Boundary-Layer Meteorology

, Volume 117, Issue 3, pp 525–550 | Cite as

Determination of the Turbulent Temperature–Humidity Correlation from Scintillometric Measurements

  • Andreas Lüdi
  • Frank Beyrich
  • Christian Mätzler


We report on the investigation and successful application of the bichromatic correlation of optical and microwave signals for determining the area-averaged correlation of temperature–humidity fluctuations. The additional technical effort is marginal compared to the common ‘two-wavelength method’, which has (in contrast) the restriction that only two of the three relevant meteorological structure parameters can be deduced. Therefore, in the past, it was often assumed that the turbulent humidity and temperature fluctuations are perfectly positively or negatively correlated. However, as shown in this study, over non-homogeneous terrain when the flow conditions are not ideal, this assumption is questionable. The measurements were analysed statistically, and were compared to in situ measurements of the Bowen ratio Bo and the correlation of temperature–humidity fluctuations using eddy-covariance techniques. The latter is in good agreement to that derived by scintillometry. We found that the correlation is not ±1 but as low as −0.6 for Bo smaller than −2, and up to 0.8 for Bo larger than 1.


Area-averaged fluxes Bichromatic correlation Correlation of temperature–humidity fluctuations Electromagnetic waves Heterogeneous land surface Microwave and optical scintillometer 


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  1. Andreas, E. L. 1987‘On the Kolmogorov constants for the temperature–humidity Cospectrum and the Refractive Index Spectrum’J. Atmos. Sci.4423992406CrossRefGoogle Scholar
  2. Andreas, E. L. 1988‘Estimating C n 2 over Snow and Sea Ice from Meteorological Data’J. Opt. Soc. Amer. A5481495Google Scholar
  3. Andreas, E. L. 1989‘Two-wavelength Method of Measuring Path-averaged Turbulent Surface Heat Fluxes’J. Atmos. Ocean. Tech.6280292Google Scholar
  4. Andreas, E. L. 1990‘Three-wavelength Method of Measuring Path-averaged Turbulent Heat Fluxes’J. Atmos. Ocean. Tech.7801814Google Scholar
  5. Andreas, E. L., Hill, R. J., Gosz, J. R., Moore, D. I., Otto, D. W., Sarma, A. D. 1998‘Statistics of Surface-layer Turbulence over Terrain with Metre-scale Heterogeneity’Boundary-Layer Meteorol.86379408Google Scholar
  6. Beyrich, F., Bange, J., Bernhofer, C., Foken, T., Hennemuth, B., Huneke, S., Kohsiek, W., Leps, J.-P., Lohse, H., Lüdi, A., Mauder, M. and Meijninger, W. M. L.: 2004, ‘Energy and Water Vapour Fluxes over a Heterogeneous Land Surface: The LITFASS-2003 Experiment’, in Proceedings of the 16th Symposium on Boundary Layers and Turbulence, Portland, Maine U.S.A.Google Scholar
  7. Beyrich, F., Bruin, H. A. R., Meijninger, W. M. L., Schipper, W., Lohse, H. 2002‘Results from One-year Continuous Operation of a Large Aperture Scintillometer over a Heterogeneous Land Surface’Boundary-Layer Meteorol.1058597CrossRefGoogle Scholar
  8. Caccia, J. L., Azouit, M., Vernin, J. 1987‘Wind and C n 2 Profiling by Single-star Scintillation Analysis’Apple Opt.2612881294Google Scholar
  9. Bruin, H. A. R., Kohsiek, W., Hurk, B. J. J. M. 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’Boundary-Layer Meteorol.63231257CrossRefGoogle Scholar
  10. Green, A. E., Astill, M. S., McAneney, K. J., Nieveen, J. P. 2001‘Path-averaged Surface Fluxes Determined from Infrared and Microwave Scintillometers’Agric. For. Meteorol.109233247CrossRefGoogle Scholar
  11. Green, A. E., Green, S. R., Astill, M. S., Caspari, H. W. 2000‘Estimating Latent Heat Flux from a Vineyard Using Scintillometry’J. Terr. Atmos. Ocean. Sci.11525542Google Scholar
  12. Hill, R.J. 1988‘Comparison of Scintillation Methods for Measuring the Inner Scale of Turbulence’Appl. Opt.2721872193Google Scholar
  13. Hill, R. J. 1989‘Implications of Monin-Obukhov Similarity Theory for Scalar Quantities’J. Atmos. Sci.4622362244Google Scholar
  14. Hill, R. J. 1997‘Algorithms for Obtaining Atmospheric Surface-layer Fluxes from Scintillation Measurements’J. Atmos. Ocean. Tech.14456467Google Scholar
  15. Hill, R. J., Bohlander, R. A., Clifford, S. F., McMillan, R. W., Priestley, J. T., Schoenfeld, W. P. 1988‘Turbulence-induced Millimeter-wave Scintillation Compared with Micrometeorological Measurements’IEEE Trans. Geosci. Remote Sens.26330342Google Scholar
  16. Hill, R. J., Clifford, S. F., Lawrence, R. S. 1980‘Refractive-index and Absorption Fluctuations in the Infrared Caused by Temperature, Humidity, and Pressure Fluctuations’J. Opt. Soc. Amer.7011921205Google Scholar
  17. Hill, R. J., Lataitis, R. J. 1989‘Effect of Refractive Dispersion on the Bichromatic Correlation of Irradiances for Atmospheric Scintillation’Appl. Opt.2841214125Google Scholar
  18. Ishimaru, A. 1978Wave Propagation and Scattering in Random MediaAcademic PressNew York, San Francisco339Google Scholar
  19. Kohsiek, W., Herben, A. J. 1983‘Evaporation Derived from Optical and Radio-wave Scintillation’Appl. Opt.2225662569Google Scholar
  20. Liebe, H. J., Hufford, G. A., and Cotton, M. G.: 1993,‘Propagation Modeling of Moist Air and Suspended Water/Ice Particles at Frequencies Below 1000 GHz’, in: AGARD 52nd Specialists’ Meeting of the Electromagnetic Wave Propagation Panel. Mallorca, Spain.Google Scholar
  21. Lüdi, A.: 2002, ‘Determination of the Structure Constants of Temperature, Humidity and temperature–humidity by Scintillometry at two Wavelengths’, IAP Research Report 2002-13, Institute of Applied Physics, University of Bern, Bern, Switzerland. (in German), 8 pp.Google Scholar
  22. Lüdi, A., Magun, A. 2005‘Refractivity Structure Constant and Length Scales from mm Wave Propagation in the Stably Stratified Troposphere’J. Atmos. Sol. Terr. Phys.67435447Google Scholar
  23. Martin, L., Mätzler, C., and Kämpfer, N.: 2000, ‘Transmission Measurements at 94 GHz to Validate the Liebe Model’, in AP 2000 Millennium Conference on Antennas and Propagation, SP-444, ESA Publication Division. Davos, Switzerland.Google Scholar
  24. Meijninger, W. M. L., Green, A. E., Hartogensis, O. K., Kohsiek, W., Hoedjes, J. C. B., Zuurbier, R. M., Bruin, H. A. R. 2002a‘Determination of Area-averaged Water Vapour Fluxes with Large Aperture and Radio Wave Scintillometers over a Heterogeneous Surface Flevoland Field Experiment’Boundary-Layer Meteorol.1056383Google Scholar
  25. Meijninger, W. M. L., Hartogensis, O. K., Kohsiek, W., Hoedjes, J. C. B., Zuurbier, R. M., Bruin, H. A. R. 2002b‘Determination of Area-averaged Sensible Heat Fluxes with a Large Aperture Scintillometer over a Heterogeneous Surface – Flevoland Field Experiment’Boundary-Layer Meteorol.1053762Google Scholar
  26. Moene, A. F., Meijninger, W. M. L., Hartogensis, O. K., Heusinkveld, B. G., Bruin, H. A. R. 2005‘The Effects of Finite Accuracy in the Manufacturing of large Aperture Scintillometers’Wageningen University, Meteorology and Air Quality GroupWageningen, The Netherlands19Internal report 2005/1Google Scholar
  27. Nieveen, J. P., Green, A. E., Kohsiek, W. 1998‘Using a Large-aperture Scintillometer to Measure Absorption and Refractive Index Fluctuations’Boundary-Layer Meteorol.87101116CrossRefGoogle Scholar
  28. Ochs, G. R. and Hill, R. J.: 1982, ‘A Study of Factors Influencing the Calibration of Optical Cn2 Meters’, NOAA Tech. Memo. ERL WPL-106, NOAA, 24 pp.Google Scholar
  29. Ochs, G. R., Wang, T. I. 1978‘Finite Aperture Optical Scintillometer for Profiling Wind and C n 2 Appl. Opt.1737743778Google Scholar
  30. Phelps, G. T., Pond, S. 1971‘Spectra of the Temperature and Humidity Fluctuations and the Turbulent Fluxes of Momentum, Moisture and Sensible Heat over the Ocean’J. Atmos. Sci.28918928CrossRefGoogle Scholar
  31. Priestley, J. T., Hill, R. J. 1985‘Measuring High-frequency Humidity, Temperature and Radio Refractive Index in the Surface Layer’J. Atmos. Ocean. Tech.60233251Google Scholar
  32. Tatarskii, V. I. 1971The Effects of the Turbulent Atmosphere on Wave PropagationIsreal Program for Scientific Translation Ltd.Jerusalem472Google Scholar
  33. Wang, T. I., Ochs, G. R., Clifford, S. F. 1978‘A Saturation-resistant Optical Scintillometer to Measure C n 2 J. Opt. Soc. Amer.68334338Google Scholar
  34. Wesely, M. L., Alcaraz, E. C. 1973‘Diurnal Cycles of the Refractive Index Structure Function Coefficient’J. Geophys. Res.7862246232Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  • Andreas Lüdi
    • 1
  • Frank Beyrich
    • 2
  • Christian Mätzler
    • 1
  1. 1.Institute of Applied PhysicsUniversity of BernBernSwitzerland
  2. 2.Meteorological Observatory LindenbergGerman Meteorological Service (DWD)LindenbergGermany

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