Convective profile constants revisited

This paper examines the interpolation between Businger-Dyer (Kansas-type) f ormulae, phi(u) = (1 -16 zeta)(-1/4) and phi(t) = (1 - 16 zeta)(-1/2), and free convection forms. Based on matching constraints, the constants, a(u) a nd a(t), in the convective flux-gradient relations, phi(u) = (1 - a(u)zeta )(-1/3) and phi(t) = (1 - a(t)zeta )(-1/3), are determined. It is shown tha t a(u) and a(t) cannot be completely independent if convective forms are bl ended with the Kansas formulae. In other words, these relationships already carry information about a(u) and a(t). This follows because the Kansas rel ations cover a wide stability range (up to zeta = -2), which includes a low er part of the convective sublayer (about 0.1 < -zeta < 2). Thus, there is a subrange where both Kansas and convective formulae are valid. Matching Ka nsas formulae and free convection relations within the subrange 0.1 < -zeta < 2 and independently smoothing of the blending function are used to deter mine a(u) and a(t). The values a(u) = 10 for velocity and a(t) = 34 for sca lars (temperature and humidity) give a good fit. This new approach eliminat es the need for additional independent model constants and yields a 'smooth ' blending between Kansas and free-convection profile forms in the COARE bu lk algorithm.