(1), (2) and (3) apply a transient Ekman flow model with vertical velocity due to in- and outflows and including density effects. As the in-and outflows may act at different
levels, they generate vertical motions in the model. The water-air boundary conditions are: equation(4a) τax=μeffρ∂ρU∂z, equation(4b) τay=μeffρ∂ρV∂z, where τax and τay denote the eastward and northward wind stress components respectively, calculated using a standard bulk formulation: AG-014699 solubility dmso equation(5a) τax=ρaCDUaWa,τax=ρaCDUaWa, equation(5b) τay=ρaCDVaWa,τay=ρaCDVaWa, where ρa (1.3 kg m− 3) is the air density, CD the air Smad inhibitor drag coefficient, Ua and Va the wind components the x and y directions respectively, and Wa the wind speed =Ua2+Va2. The air drag coefficient for the natural atmosphere (CDN) is calculated according to Hasselmann et al.
(1988) by equation(5c) CDN=0.8+0.065maxWa7.5×10−3. The roughness lengths for momentum (Zo), heat (ZH) and humidity (ZE) are assumed to be dependent on the neutral values as equation(5d) Zo=zrefexpκCDN, equation(5e) ZH=zrefexpκCDNCHN, equation(5f) Zo=zrefexpκCDNCEN, where Zref is the reference height (= 10 m), κ(= 0.4) is von Karman’s constant, CHN (= 1.14 × 10− 3) is the neutral bulk coefficient for the sensible heat flux and CEN (= 1.12 × 10− 3) is the neutral bulk coefficient for the latent medroxyprogesterone heat flux. According to Launiainen (1995), the stability dependence of the bulk coefficients is: equation(5g) CD=κ2lnZrefZo−ψm2, equation(5h) CH=κ2lnZrefZo−ψmlnZrefZH−ψh, equation(5i) CH=κ2lnZrefZo−ψmlnZrefZH−ψh, where ψm, (ψh) are the integrated forms of the non-dimensional gradients of momentum (heat). They are calculated as follows: For stable and
neutral conditions the Richardson number (Rb) is used to define a stable (Rb > 0) and an unstable condition (Rb < 0): equation(5j) Rb=gZrefTa−TsTs+273.15Wa2. The non-dimensional fraction (ς) is calculated by knowing the air temperature at 2 m height (Ta) and the sea surface temperature (Ts): equation(5k) ς=Rb1.18lnZrefZo−1.5lnZoZH−1.37++Rb21.891lnZrefZo+4.22, where L is the Monin-Obukov length. During a strongly stable situation, ς is less than or equal to 0.5, and equation(5l) ψm≈ψh=−cψ2cψ3cψ4−ςcψ1−cψ2ς−cψ3cψ4exp−ςcψ4, where cψ1, cψ2, cψ3 and cψ4 are 0.7, 0.75, 5 and 0.35 respectively. For unstable conditions ς is calculated as equation(5m) ς=Rbln2Zref/ZolnZref/ZH−0.55.