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Approximate Analytical Solution to Diurnal Atmospheric Boundary-Layer Growth Under Well-Watered Conditions

Publication ,  Journal Article
Rigby, JR; Yin, J; Albertson, JD; Porporato, A
Published in: Boundary-Layer Meteorology
July 29, 2015

Simplified numerical models of the atmospheric boundary layer (ABL) are useful both for understanding the underlying dynamics and potentially providing parsimonious modelling approaches for inclusion in larger models. Herein the governing equations of a simplified slab model of the uniformly mixed, purely convective, diurnal ABL are shown to allow immediate solutions for the potential temperature and specific humidity as functions of the ABL height and net radiation when expressed in integral form. By employing a linearized saturation vapour relation, the height of the mixed layer is shown to obey a non-linear ordinary differential equation with quadratic dependence on ABL height. A perturbation solution provides general analytical approximations, of which the leading term is shown to represent the contribution under equilibrium evaporation. These solutions allow the diurnal evolution of the height, potential temperature, and specific humidity (i.e., also vapour pressure deficit) of the mixed layer to be expressed analytically for arbitrary radiative forcing functions.

Duke Scholars

Published In

Boundary-Layer Meteorology

DOI

EISSN

1573-1472

ISSN

0006-8314

Publication Date

July 29, 2015

Volume

156

Issue

1

Start / End Page

73 / 89

Related Subject Headings

  • Meteorology & Atmospheric Sciences
  • 3701 Atmospheric sciences
  • 0401 Atmospheric Sciences
 

Citation

APA
Chicago
ICMJE
MLA
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Rigby, J. R., Yin, J., Albertson, J. D., & Porporato, A. (2015). Approximate Analytical Solution to Diurnal Atmospheric Boundary-Layer Growth Under Well-Watered Conditions. Boundary-Layer Meteorology, 156(1), 73–89. https://doi.org/10.1007/s10546-015-0018-8
Rigby, J. R., J. Yin, J. D. Albertson, and A. Porporato. “Approximate Analytical Solution to Diurnal Atmospheric Boundary-Layer Growth Under Well-Watered Conditions.” Boundary-Layer Meteorology 156, no. 1 (July 29, 2015): 73–89. https://doi.org/10.1007/s10546-015-0018-8.
Rigby JR, Yin J, Albertson JD, Porporato A. Approximate Analytical Solution to Diurnal Atmospheric Boundary-Layer Growth Under Well-Watered Conditions. Boundary-Layer Meteorology. 2015 Jul 29;156(1):73–89.
Rigby, J. R., et al. “Approximate Analytical Solution to Diurnal Atmospheric Boundary-Layer Growth Under Well-Watered Conditions.” Boundary-Layer Meteorology, vol. 156, no. 1, July 2015, pp. 73–89. Scopus, doi:10.1007/s10546-015-0018-8.
Rigby JR, Yin J, Albertson JD, Porporato A. Approximate Analytical Solution to Diurnal Atmospheric Boundary-Layer Growth Under Well-Watered Conditions. Boundary-Layer Meteorology. 2015 Jul 29;156(1):73–89.
Journal cover image

Published In

Boundary-Layer Meteorology

DOI

EISSN

1573-1472

ISSN

0006-8314

Publication Date

July 29, 2015

Volume

156

Issue

1

Start / End Page

73 / 89

Related Subject Headings

  • Meteorology & Atmospheric Sciences
  • 3701 Atmospheric sciences
  • 0401 Atmospheric Sciences