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Boundary-Layer Meteorology

, Volume 150, Issue 1, pp 49–67 | Cite as

An Optimal Inverse Method Using Doppler Lidar Measurements to Estimate the Surface Sensible Heat Flux

  • T. M. Dunbar
  • J. F. Barlow
  • S. E. Belcher
Article
  • 382 Downloads

Abstract

Inverse methods are widely used in various fields of atmospheric science. However, such methods are not commonly used within the boundary-layer community, where robust observations of surface fluxes are a particular concern. We present a new technique for deriving surface sensible heat fluxes from boundary-layer turbulence observations using an inverse method. Doppler lidar observations of vertical velocity variance are combined with two well-known mixed-layer scaling forward models for a convective boundary layer (CBL). The inverse method is validated using large-eddy simulations of a CBL with increasing wind speed. The majority of the estimated heat fluxes agree within error with the proscribed heat flux, across all wind speeds tested. The method is then applied to Doppler lidar data from the Chilbolton Observatory, UK. Heat fluxes are compared with those from a mast-mounted sonic anemometer. Errors in estimated heat fluxes are on average 18 %, an improvement on previous techniques. However, a significant negative bias is observed (on average \(-63\,\%\)) that is more pronounced in the morning. Results are improved for the fully-developed CBL later in the day, which suggests that the bias is largely related to the choice of forward model, which is kept deliberately simple for this study. Overall, the inverse method provided reasonable flux estimates for the simple case of a CBL. Results shown here demonstrate that this method has promise in utilizing ground-based remote sensing to derive surface fluxes. Extension of the method is relatively straight-forward, and could include more complex forward models, or other measurements.

Keywords

Convective boundary layer Doppler lidar Inverse methods Surface energy balance 

Notes

Acknowledgments

The authors wish to thank Alan Grant for running the LEM to provide CBL simulations, and guidance in interpretation of the results. T. Dunbar was funded through a Natural Environment Research Council Grant Reference Number NE/F00706X/1.

References

  1. Angevine WM, Doviak RJ, Sorbjan Z (1994) Remote sensing of vertical velocity variance and surface heat flux in a convective boundary layer. J Appl Meteorol 33:977–983CrossRefGoogle Scholar
  2. Bannister R (2003) The method of least squares to invert an orbit problem. Am J Phys 71:1268–1275CrossRefGoogle Scholar
  3. Barlow JF, Dunbar TM, Neimitz EG, Wood CR, Gallagher MW, Davies F, O’Connor E, Harrison RM (2011) Boundary layer dynamics over London, UK as observed using Doppler lidar during Repartee-II. Atmos Chem Phys 11:2111–2125CrossRefGoogle Scholar
  4. Beare RJ (2008) The role of shear in the morning transition boundary layer. Boundary-Layer Meteorol 129:395–410CrossRefGoogle Scholar
  5. Bouniol D, Illingworth A, Hogan R (2004) Deriving turbulent kinetic energy dissipation rate within clouds using ground based radar. In: Proceedings of ERAD, pp 281–285Google Scholar
  6. Chai T, Lin CL (2004) Retrieval of microscale flow structures from high-resolution Doppler lidar data using an adjoint model. J Atmos Sci 61:1500–1520CrossRefGoogle Scholar
  7. Cleugh HA, Grimmond CSB (2001) Modelling regional scale surface energy exchanges and CBL growth in a heterogeneous, urban–rural landscape. Boundary-Layer Meteorol 98:1–31CrossRefGoogle Scholar
  8. Davis JC, Collier CG, Davies F, Bozier KE (2008) Spatial variations of sensible heat flux over an urban area measured using Doppler lidar. Meteorol Appl 15:367–380CrossRefGoogle Scholar
  9. Deardorff JW (1970) Convective velocity and temperature scales for the unstable planetary boundary layer and for Rayleigh convection. J Atmos Sci 27:1211–1213CrossRefGoogle Scholar
  10. Drennan WD, Zhang JA, French JR, McCormick C, Black PG (2007) Turbulent fluxes in the hurricane boundary layer. Part II: latent heat flux. J Atmos Sci 64:1103–1115CrossRefGoogle Scholar
  11. Engelbart DAM, Kallistratova M, Kouznetsov R (2007) Determination of the turbulent fluxes of heat and momentum in the ABL by ground-based remote-sensing techniques (a review). Meteorol Z 16:326–335CrossRefGoogle Scholar
  12. Gal-Chen T, Xu M (1992) Estimations of atmospheric boundary-layer fluxes and other turbulence parameters from Doppler lidar data. J Geophys Res 97:409–423CrossRefGoogle Scholar
  13. Hogan R (2007) A variational scheme for retrieving rainfall rate and hail reflectivity fraction from polarization radar. J Appl Meteorol 46:1544–1564Google Scholar
  14. Hogan RJ, Grant ALM, Illingworth AJ, Pearson GN, O’Connor EJ (2008) Vertical velocity variance and skewness in clear and cloud-topped boundary layers as revealed by Doppler lidar. Q J R Meteorol Soc 135:635–643CrossRefGoogle Scholar
  15. Kaimal JC, Wyngaard JC, Haugen DA, Cote OR, Izumi Y, Caughey SJ, Readings CJ (1976) Turbulence structure in the convective boundary layer. J Atmos Sci 33:2152–2169CrossRefGoogle Scholar
  16. Lenschow DH, Wulfmeyer V (2000) Measuring second through fourth order moments in noisy data. J Atmos Ocean Technol 17:1330–1347CrossRefGoogle Scholar
  17. Lenschow DH, Wyngaard JC, Pennell WT (1980) Mean-field and second-moment budgets in a Baroclinic, convective boundary layer. J Atmos Sci 37:1313–1326CrossRefGoogle Scholar
  18. Lenschow DH, Mann J, Kristensen L (1994) How long is long enough when measuring fluxes and other turbulence statistics? J Atmos Ocean Technol 11:661–673CrossRefGoogle Scholar
  19. Lenschow DH, Lothon M, Mayor SD, Sullivan PP, Canut G (2012) A comparison of higher-order vertical velocity moments in the convective boundary layer from lidar with in situ measurements and LES. Boundary-Layer Meteorol 143:107–123CrossRefGoogle Scholar
  20. Lorenc AC (1986) Analysis methods for numerical weather prediction. Q J R Meteorol Soc 112:1177–1194CrossRefGoogle Scholar
  21. Newsom RK, Banta RM (2004) Assimilating coherent Doppler lidar measurements into a model of the atmospheric boundary layer. Part I: algorithm development and sensitivity to measurement error. J Atmos Ocean Technol 21:1328–1345CrossRefGoogle Scholar
  22. O’Connor EJ, Illingworth AJ, Brooks IM, Westbrook CD, Hogan RJ, Davies F, Brooks BJ (2010) A method for estimating the turbulent kinetic energy dissipation rate from a vertically-pointing Doppler lidar and independent evaluation from balloon-borne in-situ measurements. J Atmos Ocean Technol 27:1652–1664CrossRefGoogle Scholar
  23. Pearson G, Davies F, Collier C (2009) An analysis of the UFAM pulsed Doppler lidar for observing the boundary layer. J Atmos Ocean Technol 26:240–250CrossRefGoogle Scholar
  24. Rodgers CD (2000) Inverse methods for atmospheric sounding. World Scientific Publishing, London, pp i–xviGoogle Scholar
  25. Roth M (2000) Review of atmospheric turbulence over cities. Q J R Meteorol Soc 26:941–990CrossRefGoogle Scholar
  26. Rudd AC, Robins AG, Lepley JJ, Belcher SE (2011) An inverse method for determining source characteristics for emergency response applications. Boundary-Layer Meteorol 144:1–20CrossRefGoogle Scholar
  27. Rye BJ, Hardesty RM (1993) Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. II: correlogram accumulation. IEEE Trans Geosci Remote Sens 31:28–35CrossRefGoogle Scholar
  28. Shutts GJ, Gray MEB (1994) A numerical modelling study of the geostrophic adjustment process following deep convection. Q J R Meteorol Soc 120:1145–1178Google Scholar
  29. Sorbjan Z (1988) Local similarity in the convective boundary layer. Boundary-Layer Meteorol 45:237–250CrossRefGoogle Scholar
  30. Sorbjan Z (1990) Similarity scales and universal profiles of statistical moments in the convective boundary layer. J Appl Meteorol 29:762–775CrossRefGoogle Scholar
  31. Sorbjan Z (1991) Evaluation of local similarity functions in the convective boundary layer. J Appl Meteorol 30:1565–1583CrossRefGoogle Scholar
  32. Sullivan PP, Patton EG (2011) The effect of mesh resolution on convective boundary layer statistics and structures generated by large-eddy simulation. J Atmos Sci 68:8995–9005CrossRefGoogle Scholar
  33. Willmott CJ, Ackleson SG, Davis RE, Feddema JJ, Klink KM, Legates DR, O’Donnell J, Rowe CM (1985) Statistics for the evaluation and comparison of models. J Geophys Res 90:2395–2415CrossRefGoogle Scholar
  34. Young GS (1988) Turbulence structure of the convective boundary layer. Part I: variability of normalized turbulence statistics. J Atmos Sci 45:719–726CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of MeteorologyUniversity of ReadingReadingUK

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