This paper examines the interpolation betweenBusinger–Dyer (Kansas-type) formulae,ϕu = (1 -1 6ζ )-1/4 andϕt = (1 - 16ζ )-1/2, and free convection forms. Based on matching constraints, the constants, au and at, in the convective flux-gradient relations, ϕu = (1 - auζ )-1/3 and ϕt = (1 - atζ )-1/3, are determined. It isshown that au and at cannot be completely independent if convective forms are blended with theKansas formulae. In other words, these relationships already carryinformation about au and at. This follows because the Kansas relations cover a wide stability range (up to ζ = - 2), which includes a lower part of the convective sublayer (about 0.1 < - ζ < 2). Thus, there is a subrange where both Kansas and convective formulae are valid. Matching Kansas formulae and free convection relations within thesubrange 0.1 < -ζ < 2 and independently smoothing ofthe blending function are used to determine au and at. The values au = 10 for velocity and at = 34for scalars (temperature and humidity) give a good fit. This new approacheliminates the need for additional independent model constants and yields a`smooth' blending between Kansas and free-convection profileforms in the COARE bulk algorithm.
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