Improvement of Vertical Diffusion Analytic Schemes Under Stable Atmospheric Conditions

Based on gradient transport theory or K-theory, turbulent transport in the atmosphere has long been parameterized using the eddy diffusivity. Due to its simplicity, this approach has often been applied in many numerical models but rarely tested with observations. Here, the widely used O’Brien cubic polynomial approach has been validated together with an exponential approach against eddy diffusivity profiles determined from measurements and from large-eddy simulation data in stable conditions. Verification is completed by analyzing the variability effects on pollutant concentrations of two different vertical diffusion (K(z)) schemes incorporated in an atmospheric chemical model. It is shown that the analytical, exponential solution agrees better with observations than the O’Brien profile and should be used henceforth in practical applications.

[1]  J. Deardorff Convective Velocity and Temperature Scales for the Unstable Planetary Boundary Layer and for Rayleigh Convection , 1970 .

[2]  Yuh-Lang Lin,et al.  Large-Eddy Simulations of the Atmospheric Boundary Layer Using a New Subgrid-Scale Model – II. Weakly and moderately stable cases , 2001 .

[3]  U. Schumann,et al.  Large‐eddy simulation of a neutrally stratified boundary layer: A comparison of four computer codes , 1994 .

[4]  A. Smedman,et al.  Diagnostic and prognostic equations for the depth of the stably stratified Ekman boundary layer , 2002 .

[5]  A. Monin,et al.  Basic laws of turbulent mixing in the surface layer of the atmosphere , 2009 .

[6]  R. Larsen,et al.  Vertical diffusion in the lower atmosphere using aircraft measurements of 222Rn , 1997 .

[7]  B. Grisogono,et al.  The low‐level katabatic jet height versus Monin–Obukhov height , 2007 .

[8]  B. Grisogono,et al.  A Total Turbulent Energy Closure Model for Neutrally and Stably Stratified Atmospheric Boundary Layers , 2007 .

[9]  I. Esau,et al.  Universal dependences between turbulent and mean flow parameters instably and neutrally stratified Planetary Boundary Layers , 2006 .

[10]  I. Esau,et al.  The effect of baroclinicity on the equilibrium depth of neutral and stable planetary boundary layers , 2003 .

[11]  J. Deardorff Numerical Investigation of Neutral and Unstable Planetary Boundary Layers , 1972 .

[12]  J. Garratt,et al.  On the sensitivity of mesoscale models to surface-layer parameterization constants , 1989 .

[13]  S. Burns,et al.  An Evaluation of Bulk Ri-Based Surface Layer Flux Formulas for Stable and Very Stable Conditions with Intermittent Turbulence , 2003 .

[14]  L. Mahrt The influence of nonstationarity on the turbulent flux–gradient relationship for stable stratification , 2007 .

[15]  P. V. Velthoven,et al.  Evaluation of archived and off-line diagnosed vertical diffusion coefficients from ERA-40 with 222 Rn simulations , 2004 .

[16]  Christian Seigneur,et al.  Application and Evaluation of Two Air Quality Models for Particulate Matter for a Southeastern U.S. Episode , 2004, Journal of the Air & Waste Management Association.

[17]  P. Calanca,et al.  An extended similarity theory for the stably stratified atmospheric surface layer , 2000 .

[18]  L. Mahrt,et al.  Extremely Weak Mixing in Stable Conditions , 2006 .

[19]  Larry Mahrt,et al.  Stratified Atmospheric Boundary Layers , 1999 .

[20]  Jielun Sun,et al.  The Very Stable Boundary Layer on Nights with Weak Low-Level Jets , 2007 .

[21]  Dragutin T. Mihailovic,et al.  Intercomparison of two K-schemes: Local versus non-local in calculating concentrations of pollutants in chemical and air-quality models , 2007, Environ. Model. Softw..

[22]  P. Samson,et al.  Sensitivity of Urban Airshed Model (UAM-IV) Calculated Air Pollutant Concentrations to the Vertical Diffusion Parameterization during Convective Meteorological Situations , 1996 .

[23]  S. Rao,et al.  Uncertainties in Episodic Ozone Modeling Stemming from Uncertainties in the Meteorological Fields , 2001 .

[24]  R. Stull Stable Boundary Layer , 1988 .

[25]  W. Brutsaert,et al.  Similarity of scalars under stable conditions , 1996 .

[26]  B. Grisogono,et al.  The critical bulk Richardson number in urban areas: verification and application in a numerical weather prediction model , 2006 .

[27]  Similarity theory and calculation of turbulent fluxes at the surface for the stably stratified atmospheric boundary layer , 2006, physics/0612209.

[28]  B. Grisogono,et al.  Justifying the WKB approximation in pure katabatic flows , 2002 .

[29]  J. O'Brien,et al.  A Note on the Vertical Structure of the Eddy Exchange Coefficient in the Planetary Boundary Layer , 1970 .

[30]  R. Volkamer,et al.  Modelling constraints on the emission inventory and on vertical dispersion for CO and SO 2 in the Mexico City Metropolitan Area using Solar FTIR and zenith sky UV spectroscopy , 2006 .

[31]  M. Best,et al.  Modelling the local surface exchange over a grass‐field site under stable conditions , 2001 .

[32]  Judith A. Curry,et al.  A Large Eddy Simulation Study of a Quasi-Steady, Stably Stratified Atmospheric Boundary Layer , 2000 .

[33]  Erik Berge,et al.  A regional scale multilayer model for the calculation of long‐term transport and deposition of air pollution in Europe , 1998 .

[34]  F. Porté-Agel,et al.  On Monin–Obukhov Similarity In The Stable Atmospheric Boundary Layer , 2001 .

[35]  John C. Wyngaard,et al.  Top-down and bottom-up diffusion of a scalar in the convective boundary layer , 1984 .

[36]  R. Stull An Introduction to Boundary Layer Meteorology , 1988 .