Skip to main content

Theory of series of exponents and their application for analysis of radiation processes

  • Chapter
Global Climatology and Ecodynamics

Part of the book series: Springer Praxis Books ((ENVIRONSCI))

Abstract

Academician K. Ya. Kondratyev in one of his first monographs (Kondratyev, 1950) stressed the availability of the idea put forward by Academician V.A. (1968) which is associated now with the term “series of exponents”. This involves computation of values integrated over the frequency spectrum necessary for analysis of radiation processes: in this case, a “palisade” of a great number of spectral lines gives rise to not purely technical difficulties.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  • Ambarzumyan V.A. (1968). Present natural sciences and philosophy. Achievements of Physical Sciences, 96(1), 3–19 [in Russian].

    Google Scholar 

  • Anderson G.P., Clough S.A., Kneizys F.X., Chetwynd J.H., and Shettle E.P. (1986). AFGL Atmospheric Constituent Profiles (0–120 km), AFGL-TR-86-0110. Environmental Research Papers, No. 954.

    Google Scholar 

  • Bogdanova Yu.V. and Rodimova O.B. (2005). One-parameter approximation for the CO2 transmission functions in the 15 mm region. Computer Technologies, 10(1), 87–93 [in Russian].

    Google Scholar 

  • Chou M.-D. and Kouvaris L. (1991). Calculations of transmission functions in the infrared CO2 and O3 bands. J. Geophys. Res., 96(D5), 9003–9012.

    Article  Google Scholar 

  • Chou M.-D., Ridgway W.L., and Yan M.M.-H. (1993). One-parameter scaling and exponential-sum fitting for water vapor and CO2 infrared transmission functions. J. Atmos. Sci., 50, 2294–2303.

    Article  Google Scholar 

  • Chou M.-D., Ridgway W.L., and Yan M.M.-H. (1995). Parameterizations for water vapor IR radiative transfer in both the middle and lower atmospheres. J. Atmos. Sci., 52, 1159–1167.

    Article  Google Scholar 

  • Evgrafov M.A. (1968). Analytical Functions. Science, Moscow, 472pp. [in Russian].

    Google Scholar 

  • Firsov K.M. and Chesnokova T.Yu. (1998). A new method of treating overlapping absorption bands of atmospheric gases in radiative transfer parameterization. Atmospheric and Oceanic Optics, 11, 356–360.

    Google Scholar 

  • Firsov K.M., Mitsel A.A., Ponomarev Yu.N., and Ptashnik I.V. (1998). Parameterization of transmittance for application in atmospheric optics. J. Quantitative Spectroscopy and Radiative Transfer, 59(3/5), 203–213.

    Article  Google Scholar 

  • Firsov K.M., Chesnokova T.Yu., Belov V.V., Serebrennikov A.B., and Ponomarev Yu.N. (2002). Series of exponents in computations of radiation transfer by Monte Carlo method in spatially non-homogeneous aerosol-gaseous media. Computer Technologies, 7(5), 77–87 [in Russian].

    Google Scholar 

  • Fomin B.A. and Gershanov Yu.V. (1996). Tables of the Benchmark Calculations of Atmospheric Fluxes for ICRCCM Test Cases, Part II: Shortwave Results. Russian Research Center, Kurchatov Institute, Moscow, IAE 5990/1, 42pp.

    Google Scholar 

  • Fouquart Y., Bonnel B., and Ramaswamy V. (1991). Intercomparing shortwave radiation codes for climate studies. J. Geophys. Res., 96, 8955–8968.

    Article  Google Scholar 

  • Goody R., West R., Chen L., and Crisp D. (1989). The correlated-k method for radiation calculations in nonhomogeneous atmospheres. JQSRT, 42(6), 539–550.

    Article  Google Scholar 

  • Kistenev Yu.V., Ponomarev Yu.N., and Firsov K.M. (2002). Analysis of temperature dependence in cumulative spectra of rotational-vibrational absorption bands of atmospheric gases. Atmospheric and Oceanic Optics, 15, 689–691.

    Google Scholar 

  • Kistenev Yu.V., Ponomarev Yu.N., Firsov K.M., and Gerasimov D.A. (2003). Use of lacunarity parameter in analysis of the errors in atmospheric transmittance inhomogeneities calculated using exponential series. Atmospheric and Oceanic Optics, 16, 247–250.

    Google Scholar 

  • Kneizys F.X., Robertson D.S., Abreu L.W., Acharya P., Anderson G.P., Rothman L.S., Chetwynd J.H., Selby J.E.A., Shetle E.P., Gallery W.O., Berk A., Clough S.A., and Bernstein L.S. (1996). The MODTRAN 2/3 Report and LOWTRAN 7 Model. Phillips Laboratory, Geophysics Directorate, Hanscom Air Force Base, MA, 260pp.

    Google Scholar 

  • Kondratyev K.Ya. (1950). Long-wave Radiation Transfer in the Atmosphere. Gostechizdat, Leningrad, 278pp. [in Russian].

    Google Scholar 

  • Lacis A.A. and Hansen J.E. (1974). A parameterization for the absorption of solar radiation in the Earth’s atmosphere. J. Atmos. Sci., 31, 118–133.

    Article  Google Scholar 

  • Lacis A. and Oinas V. (1991). A description of the correlated k-distribution method for modeling nongray gaseous absorption, thermal emission, and multiple scattering in vertically inhomogeneous atmospheres. J. Geophys. Res., 96, 9027–9063.

    Article  Google Scholar 

  • Leont’ev A.F. (1976). Series of Exponents. Science, Moscow, 536 pp. [in Russian].

    Google Scholar 

  • Leont’ev A.F. (1980). Sequence of Polynomials of Exponents. Science, Moscow, 384 pp. [in Russian].

    Google Scholar 

  • Leont’ev A.F. (1983). Integral Functions. Series of Exponents. Science Publ. Moscow, 175 pp. [in Russian].

    Google Scholar 

  • Li Z., Trishchenko A., and Cribb, M. (2000). Analysis of cloud spectral radiance/irradiance at the surface and top of the atmosphere from modeling and observations. Proceedings of the Tenth Atmospheric Radiation Measurement (ARM) Science Team Meeting. Available at http://www.arm.gov/publications/proceedings/conf10/abstracts/li-z.pdf

  • Liou K.N. and Sasamori T. (1975). On the transfer of solar radiation in aerosol atmosphere. J. Atmos. Sci., 32, 2166–2177.

    Article  Google Scholar 

  • Nesmelova L.I. and Tvorogov S.D. (1996). Some applications of the exponential series for calculating the absorption function. Atmospheric and Oceanic Optics, 9, 727–729.

    Google Scholar 

  • Nesmelova L.I., Rodimova O.B., and Tvorogov S.D. (1997). Calculation of transmission functions in near infrared region using series of exponents. Atmospheric and Oceanic Optics, 10, 923–927.

    Google Scholar 

  • Nesmelova L.I., Rodimova O.B., and Tvorogov S.D. (1999). Application of exponential series to calculation of radiative fluxes in the molecular atmosphere. Atmospheric and Oceanic Optics, 12, 735–739.

    Google Scholar 

  • Rodimova O.B. and Bogdanova Yu.V. (2006). Calculation of radiation fluxes due to CO2 in the IR spectral region. Computer Technologies, 11, 44–51 [in Russian].

    Google Scholar 

  • Sobolev B.V. (1972). Light Scattering in the Planetary Atmospheres. Science, Moscow, 335pp. [in Russian].

    Google Scholar 

  • Tarasova T.A. and Fomin B.A. (2000). Solar radiation absorption due to water vapor: Advanced broadband parameterizations. J. Appl. Meteorol., 39, 1947–1951.

    Article  Google Scholar 

  • Tvorogov S.D. (1994). Some aspects of the problem of representation of the absorption function by a series of exponents. Atmospheric and Oceanic Optics, 7, 165–171.

    Google Scholar 

  • Tvorogov S.D. (1997). Use of Dirichlet series in atmospheric optics. Atmospheric and Oceanic Optics, 10, 249–254.

    Google Scholar 

  • Tvorogov S.D. (1999). Application of exponential series to frequency integration of the radiative transfer equation. Atmospheric and Oceanic Optics, 12, 730–734.

    Google Scholar 

  • Tvorogov S.D. (2001). Construction of exponential series directly from information on the transmission function. Atmospheric and Oceanic Optics, 14, 670–673.

    Google Scholar 

  • Tvorogov S.D., Nesmelova L.I., and Rodimova O.B. (1996). Representation of the transmission function by the series of exponents. Atmospheric and Oceanic Optics, 9, 239–242.

    Google Scholar 

  • Tvorogov S.D., Nesmelova L.I., and Rodimova O.B. (2000). k-distribution of transmission function and theory of Dirichlet series. J. Quantitative Spectroscopy and Radiative Transfer, 66, 243–262.

    Article  Google Scholar 

  • Tvorogov S.D., Rodimova O.B., and Nesmelova L.I. (2005). On the correlated k-distribution approximation in atmospheric calculations. Optical Engineering, 44(7), 071202/1–071202/10.

    Article  Google Scholar 

  • Van de Hulst M.C. and Irvine W.M. (1963). Scattering in model planetary atmospheres. Meteorol. Soc. Roy. Sci. Liège, 5–7(1), 78–86.

    Google Scholar 

  • WCP (1986). A Preliminary Cloudless Standard Atmosphere for Radiation Computation. World Climate Research Program, Technical Report WCP-112, WMO/TD No. 24. World Meteorological Organization, Geneva, 60pp.

    Google Scholar 

  • West R., Crisp D., and Chen L. (1990). Mapping transformations for broadband atmospheric radiation calculations. J. Quantitative Spectroscopy and Radiative Transfer, 43, 191–199.

    Article  Google Scholar 

  • Zhuravleva T.B. and Firsov K.M. (2004). Algorithms for calculation of sunlight fluxes in the cloudy and cloudless atmosphere. Atmospheric and Oceanic Optics, 17, 799–806.

    Google Scholar 

  • Zhuravleva T.B. and Firsov K.M. (2005). On variability of the radiative characteristics in the 940-nm band at variations of water vapor in the atmosphere: Numerically simulated results. Atmospheric and Oceanic Optics, 18, 696–702.

    Google Scholar 

  • Zuev V.V. (1966). Atmospheric Transparency for Visible and Infrared Light, Soviet Radio, Moscow, 318pp. [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Praxis Publishing Ltd, Chichester, UK

About this chapter

Cite this chapter

Tvorogov, S.D., Zhuravleva, T.B., Rodimova, O.B., Firsov, K.M. (2009). Theory of series of exponents and their application for analysis of radiation processes. In: Global Climatology and Ecodynamics. Springer Praxis Books. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78209-4_9

Download citation

Publish with us

Policies and ethics