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Using All Observed Information in a Variational Approach to Measuring z0m and z0t

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  • 1 Air Quality Modeling and Integration Research Division, Meteorological Service of Canada, Downsview, Ontario, Canada
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Abstract

A variational method is developed to estimate the aerodynamic roughness length and roughness scaling length for temperature based on wind and temperature measurements conducted routinely at an observational network. The problem is formulated to find optimal estimates of roughness lengths for momentum and heat transfer through a minimization of a cost function with respect to these two roughness lengths that measures the errors between observed and predicted wind and temperature profiles. The method has been applied to data collected in two experimental campaigns. Some results are compared with other methods used to compute the aerodynamic roughness length. The variational computations show that the aerodynamic roughness lengths agree well with the estimated z0m in the experimental campaigns. The roughness scaling lengths for temperature z0t are in most cases one order of magnitude smaller than z0m. It was found that the variations of z0m and z0t during the course of a day are not likely to follow a simple functional relationship, especially during the daytime, during which both z0m and z0t are highly oscillatory. The error test shows that z0m and z0t generated from the variational method are not very sensitive to measurement errors.

Corresponding author address: Dr. Jianmin Ma, ARQI, Air Quality Research Branch, Meteorological Service of Canada, 4905 Dufferin St., Downsview, ON M3H 5T4, Canada.

jianmin.ma@ec.gc.ca

Abstract

A variational method is developed to estimate the aerodynamic roughness length and roughness scaling length for temperature based on wind and temperature measurements conducted routinely at an observational network. The problem is formulated to find optimal estimates of roughness lengths for momentum and heat transfer through a minimization of a cost function with respect to these two roughness lengths that measures the errors between observed and predicted wind and temperature profiles. The method has been applied to data collected in two experimental campaigns. Some results are compared with other methods used to compute the aerodynamic roughness length. The variational computations show that the aerodynamic roughness lengths agree well with the estimated z0m in the experimental campaigns. The roughness scaling lengths for temperature z0t are in most cases one order of magnitude smaller than z0m. It was found that the variations of z0m and z0t during the course of a day are not likely to follow a simple functional relationship, especially during the daytime, during which both z0m and z0t are highly oscillatory. The error test shows that z0m and z0t generated from the variational method are not very sensitive to measurement errors.

Corresponding author address: Dr. Jianmin Ma, ARQI, Air Quality Research Branch, Meteorological Service of Canada, 4905 Dufferin St., Downsview, ON M3H 5T4, Canada.

jianmin.ma@ec.gc.ca

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