Direct Solution of Various Micrometeorological Problems via the Lambert-W Function

Mark Kelly*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


For a family of relatively common problems in micrometeorology, whose forms previously required iterative or indirect treatment, analytical solution is possible via the Lambert-W function. Use of this function reduces computational time and the need for approximations, while offering a clearer view of the character and solution of such problems. This note provides a generalized form for such problems, and demonstrates its use for three applications: internal boundary-layer growth due to a change in surface roughness; flow displacement over a canopy; and determination of friction velocity and roughness length over the sea.
Original languageEnglish
JournalBoundary-Layer Meteorology
Pages (from-to)163-168
Number of pages6
Publication statusPublished - 2021


  • Analytical solution
  • Internal boundary layer
  • Logarithmic profile
  • Log-linear equations
  • Roughness length


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