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Formulation of turbulence diffusion relationships under stable atmospheric conditions and its effect on pollution dispersion

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Abstract

In this article, we formulate Monin–Obukhov similarity theory (MOST)-based relationships, for normalized standard deviations of wind velocity components under the local scaling framework, and investigate their applicability under stable and highly stable atmospheric conditions. We used the fast response data collected using an ultrasonic anemometer over a flat terrain of Kalpakkam in India and a complex hilly terrain at Cadarache, France, for arriving at these formulations. The study shows that after filtering of the submesoscale motions from the sonic anemometer data, the turbulence diffusion relationships follow local scaling, under stable conditions. The study further indicates that these relationships follow similar behavior for the sites taken for this study. At neutral conditions, the values of the scaled standard deviations are found to be 1.9 ± 0.07, 1.8 ± 0.06 and 1.3 ± 0.02, for longitudinal, crosswind and vertical component, respectively, for the complex terrain and 1.8 ± 0.03, 1.9 ± 0.06 and 1.1 ± 0.04, respectively, for the flat terrain. The research also investigates the effect of the new diffusion relationships in simulating atmospheric dispersion, using the Lagrangian particle dispersion model FLEXPART-WRF. Simulations using these new diffusion relationships show a higher dose estimate relative to the model default Hanna’s method, in the case of radioactivity dispersion. Detailed comparisons of the simulated dose rate estimates against measurements using Environmental Radiation Monitors (ERM) indicate that the new relationships give better correlation (r2 = 0.62) under stable conditions over model default relationships (r2 = 0.50).

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Courtesy: The Royal Meteorological Society (Duine et al., 2017, Quarterly Journal of Royal Meteorological Society)

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References

  • Anderson P (2009) Measurement of Prandtl number as a function of Richardson number avoiding self correlation. Bound Layer Meteorol 131:345–362

    Google Scholar 

  • Arnold D, Maurer C, Wotawa G, Draxler R, Saito K, Seibert P (2015) Influence of the meteorological input on the atmospheric transport modelling with FLEXPART of radionuclides from the Fukushima Daiichi nuclear accident. J Environ Radioact 139:212–225

    Google Scholar 

  • Baas P, Steeneveld G, van de Weil B, Holtslag A (2006) Exploring self-correlation in the flux-gradient relationships for stably stratified conditions. J Atmos Sci 63:3045–3054

    Google Scholar 

  • Babić K, Rotach MW, Klaić ZB (2016) Evaluation of local similarity theory in the wintertime nocturnal boundary layer over heterogeneous surface. Agric For Meteorol 228:164–179

    Google Scholar 

  • Basu S, Porte-Agel F, Foufoula-Georgiou E, Vinuesa JF, Pahlow M (2006) Revisiting the local scaling hypothesis in stably stratified atmospheric boundary-layer turbulence: an integration of field and laboratory measurements with large-eddy simulations. Bound Layer Meteorol 119:473–500

    Google Scholar 

  • Belušić D, Mahrt L (2008) Estimation of length scales from mesoscale networks. Tellus A: Dyn Meteorol Oceanogr 60(4):706–715

    Google Scholar 

  • Businger J, Arya SPS (1974) Height of the mixed layer in the stably stratified planetary boundary layer, advances in geophysics, 18A. Academic Press, New York, pp 73–92

    Google Scholar 

  • Businger JA, Wyngaard JC, Izumi Y, Bradley EF (1971) Flux-profile relationships in the atmospheric surface layer. J Atmos Sci 28(2):181–189

    Google Scholar 

  • Caughey SJ (1977) Boundary-layer turbulence spectra in stable conditions. Bound Layer Meteorol 11(1):3–14

    Google Scholar 

  • Chu CR, Parlange MB, Katul GG, Albertson JD (1996) Probability density functions of turbulent velocity and temperature in the atmospheric surface layer. Water Resour Res 32:1681–1688

    Google Scholar 

  • De Bruin HAR, Kohsiek W, van den Hurk JJM (1993) a verification of some methods to determine the fluxes of momentum, sensible heat, and water vapour using standard deviation and structure parameter of scalar meteorological quantities. Bound Layer Meteorol 63:231–257

    Google Scholar 

  • De Franceschi M, Zardi D, Tagliazucca M, Tampieri F (2009) Analysis of second-order moments in surface layer turbulence in an Alpine valley. Q J R Meteorol Soc 135(644):1750–1765

    Google Scholar 

  • Dharamaraj T, Chintalu GR, Raj PE (2009) Turbulence characteristics in the atmospheric surface layer during summer monsoon of 1997 over a semi-arid location in India. Meteorol Atmos Phys 104:113–123

    Google Scholar 

  • Dias NL, Brutsaert W (1996) Similarity of scalars under stable stratification. Bound Layer Meteorol 80:355–373

    Google Scholar 

  • Dias NL, Brutsaert W, Wesley ML (1995) z-Less stratification under stable conditions. Bound Layer Meteorol 75:175–187

    Google Scholar 

  • Duine GJ, Hedde T, Roubin P, Durand P, Lothon M, Lohou F, Augustin P, Fourmentin M (2017) Characterization of valley flows within two confluent valleys under stable conditions: observations from the KASCADE field experiment. Q J R Meteorol Soc 143(705):1886–1902

    Google Scholar 

  • Dyer AJ (1974) A review of flux-profile relationships. Bound Layer Meteorol 7(3):363–372

    Google Scholar 

  • Emeis S (2010) A simple analytical wind park model considering atmospheric stability. Wind Energy 13(5):459–469

    Google Scholar 

  • Emeis S (2013) Wind energy meteorology—atmospheric physics for wind power generation. Springer, Dordrecht, p 150

    Google Scholar 

  • Fernando HJS (2003) Turbulent patches in a stratified shear flow. Phys Fluids 15(10):3164

    Google Scholar 

  • Garratt JR (1994) The atmospheric boundary layer. Earth Sci Rev 37(1–2):89–134

    Google Scholar 

  • Geng X, Xie Z, Zhang L (2017) Influence of emission rate on atmospheric dispersion modeling of the Fukushima Daiichi nuclear power plant accident. Atmospheric Pollution Research 8(3):439–445

    Google Scholar 

  • Hanna SR (1982) Applications in air pollution modeling. In: Nieuwstadt FTM, van Dop H (eds) Atmospheric turbulence and air pollution modelling. Reidel, Boston

  • Högström U (1988) Non-dimensional wind and temperature profiles in the atmospheric surface layer. a re-evaluation. Bound Layer Meteorol 42:55–78

    Google Scholar 

  • Howell JF, Sun J (1999) Surface-layer fluxes in stable conditions. Bound Layer Meteorol 90:495–520

    Google Scholar 

  • Hsieh CI, Katul GG (1997) Dissipation methods, taylor’s hypothesis, and stability correction functions in the atmospheric surface layer. J Geophys Res 102:16391–16405

    Google Scholar 

  • Kantha LH, Clayson CA (2000) Small scale processes in geophysical fluid flows. Academic Press, San Diego, p 883

    Google Scholar 

  • Klipp C, Mahrt L (2004) Flux-gradient relationship, self-correlation and intermittency in the stable boundary layer. Q J R Meteorol Soc 130:2087–2104

    Google Scholar 

  • Kunkel KE, Walters DL (1981) Intermittent turbulence in measurements of the temperature structure parameter under very stable conditions. Bound Layer Meteorol 22:49–60

    Google Scholar 

  • Lange M, Focken U (2005) Physical approach to short-term wind power prediction. Springer, Berlin, p 167

    Google Scholar 

  • Mahrt L (1998) Stratified atmospheric boundary layers and breakdown of models. Theor Comput Fluid Dyn 11:263–279

    Google Scholar 

  • Mahrt L (1999) Stratified atmospheric boundary layers. Bound Layer Meteorol 90:375–396

    Google Scholar 

  • Mahrt L (2011) Surface wind direction variability. J Appl Meteorol Clim 50(144–152):2011. https://doi.org/10.1175/2010JAMC2560.1

    Article  Google Scholar 

  • Mahrt L (2014) Stably stratified atmospheric boundary layers. Annu Rev Fluid Mech 46:23–45

    Google Scholar 

  • Mahrt L, Vickers D (2006) Extremely weak mixing in stable conditions. Boundary-Layer Meteorol 119(1):19–39

    Google Scholar 

  • Mellor GL, Yamada T (1982) Development of a turbulence closure model for geophysical fluid problems. Rev Geophys 20(4):851–875

    Google Scholar 

  • Mestayer PG, Anquetin S (1995) Climatology of cities. In: Gyr A, Rys F-S (eds) Diffusion and transport of pollutants. Kluwer Academics, New York, pp 165–189

    Google Scholar 

  • Monin AS, Obukhov AM (1954) Basic laws of turbulent mixing in the ground layer of the atmosphere. Trans Geophys Inst Akad Nauk USSR 151:163–187

    Google Scholar 

  • Monteiro C, Bessa R, Miranda V, Botterud A, Wang J, Conzelmann G (2009) Wind power forecasting: state of-the-art 2009. Argonne National Laboratory, Lemont, p 216

    Google Scholar 

  • Nieuwstadt FTM (1984) The turbulent structure of the stable, nocturnal boundary layer. J Atmos Sci 41:2202–2216

    Google Scholar 

  • Oza RB, Daoo VJ, Sitaraman V, Krishnamoorthy TM (1999) Plume gamma dose evaluation under non-homogeneous non-stationary meteorological conditions using particle trajectory model for short term releases. Radiat Prot Dosim 82(3):201–206

    Google Scholar 

  • Pahlow M, Parlange MB, Porte-Agel F (2001) On Monin-Obukhov similarity in the stable atmospheric boundary layer. Bound Layer Meteorol 99:225–248

    Google Scholar 

  • Panosfsky HA, Dutton JA (1984) Atmospheric turbulence: Models and methods for engineering applications. JohnWileySons, NewYork

    Google Scholar 

  • Pardyjak ER, Monti P, Fernando HJS (2002) Flux Richardson number measurements in stable atmospheric shear flows. J Fluid Mech 459:307–316

    Google Scholar 

  • Petersen EL, Mortensen NG, Landberg L, Hjstrup J, Frank HP (1998) Wind power meteorology Part I climate and turbulence. Wind Energy 1(1):2–22

    Google Scholar 

  • Prasad KH, Srinivas CV, Satyanarayana ANV, Naidu CV, Baskaran R, Venkatraman B (2015) Formulation of stability-dependent empirical relations for turbulent intensities from surface layer turbulence measurements for dispersion parameterization in a lagrangian particle dispersion model. Meteorol Atmos Phys 127(4):435–450

    Google Scholar 

  • Prasad KH, Srinivas CV, Singh AB, Naidu CV, Baskaran R, Venkatraman B (2018) Turbulence characteristics of surface boundary layer over the Kalpakkam tropical coastal station, India. Meteorol Atmos Phys 131:1–17

    Google Scholar 

  • Rakesh PT, Venkatesan R, Srinivas CV (2013) Formulation of TKE based empirical diffusivity relations from turbulence measurements and incorporation in a Lagrangian particle dispersion model. Environ Fluid Mech 13(4):353–369

    Google Scholar 

  • Rakesh PT, Venkatesan R, Hedde T, Roubin P, Baskaran R, Venkatraman B (2015) Simulation of radioactive plume gamma dose over a complex terrain using Lagrangian particle dispersion model. J Environ Radioact 145:30–39

    Google Scholar 

  • Seaman NL, Gaudet BJ, Stauffer DR, Mahrt L, Richardson SJ, Zielonka JR, Wyngaard JC (2012) Numerical prediction of submesoscale flow in the nocturnal stable boundary layer over complex terrain. Mon Weather Rev 140(3):956–977

    Google Scholar 

  • Skamarock WC, Klemp JB, Dudhia J, Gill DO, Barker DM, Wang W, Powers JG (2005) A description of the advanced research WRF version 2 (No. NCAR/TN-468+ STR). National Center For Atmospheric Research Boulder Co Mesoscale and Microscale Meteorology Div

  • Smedman A (1988) Observations of a multi-level turbulence structure in a very stable boundary layer. Bound Layer Meteorol 44:231–253

    Google Scholar 

  • Soler MR, Arasa R, Merino M, Olid M, Ortega S (2011) Modelling local sea-breeze flow and associated dispersion patterns over a coastal area in north-east Spain: a case study. Bound Layer Meteorol 140(1):37–56

    Google Scholar 

  • Sorbjan Z (1986a) On similarity in the atmospheric boundary layer. Bound Layer Meteorol 34:377–397

    Google Scholar 

  • Sorbjan Z (1986b) On the vertical distribution of passive species in the atmospheric boundary layer. Bound Layer Meteorol 35:73–81

    Google Scholar 

  • Sorbjan Z (2006) Local structure of turbulence in stably stratified boundary layers. J Atmos Sci 63(5):1526–1537

    Google Scholar 

  • Sorbjan Z (2010) Gradient-based scales and similarity laws in the stable boundary layer. Q J R Meteorol Soc 136(650):1243–1254

    Google Scholar 

  • Srinivas CV, Venkatesan R, Baskaran R, Rajagopal V, Venkatraman B (2012) Regional scale atmospheric dispersion simulation of accidental releases of radionuclide from Fukushima Dai-ichi reactor. Atmos Environ 61:66–84

    Google Scholar 

  • Srinivas CV, Rakesh PT, Baskaran R, Venkatraman B (2017) Source term assessment using inverse modeling and environmental radiation measurements for nuclear emergency response. Air Qual Atmos Health 10(9):1077–1087

    Google Scholar 

  • Stohl A, Forster C, Frank A, Seibert P, Wotawa G (2005) The Lagrangian particle dispersion model FLEXPART version 62. Atmos Chem Phys 5(9):2461–2474

    Google Scholar 

  • Stull RB (1988) An introduction to boundary layer meteorology. Kluwer Academic Publishers, Dordrecht, p 670

    Google Scholar 

  • Van de Wiel BJH, Moene AF, Hartogensis OK, De Bruin HAR, Holtslag AAM (2003) Intermittent turbulence in the stable boundary layer over land. Part III: a classification for observations during CASES-99. J Atmos Sci 60(20):2509–2522

    Google Scholar 

  • van den Berg G (2008) Wind turbine power and sound in relation to atmospheric stability. Wind Energy 11(2):151–169

    Google Scholar 

  • Wei P, Cheng S, Li J, Su F (2011) Impact of boundary-layer anticyclonic weather system on regional air quality. Atmos Environ 45(14):2453–2463

    Google Scholar 

  • Wyngaard JC (1975) Modelling the planetary boundary layer-extension to the stable case. Bound Layer Meteorol 9:441–460

    Google Scholar 

  • Zhu Q, Liu Y, Jia R, Hua S, Shao T, Wang B (2018) A numerical simulation study on the impact of smoke aerosols from Russian forest fires on the air pollution over Asia. Atmos Environ 182:263–274

    Google Scholar 

  • Zilitinkevich S, Baklanov A (2002) Calculation of the height of the stable boundary layer in practical applications. Bound Layer Meteorol 105(3):389–409

    Google Scholar 

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Acknowledgements

Authors express their sincere thanks to Director, Indira Gandhi Center for Atomic Research. Station Director, Madras Atomic Power Station, is acknowledged for providing the Ar41 release data used in the present study. Authors convey special thanks to the KASCADE team (Commissariat à l'énergie atomique et aux énergies alternatives-DEN-Cad/Laboratoire de Modélisation des Transferts dans l'Environnement and Laboratoired’Aerologie UMR 5560) for providing the datasets for the present study. The KASKADE dataset is now available at https://kascade.sedoo.fr.

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Correspondence to P. T. Rakesh.

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Rakesh, P.T., Venkatesan, R., Roubin, P. et al. Formulation of turbulence diffusion relationships under stable atmospheric conditions and its effect on pollution dispersion. Meteorol Atmos Phys 132, 909–924 (2020). https://doi.org/10.1007/s00703-020-00729-2

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