The von Kármán constant retrieved from CASES-97 dataset using a variational method

Abstract

A variational method is developed to retrieve the von Kármán constant κ from the CASES-97 dataset, collected near Wichita, Kansas, the United States from 6 April to 24 May 1997. In the variational method, a cost function is defined to measure the difference between observed and computed gradients of wind speed, air temperature and specific humidity. An optimal estimated von Kármán constant is obtained by minimizing the cost function through adjusting values of the von Kármán constant. Under neutral stratification, the variational analysis confirms the conventional value of κ (=0.40). For non-neutral stratification, however, κ varies with stability. The computational results show that the κ decreases monotonously from stable to unstable stratification. The variational calculated mean value of the von Kármán constant is 0.383∼0.390 when the atmospheric stratification is taken into consideration. Relations between κ and surface momentum and heat flux are also examined.