Stable Boundary Layer Height Parameterization: Learning from Artificial Neural Networks

Author(s)
Wei Li

Affiliation(s)

Department of Marine, Earth, and Atmospheric Sciences, North Carolina State University, Raleigh, USA.

Department of Marine, Earth, and Atmospheric Sciences, North Carolina State University, Raleigh, USA.

ABSTRACT

Artificial neural networks (ANN) are employed using
different combinations among the surface friction velocity *u _{*}*, surface buoyancy flux

Cite this paper

W. Li, "Stable Boundary Layer Height Parameterization: Learning from Artificial Neural Networks,"*Atmospheric and Climate Sciences*, Vol. 3 No. 4, 2013, pp. 523-531. doi: 10.4236/acs.2013.34055.

W. Li, "Stable Boundary Layer Height Parameterization: Learning from Artificial Neural Networks,"

References

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[2] J. A. Salmond and I. G.McKendry, “A Review of Turbulence in the Very Stable Boundary Layer and Its Implications for Air Quality,” Progress in Physical Geography, Vol. 29, No. 2, 2005, pp. 171-188. http://dx.doi.org/10.1191/0309133305pp442ra

[3] G. J. Steeneveld and A. A. M. Holtslag, “Meteorological Aspects of Air Quality,” Air Quality in the 21st Century, Nova Science Publishers, New York, 2009, pp. 67-114.

[4] W. Brutsaert, “Radiation, Evaporation and the Maintenance of the Turbulence under Stable Conditions in the Lower Atmosphere,” Boundary-Layer Meteorology, Vol. 2, No. 3, 1972, pp. 309-325. http://dx.doi.org/10.1007/BF02184772

[5] L. Mahrt, “Modeling the Height of the Stable Boundary Layer,” Boundary-Layer Meteorology, Vol. 21, No. 1, 1981, pp. 3-19. http://dx.doi.org/10.1007/BF00119363

[6] S. A. Kitaigorodskii, “On the Computation of the Thickness of the Wind-Mixing Layer in the Ocean,” Izvestiya AN SSSR, Geophysical Series, Vol. 3, 1960, pp. 425-431.

[7] S. S. Zilitinkevich, “On the Determination of the Height of the Ekman Boundary Layer,” Boundary-Layer Meteorology, Vol. 3, No. 2, 1972, pp. 141-145. http://dx.doi.org/10.1007/BF02033914

[8] R. T. Pollard, P. B. Rhines and R. Thompson, “The Deepening of the Wind-Mixed Layer,” Geophysical Fluid Dynamics, Vol. 3, 1973, pp. 381-404.

[9] S. A. Kitaigorodskii and S. M. Joffre, “In Search of Simple Scaling for the Heights of the Stratified Atmospheric Boundary Layer,” Tellus, Vol. 40A, No. 5, 1988, pp. 419-443. http://dx.doi.org/10.1111/j. 1600-0870.1988. tb00359.x

[10] S. S. Zilitinkevich and D. V. Mironov, “A Multi-Limit Formulation for the Equilibrium Depth of a Stably Stratified Boundary Layer,” Boundary-Layer Meteorology, Vol. 81, No. 3-4, 1996, pp. 325-351. http://dx.doi.org/10.1007/BF02430334

[11] S. S. Zilitinkevich, A. Baklanov, J. Rost, A. S. Smedman, V. Lykosov and P. Calanca, “Diagnostic and Prognostic Equations for the Depth of the Stably Stratified Ekman Boundary Layer,” Quarterly Journal of the Royal Meteorological Society, Vol. 128, No. 1, 2002, pp. 25-46. http://dx.doi.org/10.1256/ 00359000260498770

[12] S. S. Zilitinkevich and A. Baklanov, “Calculation of the Height of Stable Boundary Layers in Practical Applications,” Boundary-Layer Meteorology, Vol. 105, No. 3, 2002, pp. 389-409. http://dx.doi.org/ 10.1023/A:1020376832738

[13] D. Vickers and L. Mahrt, “Evaluating Formulations of the Stable Boundary Layer Height,” Journal of Applied Meteorology, Vol. 43, No. 11, 2004, pp. 1736-1749. http://dx.doi.org/10.1175/JAM2160.1

[14] G. J. Steeneveld, B. J. H. Van de Wiel and A. A. M. Holtslag, “Diagnostic Equations for the Stable Boundary Layer Height: Evaluation and Dimensional Analysis,” Journal of Applied Meteorology and Climatology, Vol. 46, No. 2, 2007, pp. 212-225. http://dx.doi.org/10.1175/JAM2454.1

[15] B. Kosovic and J. A. Curry, “A Large Eddy Simulation Study of a Quasi-Steady, Stably Stratified Atmospheric Boundary Layer,” Journal of the Atmospheric Sciences, Vol. 57, No. 8, 2000, pp. 1052-1068. http://dx.doi.org/10.1175/1520-0469(2000)057<1052:ALESSO>2.0.CO;2

[16] S. S. Zilitinkevich and I. Esau, “The Effect of Baroclinicity on the Equilibrium Depth of Neutral and Stable Planetary Boundary Layers,” Quarterly Journal of the Royal Meteorological Society, Vol. 129, No. 595, 2003, pp. 3339-3356. http://dx.doi.org/10.1256/qj.02.94

[17] B. Kosovic and J. K. Lundquist, “Influences on the Height of the Stable Boundary Layer,” 16th Symposium on Boundary Layers and Turbulence, American Meteor Society, Portland, 23 June 2004, Preprints.

[18] G. J. Steeneveld, B. J. H. Van de Wiel and A. A. M. Holtslag, “Notes and Correspondence: Comments on Deriving the Equilibrium Height of the Stable Boundary Layer,” Quarterly Journal of the Royal Meteorological Society, Vol. 133, No. 622, 2007, pp. 261-264. http://dx.doi.org/10.1002/qj.26

[19] C. Sim, S. Basu and L. Manuel, “On Space-Time Resolution of Inflow Representations for Wind Turbine Loads Analysis,” Energies, Vol. 5, No. 7, 2012, pp. 2071-2092. http://dx.doi.org/10.3390/en5072071

[20] D. H. Lenschow, X. S. Li, C. J. Zhu and B. B. Stankov, “The Stably Stratified Boundary Layer over the Great Plains. I. Mean and Turbulent Structure,” Boundary-Layer Meteorology, Vol. 42, No. 1-2, 1988, pp. 95-121. http://dx.doi.org/10.1007/BF00119877

[21] S. J. Caughey, J. C. Wyngaard and J. C. Kaimal, “Turbulence in the Evolving Stable Layer,” Journal of the Atmospheric Sciences, Vol. 36, No. 6, 1979, pp. 1041-1052.

[22] J. W. Melgarejo and J. W. Deardorff, “Stability Functions for the Boundary Layer Resistance Laws Based upon Observed Boundary Layer Heights,” Journal of the Atmospheric Sciences, Vol. 31, No. 5, 1974, pp. 1324-1333. http://dx.doi.org/10.1175/1520-0469(1974)031<1324:SFFTBL>2.0.CO;2

[23] T. Yamada, “Prediction of the Nocturnal Surface Inversion Height,” Journal of Applied Meteorology, Vol. 18, No. 4, 1979, pp. 526-531. http://dx.doi.org/10.1175/1520-0450(1979)018<0526:POTNSI>2.0.CO;2

[24] J. R. Garratt and R. A. Brost, “Radiative Cooling Effects within and above the Nocturnal Boundary Layer,” Journal of the Atmospheric Sciences, Vol. 38, No. 12, 1981, pp. 2730-2746. http://dx.doi.org/10.1175/ 1520-0469(1981)038<2730:RCEWAA>2.0.CO;2

[25] R. K. Newsom and R. M. Banta, “Shear-Flow Instability in the Stable Nocturnal Boundary Layer as Observed by Doppler Lidar during CASES-99,” Journal of the Atmospheric Sciences, Vol. 60, No. 1, 2003, pp. 16-33. http://dx.doi.org/10.1175/1520-0469(2003)060<0016:SFIITS>2.0.CO;2

[26] F. Beyrich, “Sodar Observations of the Stable BoundaryLayer Height in Relation to the Nocturnal Low-Level Jet,” Meteorologische Zeitschrift, Vol. 3, No. 1, 1994, pp. 29-34.

[27] C. G. Rossby and R. B. Montgomery, “The Layer of Frictional Influence in Wind and Ocean Currents,” Papers in Physical Oceanography and Meteorology, Vol. 3, No. 3, 1935, pp. 1-101.

[28] M. W. Gardner and S. R. Dorling, “Artificial Neural Networks (the Multilayer Perceptron): A Review of Applications in the Atmospheric Sciences,” Atmospheric Environment, Vol. 32, No. 14-15, 1998, pp. 2627-2636. http://dx.doi.org/10.1016/S1352-2310(97)00447-0

[29] V. M. Krasnopolsky, “Neural Network Emulations for Complex Multidimensional Geophysical Mappings: Applications of Neural Network Techniques to Atmospheric and Oceanic Satellite Retrievals and Numerical Modeling,” Reviews of Geophysics, Vol. 45, No. 3, 2007, Article ID: RG3009. http://dx.doi.org/10. 1029/2006RG000200

[30] M. Gevrey, I. Dimopoulos and S. Lek, “Review and Comparison of Methods to Study the Contribution of Variables in Artificial Neural Network Models,” Ecological Modelling, Vol. 160, No. 3, 2003, pp. 249-264. http://dx.doi.org/10.1016/S0304-3800(02)00257-0

[31] D. E. Rumelhart, G. E. Hinton and R. J. Williams, “Parallel Distributed Processing: Explorations in the Microstructure of Cognition, Vol. 1,” MIT Press, Cambridge, 1986.

[32] D. Koracin and R. Berkowicz, “Nocturnal Boundary-Layer Height: Observations by Acoustic Sounders and Predictions in Terms of Surface-Layer Parameters,” Boundary-Layer Meteorology, Vol. 43, No. 1-2, 1988, pp. 65-83. http://dx.doi.org/10.1007/BF00153969

[1] P. Seibert, F. Beyrich, S. E. Gryning, S. Joffre, A. Rasmussen and P. H. Tercier, “Review and Intercomparison of Operational Methods for the Determination of the Mixing Height,” Atmospheric Environment, Vol. 34, No. 7, 2000, pp. 1001-1027. http://dx.doi.org/10.1016/S1352-2310(99)00349-0

[2] J. A. Salmond and I. G.McKendry, “A Review of Turbulence in the Very Stable Boundary Layer and Its Implications for Air Quality,” Progress in Physical Geography, Vol. 29, No. 2, 2005, pp. 171-188. http://dx.doi.org/10.1191/0309133305pp442ra

[3] G. J. Steeneveld and A. A. M. Holtslag, “Meteorological Aspects of Air Quality,” Air Quality in the 21st Century, Nova Science Publishers, New York, 2009, pp. 67-114.

[4] W. Brutsaert, “Radiation, Evaporation and the Maintenance of the Turbulence under Stable Conditions in the Lower Atmosphere,” Boundary-Layer Meteorology, Vol. 2, No. 3, 1972, pp. 309-325. http://dx.doi.org/10.1007/BF02184772

[5] L. Mahrt, “Modeling the Height of the Stable Boundary Layer,” Boundary-Layer Meteorology, Vol. 21, No. 1, 1981, pp. 3-19. http://dx.doi.org/10.1007/BF00119363

[6] S. A. Kitaigorodskii, “On the Computation of the Thickness of the Wind-Mixing Layer in the Ocean,” Izvestiya AN SSSR, Geophysical Series, Vol. 3, 1960, pp. 425-431.

[7] S. S. Zilitinkevich, “On the Determination of the Height of the Ekman Boundary Layer,” Boundary-Layer Meteorology, Vol. 3, No. 2, 1972, pp. 141-145. http://dx.doi.org/10.1007/BF02033914

[8] R. T. Pollard, P. B. Rhines and R. Thompson, “The Deepening of the Wind-Mixed Layer,” Geophysical Fluid Dynamics, Vol. 3, 1973, pp. 381-404.

[9] S. A. Kitaigorodskii and S. M. Joffre, “In Search of Simple Scaling for the Heights of the Stratified Atmospheric Boundary Layer,” Tellus, Vol. 40A, No. 5, 1988, pp. 419-443. http://dx.doi.org/10.1111/j. 1600-0870.1988. tb00359.x

[10] S. S. Zilitinkevich and D. V. Mironov, “A Multi-Limit Formulation for the Equilibrium Depth of a Stably Stratified Boundary Layer,” Boundary-Layer Meteorology, Vol. 81, No. 3-4, 1996, pp. 325-351. http://dx.doi.org/10.1007/BF02430334

[11] S. S. Zilitinkevich, A. Baklanov, J. Rost, A. S. Smedman, V. Lykosov and P. Calanca, “Diagnostic and Prognostic Equations for the Depth of the Stably Stratified Ekman Boundary Layer,” Quarterly Journal of the Royal Meteorological Society, Vol. 128, No. 1, 2002, pp. 25-46. http://dx.doi.org/10.1256/ 00359000260498770

[12] S. S. Zilitinkevich and A. Baklanov, “Calculation of the Height of Stable Boundary Layers in Practical Applications,” Boundary-Layer Meteorology, Vol. 105, No. 3, 2002, pp. 389-409. http://dx.doi.org/ 10.1023/A:1020376832738

[13] D. Vickers and L. Mahrt, “Evaluating Formulations of the Stable Boundary Layer Height,” Journal of Applied Meteorology, Vol. 43, No. 11, 2004, pp. 1736-1749. http://dx.doi.org/10.1175/JAM2160.1

[14] G. J. Steeneveld, B. J. H. Van de Wiel and A. A. M. Holtslag, “Diagnostic Equations for the Stable Boundary Layer Height: Evaluation and Dimensional Analysis,” Journal of Applied Meteorology and Climatology, Vol. 46, No. 2, 2007, pp. 212-225. http://dx.doi.org/10.1175/JAM2454.1

[15] B. Kosovic and J. A. Curry, “A Large Eddy Simulation Study of a Quasi-Steady, Stably Stratified Atmospheric Boundary Layer,” Journal of the Atmospheric Sciences, Vol. 57, No. 8, 2000, pp. 1052-1068. http://dx.doi.org/10.1175/1520-0469(2000)057<1052:ALESSO>2.0.CO;2

[16] S. S. Zilitinkevich and I. Esau, “The Effect of Baroclinicity on the Equilibrium Depth of Neutral and Stable Planetary Boundary Layers,” Quarterly Journal of the Royal Meteorological Society, Vol. 129, No. 595, 2003, pp. 3339-3356. http://dx.doi.org/10.1256/qj.02.94

[17] B. Kosovic and J. K. Lundquist, “Influences on the Height of the Stable Boundary Layer,” 16th Symposium on Boundary Layers and Turbulence, American Meteor Society, Portland, 23 June 2004, Preprints.

[18] G. J. Steeneveld, B. J. H. Van de Wiel and A. A. M. Holtslag, “Notes and Correspondence: Comments on Deriving the Equilibrium Height of the Stable Boundary Layer,” Quarterly Journal of the Royal Meteorological Society, Vol. 133, No. 622, 2007, pp. 261-264. http://dx.doi.org/10.1002/qj.26

[19] C. Sim, S. Basu and L. Manuel, “On Space-Time Resolution of Inflow Representations for Wind Turbine Loads Analysis,” Energies, Vol. 5, No. 7, 2012, pp. 2071-2092. http://dx.doi.org/10.3390/en5072071

[20] D. H. Lenschow, X. S. Li, C. J. Zhu and B. B. Stankov, “The Stably Stratified Boundary Layer over the Great Plains. I. Mean and Turbulent Structure,” Boundary-Layer Meteorology, Vol. 42, No. 1-2, 1988, pp. 95-121. http://dx.doi.org/10.1007/BF00119877

[21] S. J. Caughey, J. C. Wyngaard and J. C. Kaimal, “Turbulence in the Evolving Stable Layer,” Journal of the Atmospheric Sciences, Vol. 36, No. 6, 1979, pp. 1041-1052.

[22] J. W. Melgarejo and J. W. Deardorff, “Stability Functions for the Boundary Layer Resistance Laws Based upon Observed Boundary Layer Heights,” Journal of the Atmospheric Sciences, Vol. 31, No. 5, 1974, pp. 1324-1333. http://dx.doi.org/10.1175/1520-0469(1974)031<1324:SFFTBL>2.0.CO;2

[23] T. Yamada, “Prediction of the Nocturnal Surface Inversion Height,” Journal of Applied Meteorology, Vol. 18, No. 4, 1979, pp. 526-531. http://dx.doi.org/10.1175/1520-0450(1979)018<0526:POTNSI>2.0.CO;2

[24] J. R. Garratt and R. A. Brost, “Radiative Cooling Effects within and above the Nocturnal Boundary Layer,” Journal of the Atmospheric Sciences, Vol. 38, No. 12, 1981, pp. 2730-2746. http://dx.doi.org/10.1175/ 1520-0469(1981)038<2730:RCEWAA>2.0.CO;2

[25] R. K. Newsom and R. M. Banta, “Shear-Flow Instability in the Stable Nocturnal Boundary Layer as Observed by Doppler Lidar during CASES-99,” Journal of the Atmospheric Sciences, Vol. 60, No. 1, 2003, pp. 16-33. http://dx.doi.org/10.1175/1520-0469(2003)060<0016:SFIITS>2.0.CO;2

[26] F. Beyrich, “Sodar Observations of the Stable BoundaryLayer Height in Relation to the Nocturnal Low-Level Jet,” Meteorologische Zeitschrift, Vol. 3, No. 1, 1994, pp. 29-34.

[27] C. G. Rossby and R. B. Montgomery, “The Layer of Frictional Influence in Wind and Ocean Currents,” Papers in Physical Oceanography and Meteorology, Vol. 3, No. 3, 1935, pp. 1-101.

[28] M. W. Gardner and S. R. Dorling, “Artificial Neural Networks (the Multilayer Perceptron): A Review of Applications in the Atmospheric Sciences,” Atmospheric Environment, Vol. 32, No. 14-15, 1998, pp. 2627-2636. http://dx.doi.org/10.1016/S1352-2310(97)00447-0

[29] V. M. Krasnopolsky, “Neural Network Emulations for Complex Multidimensional Geophysical Mappings: Applications of Neural Network Techniques to Atmospheric and Oceanic Satellite Retrievals and Numerical Modeling,” Reviews of Geophysics, Vol. 45, No. 3, 2007, Article ID: RG3009. http://dx.doi.org/10. 1029/2006RG000200

[30] M. Gevrey, I. Dimopoulos and S. Lek, “Review and Comparison of Methods to Study the Contribution of Variables in Artificial Neural Network Models,” Ecological Modelling, Vol. 160, No. 3, 2003, pp. 249-264. http://dx.doi.org/10.1016/S0304-3800(02)00257-0

[31] D. E. Rumelhart, G. E. Hinton and R. J. Williams, “Parallel Distributed Processing: Explorations in the Microstructure of Cognition, Vol. 1,” MIT Press, Cambridge, 1986.

[32] D. Koracin and R. Berkowicz, “Nocturnal Boundary-Layer Height: Observations by Acoustic Sounders and Predictions in Terms of Surface-Layer Parameters,” Boundary-Layer Meteorology, Vol. 43, No. 1-2, 1988, pp. 65-83. http://dx.doi.org/10.1007/BF00153969