variational method

Abstract. A variational method is developed to retrieve the von Kármán constant κ from the CASES-97 dataset, col-lected 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 spe-cific humidity. An optimal estimated von Kármán constant is obtained by minimizing the cost function through adjusting values of the von Kármán constant. Under neutral stratifica-tion, 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 de-creases 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.