, physiology's chemical  substances,  social statistical magnitudes, behavioral statistical magnitudes etc. Thus,  terms  like Astronomic(al) Meteorology, Astronomic(al) Geo-Sciences (e.g.  http://www.tu-berlin.de/~china/deutsch/abstracts/Song.html also of strong interest to NASA too)Bioclimatology, Biometeorology, (e.g. http://geosciences.ou.edu/~isb/biomet.html ), Meteorological Macroeconomics (e.g. see International Society for Ecological Economics, also at http://www.bom.gov.au/ reference on Dr Don Gunasekera senior advisor, of Meteorological Economics, and courses of universities like http://www.cueb.edu.cn ),  seem more appropriate and give rise to secondary sciences combinations in the causality-thread, like Chronobiology (e.g. http://www.msi.umn.edu/~halberg/introd/index.html ),Astrobiology (e.g. http://astrobiology.arc.nasa.gov/) , Astroecology (e.g. www.astroecology.com) , Astrosociology (e.g. http://www.astrosociology.com/ ) ( see  also research groups like http://cosmobio.science-center.net/english/ and other in the internet like "Comite International de Recherche et d'Etude de Facteurs de l'Ambiance"  http://www.cifa-icef.org/ , also http://www.cyclesresearchinstitute.org/  and  extensive statistical studies by  Michel Gauquelin, Francoise Shneider-Gauquelin  etc.) 

In the next table we summarize the observable random cycles in the meteorological magnitudes with an astronomic causal origin. We use a color metaphorical terminology for the spectrum of their frequencies (The metaphor is that colors too are  discrete areas in the visible spectrum of light frequencies) This color terminology metaphor permit us to call in a poetic way this table "The 12-color rainbow of celestial cycles ". The atmosphere, like an invisible crystal of a regular dodecahedron, blends the external periodic input astronomic influences in a rainbow of  "colors".

The standard deviation of the random period of each "color" is called the "saturation" of the "color" and measures how well tuned or clear or not clear and with blur  is the astronomic cycle appearing in the meteorological magnitudes. In the spectrum of the spectral analysis of the random meteorological magnitude the saturation is a measure of how much discrete or continuum is the spectrum around the exact frequency of the "color". 


"The 12-color rainbow of celestial cycles "

Color Terminology Period Observable in Ecological and other life phenomena Observable Meteorological Magnitude Astronomic Source
Deep Red 11 years Tree rings, Level of lakes , dendroclimatology , etc Humidity, Solar radiation, Temperature, hazard rate of  electromagnetic storms , tornados etc Sun's magnetic poles cycle half period, sun's spot cycle period. Also observable in other stars (closets period in planets Jupiter's "year")
Magenta 2.75 years Fertility in trees Humidity, Solar radiation, Temperature, hazard rate of  electromagnetic storms etc

Stratospheric wind (QBO Quasi-Biennial-Oscillation cycles)

Sub multiple (1/4) of sunspots cycle. (closets period in planets Mar's "year")
Red 1 year 4 Seasons in the life of plants, and animal births Humidity, Solar radiation, Temperature, pressure, Wind speed , hazard rate of  tornados  etc Earth's year
Orange 9 months Women's pregnancy duration Solar wind (closets period in planets Venus' "year")
Light Orange 6 months 2 bold seasons (worm-cold division of year) Humidity, Solar radiation, Temperature, pressure, Wind speed etc Earth's year sub multiple (closest other planet period: submultiples of Mercury's "year")
Yellow 1 month Women's menstruation cycle, emotional cycles Humidity, Solar radiation, Temperature, pressure, Wind speed , hazard rate of weather storms (tornados), hazard rate of  earthquakes , solar wind etc Average period of rotation (spin) of sun, rotation of moon, and orbital moon period
Green 2 weeks Up or down, slow motion of juices in trees Weather , hazard rate of  earthquakes (in moon and sun eclipses), solar wind. Sub multiple of sun's spin period, and moon period. As the solar magnetism has 4-fold symmetry, the period of 1 week (28/4) becomes a natural division.
Turquoise 4-5 days The half period (2 days) is the average time that metabolism requires to absorb the proteins Solar wind, earth's atmospheric wind speed

An observable peak in the wind power spectrum

Sub multiple (1/6) of sun's spin period (26 days at equator),  based on the 6-fold spherical harmonic symmetry that the 5 minutes pulsation (Helioseismology) creates. Also the half period (2 days) is the  period of rotation of Venus clouds.
Blue 24 hours Day-night life functions of trees (O2, CO2 ) and animals, tides in the sea Humidity, Solar radiation, Temperature, pressure, Wind speed Sea level etc Earth's spin (day-night) period
Violet 160 minutes (~ 2.7 hours) Digestion cycle, In half period the average duration of cinema and video films (80-90 min) etc. Wind speed, Solar wind

semi-diurnal cycle

Low period of the solar ball pulsation (see Helioseismology)
Lila 58 minutes (~ 1 hour) Learning attention cycle. In half period as the duration of infomercials etc. Also according to studies, through breath, of advanced yogi the power of activities of the left and right side of the brain, alternate per hour. Wind speed, Solar wind

An observable peak in the wind power spectrum

Characteristic middle frequency  of the solar ball pulsation (see Helioseismology)
Purple 5 minutes In half period as the duration of songs, TV advertisements,  orgasm etc Wind speed, Solar wind

An observable peak in the wind power spectrum

Characteristic first observable frequency  of the solar ball pulsation. Also observable in other stars (see Helioseismology)
Law of amplitude and frequency:     The sample average of the random amplitude A of the meteorological magnitude at fixed atmospheric cube of some scale, is proportional to the square root of the average random period P: 


Law of amplitude and scale:     The sample average of the random amplitude A of the meteorological magnitude at fixed time frequency  (period)  is proportional to the square root of the scale size (side L) of the cube : 




Remark about weather forecasting mathematics and the  mathematics of stochastic meteorological periodicity. The spectral analysis and other stochastic techniques required to discover and prove the above laws in random periodicities in meteorology, formulate entirely different aspects of the atmospheric phenomena, compared to the mathematics formulations in weather forecasting. In weather forecasting we use e.g., the Navier Stokes equations o the fluids , which are deterministic partial differential equations , and we may put random initial and boundary conditions. On the other hand in the quantitative mathematical formulation of the (e.g. seasonal) random periodicities of atmospheric quantities , the particular weather of a place at a time internal (High-Low  pressures systems, cyclones and anticyclones etc) is of the nature of "noise" to the present formulations that concentrate to much more permanent , stable and eternal cyclic patterns of astronomic origin. The solar wind states, can be put as external  conditions to atmospheric wind states. In addition the mathematics used are of highly non-deterministic nature. Such models of meteorological phenomena may have a forecasting value, but this forecasting is not of the usual short-term (e.g. 5 days) nature of the particular 5 days, but of a quite  hidden (and non-phenomenological) eternal cyclic pattern that can range as well from the generic 5 days to generic 11 years or more. The origin of the laws of the sample average of the amplitude is related to the statistical formula of the sample variance of the sample average in a sample, and also to the formula of variance in random walk as a function of time steps.

For an excellent book on Weather cycles see (also page 73 shorter-term cycles in)

"Weather cycles (real or Imaginary?)" by Williams James Burroughs 2nd edition Cambridge

Remark about sunspots:  Sunspots are usually mentioned as enigmatic magnetic anomalies but in fact they are a very standard effect of any gaseous or fluid  ball or plasma ball. Sunspots are the sun's anticyclones in sun's "meteorology" , in other words with inward radial rotational motion of plasma and of course with corresponding magnetic field. Because the interior of the sun has higher temperature, the inward rotation blocks the radiation of warmer interior zones, so they appear darker. Such rotational plasma motion and parallel magnetic field is easily created by the difference of the speed of rotation of sun's plasma at the equator (26 days) and at the polar area (37 days).